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User manual - Laboratory of Applied Pharmacokinetics

1. a Cc D _ D G D D 5 a z D o w a D O id 4 DLI Patient data A Pop model data A Pop model plots A Posterior Plot A Fitted Probabilities Future Plot For Help press F1 As you can see there is a slight improvement in the fit for serum level number 3 the rest is roughly the same as with no IMM Let us accept this fit and move on to developing a future regimen for this patient using the information we have obtained by making the fit Designing a future regimen Using Minimized variance First we design a future regimen using minimized variance Select the Future regimen under the Task menu option Select the desired route Option 1 Control Peak and Trough Select Dose Interval Option 2 Control Central Compartment Conc IV Option 3 Control Central Compartment Conc Continuous IV Option 4 Control Central Compt Conc at Chosen Time after Dose IV Uption 5 Control Periph Compt Conc at Chosen lime after Dose 4 Option 6 Control Central Compt Conc at Two Chosen Times after Dose IV Select Dose Interval Option 7 Control Periph Compt Conc at Two Chosen Times after Dose IV Select Dose Interval You control the main route using one of the three radio buttons at the top and the sub route using one of the 7 vertical buttons As you can see there the PO route is not allowed for this model also there 1s no peripheral compartment
2. 08 05 85 00 48 00 Level Date Time Time latter Dol Atter Dose l evei Wun cael iss owe ube ows 5 00 08 05 85 12 18 00 3 00 08 05 85 22 24 00 1 90 08 06 85 00 04 00 5 30 08 06 85 22 36 00 f 2 90 0810 85 13 36 00 229 60 2 40 0818 85 16 00 00 424 00 1 20 4 There are 7 columns displaying information about the serum levels Most of them correspond to the fields used for displaying the dosage information The serum level number starting at 1 The date the sample was obtained shown according to the selected locale The time the sample was obtained shown hour minutes seconds The time into the regimen starting when the first dose was given The dose number just before this serum sample The time after the previous dose number The measured concentration NUON MN BW NY e The controls This section describes the menus and controls that can be used in combination with the patient view All options available for the patient view are accessible from the Patient menu option By selecting this menu option the view will automatically switch to the Patient data view There are several options available for this menu selection New patient Load patient The options may be disabled based on your previous selections You cannot save a patient s data if you have no patient loaded and so on Selection of the New patient
3. eeoe eee 6 eee e 00o e e d e d amp e o oe eee oo e o ee o e e e ee ee 0 e e e e 6 6 e000 oe 090 O ee 2 0 16 28 35 30 04 26 73 24 92 23 ESTIMATED CCr Figure 1 Comparison of Estimated CCr as described herein with measured CCr ACHIEVING TARGET GOALS MOST PRECISELY USING NONPARAMETRIC COMPARTMENTAL MODELS AND MULTIPLE MODEL DESIGN OF DOSAGE REGIMENS Roger Jelliffe David Bayard Mark Milman Michael Van Guilder and Alan Schumitzky Laboratory of Applied Pharmacokinetics USC School of Medicine ABSTRACT Multiple model MM design and stochastic control of dosage regimens permits essentially full use of all the information contained in either a Bayesian prior nonparametric EM NPEM population pharmacokinetic model or in an MM Bayesian posterior updated parameter set to achieve and maintain selected therapeutic goals with optimal precision least predicted weighted squared error The regimens are visibly more precise in the achievement of desired target goals than are current methods using mean or median population parameter values Bayesian feedback has now also been incorporated into the MM software An evaluation of MM dosage design using an NPEM population model versus dosage design based on conventional mean population parameter values is presented using a population model of Vancomycin Further feedback control was also evaluated i
4. Barbaut X and Tahani B Individualizing Drug Dosage Regimens Roles of Population Pharmacokinetic and Dynamic Models Bayesian Fitting and Adaptive Control Therap Drug Monit 15 380 393 1993 Jazwinski A Stochastic Processes and Filtering Theory Academic Press New York 1970 17 Terziivanov Dmiter unpublished data Used with permission Van Guilder M Leary R Schumitzky A Wang X Vinks S and Jelliffe R Nonlinear Nonparametric Population Modeling on a Supercomputer Presented at the 1997 ACM IEEE SC97 Conference San Jose CA November 15 21 1997 19 Mallet A A Maximum Likelihood Estimation Method for Random Coefficient Regression Models Biometrika 73 645 656 1986 20 Schumitzky A The Nonparametric Maximum Likelihood Approach to Pharmacokinetic Population Analysis Proceedings of the 1993 Western Simulation Multiconference Simulation for Health Care Society for Computer Simulation 1993 pp 95 100 21 Bertsekas D Dynamic Programming deterministic and stochastic models Englewood Cliffs NJ Prentice Hall pp 144 146 1987 22 Bertilsson L Geographic Interracial Differences in Polymorphic Drug Oxidation Clin Pharmacokinet 29 192 209 1995 23 Lindsay B The Geometry of Mixture Likelihoods A General Theory Ann Statist 11 86 94 1983 24 Schumitzky A Nonparametric EM Algorithms for Estimating Prior Distributions App Math and Computation 45 143 157 1991 25 Hurst A Yoshinaga M Mita
5. Division of Clinical Pharmacology Department of Medical Laboratory Sciences and Technology Karolinska Institute at Huddinge University Hospital Stockholm Sweden 1995 pp 28 29 Jelliffe R Schumitzky A Bayard D Milman M Van Guilder M Wang X Jiang F Barbaut X and Maire P Model Based Goal Oriented Individualised Drug Therapy Linkage of Population Modelling New Multiple Model Dosage Design Bayesian Feedback and Individualised Target Goals Clin Pharmacokinet 34 57 77 1998 Wakefield J Smith A Racine Poon A et al Bayesian Analysis of Linear and Nonlinear Population Models Applied Stats 43 201 222 1994 33 Davidian M and Gallant A The Nonlinear Mixed Effects Model with a smooth Random Effects Density Biometrika 80 475 488 1993 Table 1 Text output of the NPEM program Results of the population analysis of 10 subjects receiving intramuscular Amikacin 17 CYCLE NO 39 TODAY IS 01 26 98 THE TIME IS 18 58 54 THE TRUE NUMERICAL LOG LIKELIHOOD USING THE NUMBER THEORETIC INTEGRATION SCHEME OF THE 10 SUBJECT VECTORS GIVEN THE PRIOR DENSITY IS 484 380880981189 Note compare this value with that of 494 234411 found with the IT2B program THE DIE FERENCE BETWEEN THE GIKELIHOOD OF THE THE MAXIMUM LIKELIHOOD ESTIMATE OF THE DENSITY AND THE LIKELIHOOD OF THIS CYCLE IS LESS THAN THE FOLLOWING NUMBER O2S9IS3653112409386D 002 THE CORRESPONDING FIGURE FOR CYCLE 1 WAS 10374 SINCE IT IS
6. Response of the true patient during day event horizon 3 The horizontal dashed line is the 15 ug ml therapeutic goal MULTIPLE MODEL MM DOSAGE DESIGN ACHIEVING TARGET GOALS WITH MAXIMUM PRECISION R Jelliffe D Bayard A Schumitzky M Milman F Jiang S Leonov and V Gandhi Laboratory of Applied Pharmacokinetics USC School of Medicine 2250 Alcazar St Los Angeles CA 90033 USA 323 442 1300 jelliffe hsc usc edu ABSTRACT Most dosage regimens based on parametric population models as the Bayesian prior including most Bayesian approaches of adaptive feedback control use a single parameter value to describe the central tendency of each parameter distribution Because of this when a target goal is selected the regimen to achieve it assumes that it does so exactly However the separation or heuristic certainty equivalence principle states that whenever a system 1s controlled first by obtaining single point parameter values and then by using those values to control the system the control achieved is usually suboptimal In contrast Multiple Model dosage design is based on nonparametric population models which have essentially one set of parameter values for each subject in the population With this more likely Bayesian prior multiple predictions are possible Using these nonparametric models one can compute the dosage regimen which specifically minimizes the predicted weighted squared error with which a desired target goal can
7. or other response and the SD with which it has been measured so that one can compute the Fisher information for example as a good measure of credibility so that each serum level can be evaluated in the fitting process by a good measure of its credibility This has been discussed more fully in another paper in this collection and in other communications 14 15 In addition gamma a further measure of overall intra individual variability can also be computed by the IT2B program but not by the nonparametric methods It is used in the USC PACK IT2B program as a multiplier of all the coefficients of the assay error polynomial as determined above Because of this its nominal value is 1 0 indicating that there 1s no other source of variability that the assay error pattern itself Gamma is thus usually greater than 1 0 It not only includes the various environmental errors such as those present in preparing and administering the doses errors in recording the timing of the serum samples and also errors in which the structural model used fails to describe the events fully model misspecification but also any changes in various parameter values over time It is an overall measure of all the other sources of intraindividual variability besides that of the assay However most of these other sources are not really sources of measurement noise but are rather of noise in the differential equations describing the behavior of the drug and are best des
8. procedure as above On the other hand one can use any reasonable initial estimate of the population mean parameter values and their SD s These are then used as the Bayesian priors The IT2B method uses these priors and examines each individual patient s data to obtain the individual maximum aposteriori probability MAP Bayesian posterior parameter values for each subject using the MAP Bayesian procedure in current wide use 2 One then finds the population means and SD s of those individual posterior parameter values One can then turn around and use these new population values as the MAP Bayesian priors and can once again obtain each patient s MAP Bayesian posterior values This process can continue iteratively indefinitely The procedure ends when a convergence criterion 1s reached The IT2B method is much less prone to the problems often found with fitting data by least squares In addition it does not require nearly as many serum concentration data points per patient and can function with as few data points as only one per patient The Global Two Stage G2S method is a further refinement of the S2S and the IT2B in which the covariance and correlations between the parameters are also estimated Each of these methods and all those below require software to implement them gt In the parametric EM method the letters EM stand for the two steps in each iteration of 1 computing a conditional expectation and 2 of maximizing a condi
9. 1 0 alan forrests AMIKACIN TERZ Filg s Window Patient Popmodel Task Plot Advanced Help Le Le 7 Ce Ca 24 97 percent 12 63 percent 9 6Aipercent 8 12 percent VWgtAyvg vary Ca D Q pas amp z re O _ a 1 0 1 5 2 0 25 3 0 3 5 4 0 Concentration in central compartment mq after 24 00 hours into new regimen id 4 gt Ub fi Patient data A Pop model data A Pop model plots A Posterior Plot A Fitted Probabilities A Future Plot A Report For Help press F1 This is a scatter plot showing how well your new regimen is predicted to achieve your target goal values Remember we selected to have a trough goal af 2 0 It seems like the values are a bit low at this time for this regimen This plot is the situation after 24 hours Use the Arrow buttons or the arrow keys on your keyboard to play forward in time to see if the new regimen improves Note also how the Goal indicator changes back and forth between 2 0 and 20 0 Extended plotting options The plotting routine used in RightDose offers an extensive set of options In this appendix we examine some of these options All options are available by right clicking inside a plot view You will then get a menu providing the options Viewing Style Font Size Numeric Precision Plotting Method Data Shadows Grid Lines Ks Grid in Front Include Data Labels Mark Data Points Show Annotations Unao z a a i a a ee a T Mle
10. 14 48 var TD D gt fe Fa O L A 1 2 3 lt 5 6 Fi 8 9 10 11 T3 Concentration in central compartment mg after 0 50 hours into new regimen i14 4 gt PL Patient data A Pop model data A Pop model plots A Posterior Plot A Fitted Probabilities A Future Plot For Help press F1 Ms This plot show the concentration along the x axis and the probability along the y axis for the first goal time a goal of 12 0 5 hours into the regimen The most probably set of support points or trajectory is again indicated by a solid red dot It has a probability of 42 27 and this time it has a value of out 7 This is below your selected goal indicated by the solid vertical line The black triangle show the weighted average Use the black arrows to move forward backward in time to look at next previous goals Using minimize bias Select the Compute options under the Advanced menu option change the lambda factor to 1 and the weighting factor to 0 absolute error Repeat the steps above to compute a new future regimen Select the Concentration vs probability under the Plot menu USCPACK for Windows Beta 1 0 alan forrests Gentamicin File Edit View Window Patient Popmodel Task Plot Advanced Help bed lt lt gt p gt Le Le Le 42 27 22 20 9 16 90 14 48 WatAvg Ww JI Ww oS No an 20 i 4 C D O _ D gt fa ra t JI 1 2 3 4 5 6 Fi 8 9 10
11. NOW 89539E 02 THIS ANALYSIS HAS GONE 10374 DIVIDED BY bOS 74 3 OR lt 29 99992 OF THE WAY FROM THE APRIORI DENSITY TO THE MAXIMUM LIKELIHOOD ESTIMATE OF THE JOINT DENG LLY THE NO OF ACTIVE GRID POINTS IS NOW aa THE INITIAL NO OF GRID POINTS WAS 10007 THE FOLLOWING VALUES ARE FOR THE UPDATED DENSITY THE SCALED INEO FOR THIS CYCLE TS 100 04 z THE ENTROPY FOR THis CYCEER IS Lire ince ke THE MEANS ARE KA KS1 VS1 aes so oy ee es O00 3359 ORe o aoa THE COV MATRIX IS IN LOWER TRI FORM KA Kok Vol Os TIL320 0 000096 0 000000 0 000483 0 000017 02002320 THE STANDARD DEVIATIONS ARE RESPECTIVELY KA Kol Vou 0 437461 02000601 0 048166 THE PERCENT COEFFICIENTS OF VARIATION ARE RESP KA Kol Vol Loa tol Zag 20 BOO LG Oro OFC THE CORR MATRIX IS IN LOWER TRIANGULAR FORM KA Ko Vou 1 000000 0 32 1600 1 000000 OZ U7 OPromneM Bers 1 000000 THE 3 SETS OF LINES BELOW WILL GIVE ADDITIONAL STATISTICS POR THE VARIABLES FOR EACH SET THE LST LINE WIG GIVE THE MODE THE SKEWNESS THE KURTOSIS AND THE 2 3 s FILE VALUE OF THE DISTRIBUTION THE 2ND GINE WILE GIVE THE 29y 50 Zop AND 97 5 c TILE VALUES OF WHE DES TRIBUTION THE 3RD LINE WILL GIVE THREE ADDITIONAL AD HOC ESTIMATES OF THE STANDARD DEVIATION FOR THAT MARGINAL DENSITY THE 1ST S D ESTIMATE IS THE STANDARD DEVIATION OF A NORMAL DISTRIBUTION HAVING THE SAME 25 75 TILE RANGE AS THAT VARIABLE THE 2ND ESTIMATE I
12. The traditional method of Naive Pooling has been used for population modeling when experiments are performed on animals for example which must be sacrificed to obtain a single data point per subject Data from all subjects 1s then pooled as if it came from one single subject One can estimate pharmacokinetic parameter values but cannot estimate any of the variability that exists between the various subjects making up the population Parametric Methods for Population Modeling A good review of parametric population modeling methods is given in 1 These methods obtain means and standard deviations SD s for the pharmacokinetic parameters and correlations and covariances between them Only a few of these will be described and quite briefly here l In the Standard Two Stage S2S approach one begins by using a method such as weighted nonlinear least squares to obtain pharmacokinetic parameter estimates for each patient and their correlations and covariances between parameters The second and final stage consists of obtaining the population mean and SD of the various individual parameter values To do this one needs at least one serum concentration data point for each parameter to be estimated One can also examine the frequency distributions of the individual parameter values The Iterative Two stage Bayesian IT2B method begins by using an initial estimate of the mean parameter values They may be obtained for example by the two stage
13. a look at how good your fit was USCPACK for Windows Beta 1 0 alan forrests Gentamicin _ File Edit View W Window Patient Popmodel Task Plot ree Sade Help lt gt KA M KSI ome oS SS 077 9 380 M vs 10 Central comparment measured levels 2D Plot 3D Plot 2D Scatter Raw data Cc aie comparm aa PODEN averages id 4 DLI Patient data A Pop model data A Pop model plots A Posterior Plot Fitted Probabilities Future Plot For Help press F1 This plot show the correlation between the serum levels and the weighted average trajectory The red dots are marked with numbers indicating the serum level number as shown in the Patient data tab The closer the red dots are to the diagonal line the better the fit Again this show that the fit you just made was not too bad Fitting with IMM Lets us see what happens when we enable IMM Select Compute options under the Advanced menu set the Alpha parameter to 0 999 and press OK Make a fit using the new value for the Alpha parameter by selecting Fit model under the Task menu The Fit quality should now look like this USCPACK for Windows Beta 1 0 alan forrests Gentamicin File Edit View Window Patient Popmodel Task Plot Advanced Help hd lt p Time 0 00 hours KA M KSI 374 6 797 v VSI 10 9 2D Plot 3D Plot 2D Scatter l Raw data o 1 2 3 4 5 6 7 8 g 10 oo Central comparment weighted averages
14. be achieved Other cost functions can also be employed As Bayesian feedback from serum concentrations is obtained each set of parameter values in the nonparametric prior has its probability recomputed Using this individualized nonparametric Bayesian posterior joint density the new regimen to achieve the target with maximum precision is computed In addition a new Interacting Multiple Model IMM sequential Bayesian method has been developed to estimate such posterior densities when parameter values have been changing as in unstable patients during the time of analysis A clinical software package implementing these approaches is in development INTRODUCTION SET INDIVIDUALIZED TARGET GOALS FOR EACH PATIENT The concept of a therapeutic range of serum drug concentrations is a generalization It 1s an overall range in which most patients but certainly not all do well One must always check each individual patient to see 1f he or she is doing not only well but optimally whatever the serum concentration is found to be Figure 1 shows the usual means by which such therapeutic ranges are obtained First there is an increased incidence of therapeutic effects with increasing serum drug concentrations Later on the incidence of toxic effects becomes significant The eye is drawn to the upward bends in each line and the classification of the therapeutic range is developed However this procedure does not deal with the need to develop a gentle dosag
15. behavior of the drug In contrast when one uses nonparametric population models as the Bayesian prior for designing the initial dosage regimen there are many multiple possible models or versions of the patient which one can use one for each support point in the discrete probability joint density or distribution Each support point has its own probability of representing the patient A candidate regimen can be given to each support point with its own individual parameter values and the probability associated with that point Multiple future serum concentrations can be predicted using the parameter values for each support point and its probability In this way an entire family of serum concentrations can be predicted into the future At the time for which the chosen goal is desired it can be compared with the many serum concentrations predicted to occur at that time one from each support point and the weighted squared error with which the goal fails to be achieved can be computed Other candidate regimens can also be examined The optimal regimen is the one which specifically minimizes the weighted squared error in the achievement of the goal In this way the MM regimen has the new feature of being specifically designed to achieve target goal s with the greatest possible precision for any set of population raw data doses and serum levels available up to that time because it considers all the many possible versions or models of the patie
16. flag 2 height in cm The difference here is in the formats of age and height 6 6 94 Read Month 4 Digits Day 4 Digits and Year 4 Digits of Therapy Day CCR ML MIN 0 00 150 00 Read the Elimination Descriptor Name 4 Characters its Units 8 Characters Minimum Floating point F7 2 Maximum Floating point F7 2 HOURS MG MG HR MCG ML KG MG DL 60 00 Read the units Time units 8 Characters amount units 8 Characters rate units 8 Characters level units 8 Characters weight units 8 Characters Serum Creatinine units 8 Characters and mpertu F7 2 where MPerTU is Minutes PER Time Unit being used Compute minutes since midnight on day of each PO or IV dose or start of IV infusion 5 Read the number of doses 4 digits IM 1 540 0 00000000 0 00000000 1000 00000000 38 33874000 IM 2 540 0 00000000 0 00000000 1000 00000000 38 33874000 IM 3 540 0 00000000 0 00000000 1000 00000000 38 33874000 IM 4 540 0 00000000 0 00000000 1000 00000000 39 66926000 IM 5 540 0 00000000 0 00000000 1000 00000000 39 66926000 If second digit of File flag is not equal to 1 Then read do loop until last dose in this case repeat 5 times route name 4 chars day of therapy 4 digits minutes into the day when dose was given 4 digits infusion rate F13 8 infusion time F13 8 dose amount F13 8 genval the value of the elimination descriptor usually CCr F13 8 If second digit of File flag is equal to 1 then
17. for this population model Accept the default selection IV option 1 Control peak and trough select dose interval and press OK As we have performed a fit for the current patient and population model the program already has knowledge about the weight and creatinine clearance for this patient Do you want to use your fitted data with this regimen Body weight fes fkg x OK Creatinine clearance 27 09 tml min 1 73msq Return The latest recorded weight for this patient was 68 kg and the most recent computed creatinine clearance was 27 09 mn min 1 73msq Accept these values by pressing OK Fill in the data for IV option 1 so that your dialog box looks like the one below Enter the desired route information IV option 1 Control Peak and Trough Select Dose Interval Variable Setting Usual ranges Peak goal 12 ugm 6 00 25 00 Trough goal 1 fug mL gt 020 150 Infusion duration o5 hous Number of days in regimen 4 days Date of first planned dose April 031980 16 Low bound High bound Dose interval e x z2 Note that you can select a dose outside the usual ranges and moving too far outside these ranges will result in a warning For now press OK to continue The program now computes the cost of using the different dose intervals You control the ranges examined by altering the low and high bond options in the previous dialog box After a few seconds this dialog box appears Select the desire
18. one of the points in the plot the numerical values for that plot will be displayed in the Value display In the 3D plot the values for the two parameters and their probability will be displayed In the 2D plot the probability and the parameter value will be displayed Moving the arrow over one of the points in the 2D scatter plot parameter value will be displayed The controls There are no menu options associated with this view The Posterior plots view This view is will be shown when you have fitted a patient that has a past history drug doses and serum concentrations measurements and a specific drug population model To demonstrate this view we will load a patient and select the correct population model of the drug given to that patient Pull down the Patient menu select Load patient and load the GENT2 file for example Pull down the Pop model menu select Load population model and select Gentamicin You will now fit the patient provided by Alan Forrest and a Gentamicin population model This is simple Pull down the Task menu and select Fit model When the fitting has completed you will be automatically transferred to the Posterior plots view The display Fitting the Alan Forrest s patient to the amikacin population model produces this plot Top 4 probability Toolbar trajectories Weighted average O SANS m r USCI 4CK for Windows Beta 1 0 alan forre ts AMIKa N TERZ oj x lt 24 97 perce
19. option You will be presented here with a dialog box allowing you to enter the information about your new patient Chart number Room First name Last name Date of birth November 21 2001 H Gender Female Male Height fin Weight fkg Some of the fields in this dialog box are optional The ones you are required to fill in are the date of birth the gender the height and weight All of these values will be needed when analyzing data and or computing a new dosage regimen Click OK to use the patient data The fixed field will now look like this It even keeps the typo FRank which should be Frank Filename Time of first dose Chart Number x12345 Height 180 00 cm Gender Male Ethnicity Not in use First Name FRank Last Name Hansen Weight 200 00 Ib Dialysis patient NO Birth Date 08 29 73 28 years Most recent CCr Time of next dose Any information previously present in the data grid will be removed At this time a new patient file based on the information you entered in the dialog box has been created Note that this patient only exists in the program It has not yet been saved to a permanent file on disk The Load patient option allows you to load a patient from a file The program recognizes three different patient types the default file extensions are 1 MB This is an old format and is a plain text file It has been used in the previous DOS version of RightDose US
20. property of mathematical consistency which is present in the nonparametric methods 7 9 However the major weakness of the parametric methods is that they make parametric assumptions about the shape of the parameter distributions and cannot perceive the entire shape of the parameter distributions as the nonparametric methods do 19 20 The major weakness of the parametric approaches 1s that they only obtain such single point estimates of parameter distributions Much discussion has taken place about which is the optimal estimate of a parameter distribution the mean median or mode for example When one acts on such single point information to develop a dosage regimen to achieve a desired target goal at a desired target time the regimen that is computed is simply the one which will hit the target exactly There is no way to estimate the degree to which the regimen may fail to hit the target as there is only a single model with each parameter having only a best single point parameter estimate The Separation Principle The separation or heuristic certainty equivalence principle states that whenever the behavior of a system is controlled by separating the control process into Getting the best single point parameter estimates and then Using those single point estimates to control the system that the task of control is inevitably done suboptimally 21 as there 1s no performance criterion which is optimized This is the major weaknes
21. read do loop until last dose in this case repeat 5 times route name 4 chars day of therapy 4 digits minutes into the day when the dose was given 4 digits infusion rate F15 8 infusion time it F15 8 dose amount 263 00000000 The last dose interval in hours If the second digit of File Flag is not 1 then format F7 2 else Format F15 8 8 Read how many serum levels 4 digits 1 600 40 97 1 720 38 64 1 960 26 96 2 510 1 25 5 600 40 97 5 720 29 29 5 960 26 96 6 510 1 25 Do loop until last dose in this case repeat 8 times Read therapy day 4 digits min into the day that level was obtained 4 digits the level F7 2 2 Read how many weights 4 digit integer 1 480 5 480 54 00 54 00 Do loop until last weight in this case repeat 2 times Read therapy day 4 digits mins into day that weight was obtained 4 digits the Weight F7 2 3 Read how many serum creatinines 4 digit integer 1 480 1 1900 4 480 1 2600 15 480 1 2000 Do loop until last serum creatinine in this case repeat 3 times If the third digit of general file flag is not equal to 1 Then read therapy day 4 digits minutes into day serum creatinine obtained 4 digits serum creatinine F7 2 If the third digit of general file flag is equal to 1 Then read therapy day 4 digits minutes into day serum creatinine obtained 4 digits serum creatinine F9 4 The difference here is in the Floating point format which was
22. t t to 4 J l 15 28 23 sb 35 48 453 J4 PRED CONCS BASED ON POPULATION MEDIANS Scatterplot of serum concentrations predicted using the population median parameter values Predicted concentrations are on the horizontal axis measured ones on the vertical POINTS L S LINE AND Y LINE ENTIRE POPULATION 4 H HH ot ty H it t 4t t Oo 45 S z 40 I z 39 r ee c 38 Oo H Cc E H T k A T I Oo H 5S 3 i 15 2A 25 Sh 35 48 45 PRED CONCS BASED ON FAR MEDIANS FROM INDIW SUBJ DISTE Figure 17 Scatterplot of serum concentrations predicted using the median values of the Bayesian posterior parameter density for each subject Predicted concentrations are on the horizontal axis measured ones on the vertical ESTIMATION OF CREATININE CLEARANCE IN PATIENTS WITH UNSTABLE RENAL FUNCTION WITHOUT A URINE SPECIMEN Roger Jelliffe M D Laboratory of Applied Pharmacokinetics USC School of Medicine 2250 Alcazar Street Los Angeles CA 90033 Phone 323 442 1300 Fax 323 442 1302 Email jelliffe hsc usc edu Running title Estimation of Unstable Creatinine Clearance Keywords Creatinine Clearance Renal Function Abstract Background There is a significant need to estimate creatinine clearance easily in acutely ill patients with unstable renal function who have changing serum creatinine values and who need careful individualization of drug dosage without the difficulty of hav
23. to focus on such single numbers as summaries of experience rather than to consider the complexities of the entire collection of the many and varied individual experiences themselves In this section we discuss newer and more powerful nonparametric methods which can give us richer and more likely information from the raw data which can then be applied to patient care more optimally than by using models having only single values for the various parameters What is meant here by the word nonparametric Most of the time when we gather data and summarize it statistically we are accustomed to obtaining a single parameter value for the central tendency of a distribution such as the mean median or mode and another single parameter value to describe the dispersion about this central tendency such as the standard deviation SD The usual reason for this is that so many events in Statistics have a normal or Gaussian distribution and that the mean and the SD are the two parameters in the equation of a Gaussian distribution which define the shape of that distribution explicitly Because of this describing a distribution parametrically in terms of its own parameters the mean and SD is very common Indeed the entire concept of analysis of variance is based on the assumption that the shape of the parameter distributions in the system are best described by their own other parameters of mean and SD or covariance A great body of experience has been brou
24. used in combination with the zoom feature as it tends to make the plot cluttered Enabling gridlines Gridlines can be enabled by selecting one of the options in the Grid Lines submenu You can have gridlines in the X direction Y direction or both Maximize Select this option and the plot will expand to occupy the whole area of your desktop You can close this window by hitting the Esc key or by left clicking on the top frame of the window A Gentamicin case In this chapter we give a detailed example on the use of RightDose using a gentamicin population model Initial preparations Start RightDose and load the GENT2 MB patient data file and the gentamicin population model A description on how to load patient data files and population models can be found in the General usage chapter The initial view After loading the patient and population model the Patient data display of RightDose will look like this USCPACK for Windows Beta 1 0 alan forrests Gentamicin File Edit view Window Patient Popmodel Task Plot Advanced Help hd lt a p gt Filename G lapk USCPACK Release GENT2 MB Time of first dose 04701 80 08 00 00 Chart Number 123 Height 70 00 in Gender Male Ethnicity Not in use First Name patient LastName alan forests Weight 68 00 kg Dialysis patient NO BithDate 11 21736 43 years Most recent CCr 27 10 Time of next dose 04 03 80 16 00 00 Dose Route Date Time Time Weight Descript
25. was then taken 1f the patient was female and finally 85 of that was taken for both men and women This gave the best correlations between estimated and measured CCr when renal function was severely impaired However the 15 rediction led to underestimations of about 15 when renal function was close to normal 5 Because of this we have now modified the original algorithm to apply the above 15 reduction only for patients who have severely impaired renal function and who are on hemodialysis or peritoneal dialysis Removal of the 15 restriction results in the improved estimates shown in Figure 1 which are less biased than those found with the previous procedure 5 Further if a patient s muscle mass is clearly above or below normal as may be the case with very muscular patients or conversely in cirrhotic patients or those with AIDS for example one can simply make a rough clinical estimate of the patient s body muscle mass as a percent of normal if desired to make a further final adjustment of P There are no specific rules for this only that one might make a rough clinical estimate based on findings on physical examination The adjustment for body mass was not done either in the original study 5 or in the present one However it provides an additional degree of freedom to protect against overestimation of CCr in cachectic patients or underestimation in very muscular patients The range currently permitted in these estima
26. weight and either a pair of unstable and changing serum creatinine levels or a single stable serum creatinine all without having to collect a urine specimen which is an extremely difficult and unreliable procedure in all but research situations especially for acutely ill patients in intensive care units Comparison of Estimated with Measured Creatinine Clearance In a first set of 128 observations on 15 patients in the renal transplant unit of the Los Angeles County USC Medical Center 5 the algorithm was shown to have an accuracy essentially equal to that of Jadrny 1 In an additional set of 250 observations on a group of 14 patients who had just undergone renal transplantation the standard error of the estimate 14 9 ml min was slightly more precise that the equations of Jadrny 16 6 ml min with an overall scatter of about 25 between the estimated and the measured values as shown in Figure 1 As acontrol one must consider the traditional determination of CCr and the errors present in its estimation If one can measure a serum creatinine level with a coeffi cient of variation of 5 as is the case with many common autoanalyzer methods and if one measures urinary creatinine concentrations with a coefficient of variation of 8 as 1s also common then 1f one can collect a 24 hour urine specimen with a coefficient of variation of 5 these errors will propagate so that the resulting value of the traditionally measured creatinin
27. 00 0100 3 00 0 00 0 00 14 Iv 0811 85 16 00 00 256 00 70 30 3 00 0 100 66 00 0 00 0 00 15 Iv 084 4 85 10 00 00 322 00 7030 53 00 0100 4 00 ooo ooo 16 Iv 08 1 4 85 14 00 00 326 00 70 30 3 00 0100 56 60 0 00 0 00 17 Iv 0816 85 22 36 00 382 60 70 30 3 00 0 500 39 40 200 00 100 0 The data shown in the grid consists of three sections the doses given the measured drug concentrations and the serum creatinine Use the scroll bar to the right to scroll up and down between the three sections The doses part consists of 11 columns COND MN BW NHN 9 10 11 The dose number starting at 1 The route by which the dose was given this can be one of PO IM or IV The date the dose was given shown according to the selected locale The time the dose was given shown hour minutes seconds Time into the dosage regimen starting at 0 hour for the start of the first dose The weight of the patient at the time the dose was given The creatinine clearance at the time the dose was given The IV infusion time the duration of the infusion if the dose was given IV Doses given by other routes will have a 0 in this column The dose interval between the start of this dose to the start of the next The IV infusion rate Doses given by other routes will have a 0 in this column The drug amount given Scrolling down to the serum levels you should see something like this if your patient file has a record of serum levels
28. 07 6 60816 2 46277 8 64061 9 10 1 12 13 14 45 ry o OE j Concentration Oooo o y Fa Selected time 34 33 hours into regimen Weighted average 8 16 OK Probability M ho iw iw D nn So nn D J nN The dotted vertical line shows the value of the weighted average trajectory The solid red line shows the value of the serum level at that time The table to the right shows the concentrations and their corresponding probability The concentrations that have a probability of more than 10 are show having a different background You can left click on any plot point to see a similar display but only the times that have a serum level measurement will have the red solid vertical line More information about the fit you just made can be found in the Fitted probabilities tab The information accessible in this tab is similar to the Pop model data tab and the default plot for this tab is a 3D scatter plot USCPACK for Windows Beta 1 0 alan forrests Gentamicir _ File Edit view Window Patient Popmodel Task Plot Advanced Help hd lt lt gt Time 0 00 hours a T 2 O s a 3D Plot 2D Scatter Raw data Fit quality KETC CI Fitted Probabilities A Future Plot For Help press F1 Hh As with the Posterior plot tab you can left click on the diamonds in the upper window to control the time slice shown in the lower window Select the Fit quality button to get
29. 11 12 13 Concentration in central compartment mg after 48 50 hours into new regimen KKO Future Plot For Help press F1 fe lS Note how the serum levels are much closer to the goal Appendix A Publications related to the MM USCPACK program The following publications can be found in this appendix e POPULATION PK PD MODELING PARAMETRIC AND NONPARAMETRIC METHODS e ESTIMATION OF CREATININE CLEARANCE IN PATIENTS WITH UNSTABLE RENAL FUNCTION WITHOUT A URINE SPECIMEN e ACHIEVING TARGET GOALS MOST PRECISELY USING NONPARAMETRIC COMPARTMENTAL MODELS AND MULTIPLE MODEL DESIGN OF DOSAGE REGIMENS e MULTIPLE MODEL MM DOSAGE DESIGN ACHIEVING TARGET GOALS WITH MAXIMUM PRECISION e ANEW METHOD TO UPDATE BAYESIAN POSTERIORS FOR PHARMACOKINETIC MODELS WITH CHANGING PARAMETER VALUES Abstract POPULATION PK PD MODELING PARAMETRIC AND NONPARAMETRIC METHODS Roger Jelliffe Alan Schumitzky and Michael Van Guilder Laboratory of Applied Pharmacokinetics USC School of Medicine AS we acquire experience with the clinical and pharmacokinetic behavior of a drug it is usually optimal to store this experience in the form of a population pharmacokinetic model and then to relate the behavior of the model to the clinical effects of the drug or to a linked pharmacodynamic model The role of population modeling is thus to describe and store our experience with the behavior of a drug in a certain group or population of patients or subjects
30. 7 1 37 50 56 4 gt 1af a gt gt i Patient data Pop model data A Pop model plots A Posterior Plot J Fitted Probabilities A Future Plot For Help press F1 hh The lower portion of the report show the cost the area under the curve AUC and the 4 computed doses You can print this report by selecting Print under the File menu or by pressing Ctrl p Switch to the Future plot tab to see more visual information about the new regimen Change the plot to only show the weighted average USCPACK for Windows Beta 1 0 alan forrests Gentamicin File Edit View Window Patient Popmodel Task Plot Advanced Help hed lt gt pe 0 251 8 910 VigtAy 15 0 Ai n M on 5 E 4 D z E aa O D fe 5 75 E D O Ee D pmr An as 4 E D S a D O 25 50 75 100 125 Time hours id 4 if Patient data A Pop model data A Pop model plots A Posterior Plot A Fitted Probabilities A Future Plot For Help press F1 This plot show the weighted average serum concentration in the central compartment The past history is show to the left of the dotted vertical line the future regimen to the right Enable all subset again and select the Concentration vs probability under the Plot menu USCPACK for Windows Beta 1 0 alan forrests Gentamicin _ File Edit view Window Patient Popmodel Task Plot Advanced Help hd lt q b gt h e L Le 42 27 22 20 96 16 90 9
31. ASS 0 00000000 0 00000000 100 00000000 41 34090000 IV 2 495 100 00000000 1 00000000 100 00000000 41 34090000 IV 21005 100 00000000 1 00000000 100 00000000 27 09849000 IV 3 480 80 00000000 1 00000000 80 00000000 27 09849000 8 00000000 5 1 560 3 60 1 935 1 80 2 370 52 20 21100 9 10 3 460 4 10 1 1 480 68 00 3 1 560 1 20 2 540 1 50 3 720 as 100 00 O 1 i 2 00000 1 Appendix C A description of the mm population model file format The description comments are given below the population model sample The file description BEGIN FILE This indicates the beginning of the file USCPACK for Windows population model file File revision 1 0 The header section the current file revision is 1 0 BEGIN LOCKED SECTION The drug modeled Trimethoprim Date file was generated 11 14 2001 File genererated by program bignpem v4 3 Location where file was generated LAPK SDSC File authorized by Roger Jelliffe LAPK File lock code 2 i END LOCKED SECTION 15937389753495 This section is to be considered locked When the population model file is read by RightDose the program computes a checksum from the section between the BEGIN LOCKED SECTION and END LOCKED SECTION This checksum must match the number given in this case 15937389753495 If the file lock code is 3 or higher RightD
32. C MODEL OF VANCOMYCIN This 2 compartment model 5 was developed using the NPEM2 program in the USC PACK PC clinical collection Its parameters were Vc the apparent volume of the central serum level compartment in L kg Kcp the rate constant from the central to the peripheral compartment Kpc the rate constant in the reverse direction and Kslope the increment of the elimination rate constant Kel for each unit of creatinine clearance CCr all in hr A nonrenal component Kint was fixed at 0 002043 hr Thus the overall Kel Kint Kslope x CCr Data of 30 patients receiving Vancomycin were analyzed The file containing the population joint probability density values the 28 rows of parameter values and their probabilities was read into the program for MM design of dosage regimens 3 4 Table 1 shows the summary values of the various population parameters There were 28 support points for the population joint parameters Each support point had a value for each parameter representing a candidate model for the patient and a computed probability The graphical plot of the values for Vc and Kslope is shown in Figure 1 THE SIMULATED CLINICAL SCENARIO FOR INITIAL THERAPY DAY 1 A therapeutic goal of a stable serum vancomycin concentration of 15 ug ml to be achieved by continuous series of continuous stepwise intravenous infusions at various rates was chosen for this simulated study While it is common to give vancomycin by inte
33. C PACK 2 MB2 This is an updated version of the old MB format The file is also a plain text file but with additional fields 3 USC This is a completely new format USC files are binary files that can contain information about multiple drugs given to the same patient Note that even though this format is fully supported the current version of RightDose does not use the extended options provided by this format The Pop model data view The display The Pop model data view is very similar to the Patient data view They both have fixed fields and a data grid This view will contain information about the selected drug population PK model The top portion consists of a series of fixed fields General Model information information Ranges Routes compartments Usual ranges Drugname Bioavailibility vr Peripheral I7 Peak Central Trough Central Provider Active salt fraction MIT Cata l Peak Peripheral Model file POT Absorptive Trough Peripheral The fixed fields consist of three groups The left gives General information about the population model The name of the drug the name of the group that made the population model the bioavailability and the active salt fraction The center block Model information provides information about the compartments used in the model and the allowable routes The target Ranges block displays the common ranges for the peak and trough goals usually used with this drug Th
34. Fe U tH 44 2 40 4 i 35 Cc t t m 34 t 4 N t c 257 4 id E t rH a T p t 4 R 15 A j 18 I O J S J l 13 28 25 38 353 48 453 J3 PRED CONCE BASED ON POPULATION MEDIANS Figure 5 Showing the predicted values of the serum concentrations using the population median values of Ka Ks and Vs in the population POINTS L S LINE AND Y LINE ENTIRE POPULATION H 45 i s AA at tt t IJ E Oo H E H T Fe A T I Oo H 5 1A 15 7A z235 SA 35 4h 45 FRED CONCS BASED ON POST FAR VALUES USING FOF MEDIANS Figure 6 Showing the predicted values of the serum concentrations using the individual MAP Bayesian posterior parameter values of Ka Ks and Vs based on using the population median parameter values and their SD s as the MAP Bayesian prior in the population True Density VOAVA ZAINI WATANO oF WW Zh SSS NN X OVAN N EI N SAM AYA AK VAX AAV AYN AXA NAKA WAX AX AX XA A NY XY KAW Sy y vy aN WYNN v v M Ny YAY mT base is that of the volume of distribution V while that toward first base is the elimination rate constant K Note that there are actually two subpopulations with two clusters of were taken If the bottom or 0 0 0 0 corner is Home plate then the axis toward third distributions for K V and K are uncorrelated Figure 7 The true ph
35. Maximize Customization Dialog Export Dialog Help dak j 29 30 35 40 45 50 Time hours As you can see there is also a Help option offering detailed help for the various selections Zooming All plots in the program have been configured to allow for zooming The process of zooming is simple Press and hold the left mouse button when inside a plot Move the mouse and you will see the zooming rectangle When you then release the left mouse button the plot will expand the selected region inside the zoom rectangle To return the plot to the original status simply right click inside the plot and select Undo Zoom The customization dialog The customization dialog gives you many options for customizing your plot It does essentially give you an entry point to all other options Select the tabs to perform one or more of the following options e You can add a title and subtitle for your plot e The plotting mode can be altered to show just the data points to interpolate values between the plots or to show the plot as a bar graph e Select the subsets to show e Adjust the axis range and switch to logarithmic axes if desired e Change the fonts used to display the axis labels and plot title e Change the colors used for the background and foreground for the desk and graph e Display the different trajectories using different symbols Exporting plots Several export options are provided for both data and plot image
36. S THE STANDARD DEVIATION OF A NORMAL DIST HAVING THE SAME 2 5 97 5 s TILE RANGE AS THAT VARIABLE THE 3RD ESTIMATE IS THE AVERAGE OF THE FIRST TWO THE 4TH VALUE IN THE LINE IS THE SCALED INFO FOR THAT MARGINAL DENS KA 1 36500000 02960735293 Z 999TSSAS 105748507 les EOS OOOO ee 2 On 1790500000 2094290000 eooo Zo Dao TODS 0 45627951 LOO TZ L029 L4 Ks 0 00405000 0 40887166 162022061 OOO IAS 000273000 0 00380000 07003978095 0004083909 0 00091101 0 00050104 000070603 LIP 23032009 vol 0 23400001 Og Le Toe 2 6 1 85668144 tech PLO OO et 209955 0 Os ZeZU 000 0 30600001 0 34377668 GULLA 0 04407568 0 05762418 106 38472260 Figures and Legends SI SM em Aa T Figure 1 population e _ me he oo e OF om a OOo oe oe OP FINAL CYCLE HISTOGRAM 100 tlg deed da SS woe Le Bo derr 139 lt 2 Se KA Showing the values of the Ka the absorptive rate constant in the FINAL CYCLE HISTOGRAM 7 4 Bo Fi i 1 6 E 1 6 Fi 1 4 U E bZ H 1 C i amp 4 a H poz Azz BESS BRS RBS ABAZ BRASS 0037 04 Aba ES Figure 2 Showing the values of the Ks the increment of Kel the elimination rate constant per unit of creatinine clearance in the population FINAL CYCLE HISTOGRAM S Gh wl wf fb oto fae 82 wag WS e _ CIS MM eam AT me hw oo ee OF om OOo oe oe OP she ac Figure 3 Showing the values of the Vs the increment of the apparent volume of distribution per uni
37. School of Medicine Los Angeles CA Purpose to improve the quality of Bayesian posterior densities for pharmacokinetic models of drugs when the patient s parameter values change significantly during the period of the data analysis Methods the prior probability was assumed to be a nonparametric population model discrete joint density Parameter changes were modeled as jumps from one discrete support point in the density to another Given such discrete priors previous work in our laboratory showed that the multiple model MM estimator works well when the patient s parameters are unknown but constant However both it and the MAP Bayesian method work less well where the patient s parameter values change The interactive multiple model IMM algorithm is an effective method in the aerospace community for tracking maneuvering targets We implemented the IMM sequential Bayesian algorithm in pharmacokinetic software and compared its performance with the MM and MAP sequential Bayesian estimation methods using both simulated and real clinical data for Tobramycin therapy Results in a simulation of changing parameter values taking place at a stated time the IMM approach tracked the drug with about half the integrated total error found with the MM and MAP methods Further in examining data from a real patient whose parameter values changed significantly during therapy the IMM approach tracked the patient s data much better than the seq
38. Using RightDose In this chapter we explain the structure and use of RightDose with examples General description The image below shows the view you get when you start RightDose The actual view is called the Patient data view and will be explained in detail later Toolbar Menus Fixed fields US ACK for Windows Beta 1 0 USCPACI Timectfestdose S Gende SS Ethwicty SSCS FestName LastName Weor Dispis paters BithDae yeas MostrecereCCr Timeodnetdose Tab panel Data grid The arrows in the Toolbar can be used when stepping through a series of plots over time Pressing the leftmost triangle button when a time series is displayed will take you to the start of the series The rightmost button takes you to the end The two middle buttons take you one step forward or backward in the time series You will have several Menu options available at any time Use the menus to load new patients select drug population models change plots and so on The different menu options are in general connected to the various views you will get and they will be explained in detail later The views may have Fixed fields giving you information about the patient or the population model You will not be able to edit these fields directly The different views available are shown in the Tab panel The name of the view Patient data Pop model data Pop model plots 1s shown on the tab Pressing one of the tabs takes you to
39. adras India 1995 pp 407 426 Jelliffe R Schumitzky A Bayard D MilmanM Van Guilder M Wang X Jiang F Barbaut X and Maire P Model Based Goal Oriented Individualized Drug Therapy Linkage of Population Modelling New Multiple Model Dosage Design Bayesian Feedback and Individualized Target Goals Clin Pharmacokinet 34 57 77 1998 Bayard D and Jelliffe R Bayesian Estimation of Posterior Densities for Pharmacokinetic Models having Changing Parameter Values To be presented at the Tenth Annual International Conference on Health Sciences Simulation San Diego CA January 23 27 2000 Taright N Mentre F Mallet A and Jouvent R Nonparametric Estimation of Population Characteristics of the Kinetics of Lithium from Observational and Experimental Data Individualization of Chronic Dosing Regimen using a new Bayesian Approach Ther Drug Monit 16 258 269 1994 Jerling M Population Kinetics of Antidepressant and Neuroleptic Drugs Studies on Therapeutic Drug Monitoring Data to Evaluate Kinetic Variability Drug Interactions Nonlinear Kinetics and the Influence of Genetic Factors Ph D Thesis Stockholm Karolinska Institute at Huddinge University Hospital pp 28 29 1995 A NEW METHOD TO UPDATE BAYESIAN POSTERIORS FOR PHARMACOKINETIC MODELS WITH CHANGING PARAMETER VALUES David S Bayard and Roger W Jelliffe Senior Scientist Jet Propulsion Laboratory Pasadena CA Laboratory of Applied Pharmacokinetics USC
40. arget Individualized drug therapy therefore begins by setting such specific individualized target goals Without specific target goals there can be no individualized precise drug therapy The task of the clinician is to select and then to hit the desired target goal as precisely as possible As the initial regimen is given the clinical task is to observe the patient s response and to reevaluate whether the target goal was hit precisely or not was correctly chosen or not or if it should be changed and a new dosage regimen developed THE NEED FOR MODELS Pharmacokinetic and dynamic models provide the means to store past experience with the behavior of drugs and the tool to apply that past experience to the care of future patients This experience is usually stored in the form of a population pharmacokinetic model which is used as the Bayesian prior to design the initial regimen for the next patient who appears to belong to that population The dosage regimen to achieve the target goal is computed and given The patient is then monitored both clinically and by measuring serum concentrations The serum concentrations are used not only to note if they are within a therapeutic range but also to make a specific model of the behavior of the drug in that individual patient One can see what the probable serum concentrations were at all other times when they where not measured One can also see the computed concentrations of drugs in a peripheral nonse
41. armacokinetic population joint density from which the 20 samples Smoothed Sample Density SCHR SOR AK KAKA HNO ARI age CD AY NA sampled patients The axes are as in Figure 7 This is the distribution that NPEM should Figure 8 Graph smoothed as in Figure 7 of the actual parameter values in the twenty discover Smoothed Estimared Density 5 Levels Subject Figure 9 Smoothed estimated population joint density obtained with NPEM using all five serum levels Axes as in Figure 7 Compare this figure with Figure 8 Second Order Density Figure 10 Plot of the population density the second order density as perceived by a theoretically optimal parametric method Axes as in Figure 7 Compare this figure with Figures 8 and 9 The two subpopulations are not discovered here The true parameter distributions are perceived with great error by this method JOINT DENSITY x REX XRRO KIRN VEROON ONONO NA NNNNA NAN E A D x Q 9 ea Y Q ci Q a xs 0 0 a QR S ei s ch Q 9 S a a 9 GY AA Q PAAY S w s S RKO XX NANA ARNNN RE we AY i RRNA OOO CESE EENS o Q y ee Ne iy g AN RRE OO RA P y S Ke US Figure 11 Population joint density of Vancomycin as studied by Hurst et al VS volume of distribution o
42. ate E P 3 In this way one can use this carefully measured data of excretion to estimate daily creatinine production This estimate can be further refined as described below It should also be noted that in these patients the average serum creatinine their patients was 1 1 mg dL 2 This will be useful below The Effect of Degree of Uremia It was shown by Goldman 6 that uremic patients also have a decreased excretion and therefore production of creatinine Using data from that report creatinine production P in mg day for an average size patient is related to serum creatinine C in mg dL by P 1344 4 43 76C 4 Based on this one can now adjust the first estimate of creatinine production for age as given in Eqn 2 to the average value Cavg of the patient s C and C2 by the ratio R where P1 1344 4 43 76 x Cavg 5 and P2 1344 4 43 76 x 1 1 6 where 1 1 the average serum creatinine in Siersbaek Nielsen s patients in each age group as described above Then R P P2 and 7 the adjusted P or Pag P xR 8 In our work the best empirical correlation between measured and estimated CCr was finally found by taking 95 of Paqj In this way daily creatinine production can be estimated for men based on many careful measurements of 24 hour urinary creatinine excretion and adjusted to the patient s age weight and degree of uremia 6 In further adjustments 90 of the value for men
43. bed lt gt 44 566 12 352 L Cc 24 97 N O T E c v E a OL D La w 4 Cc wv i ha pa 4 Z D a C Q 15 20 29 30 35 40 45 Time hours ld 4 gt Patient data A Pop model data A Pop model plots A Posterior Plot Fitted Probabilities A Future Plot For Help press F1 The Blue vertical bars along the horizontal time axis show when doses were given The red diamonds show the measured serum levels and their times The information in these plots can be overwhelming due to the number of trajectories If you wish to see only the central tendency of the Bayesian posterior fits Select subsets gt Weighted average only from the Plot menu as shown below USCPACK for Windows Beta 1 0 alan forrests Gentamicin File Edit view Window Patient Popmodel Task Plot Advanced Help hed lt q p gt 0 479 16 006 15 0 Concentration in central compartment mg 0 5 10 15 25 30 35 40 45 50 55 Time hours 4 4 gt gt i Posterior Plot For Help press F1 ey S Nea As you can see there is a decent correlation between the weighted averagetrajectory and the serum level measurements You can get more information about the correlation between the trajectories and the serum levels by left clicking on one of the red diamonds Detailed information at the selected time Probability Cone 3 50e 007 6 07198 1 70963 10 07620 1 00e 014 14 89997 8 91e 0
44. bility Figure 7 shows a carefully constructed simulated population of patients This population is actually a bimodal distribution consisting of two subpopulations Half are fast and half are slow metabolizers of a drug They all have the same volume of distribution but two different elimination rate constants There was no correlation between the two parameters From this defined population twenty simulated patients were sampled at random Figure 8 shows these sampled patients exactly known parameter values smoothed and graphed as in Figure 7 Figure 8 thus shows the true empirical population parameter distribution that NPEM or any other population modeling method must now discover These twenty simulated patients each received a simulated single short infusion of a drug having one compartment behavior Five simulated serum samples were drawn at uniformly spaced times The assay SD was defined as 0 4 concentration units The resulting data of serum concentrations over time was presented to the NPEM algorithm and computer program 20 24 and also to a parametric population modeling method such as NONMEM or IT2B Figure 9 shows the NPEM results again graphed as in Figure 7 The NPEM method clearly discovered the two subpopulations of patients and closely described the shape of the known empirical original population joint distribution shown in Figure 8 Figure 10 shows the very different perception of the population when a param
45. ch the assay SD 0 12834 0 045645C where C is the serum concentration The assay SD of a blank was therefore 0 12834 ug ml and the subsequent coefficient of variation was 4 5645 In this particular analysis gamma was not computed but was held fixed at 1 0 The following results were obtained with the USC PACK IT2B program The initial very first parameter estimates and their SD s were Ka the absorption rate constant 1 5 1 5 hrl Ks the increment of elimination rate constant per unit of creatinine clearance in ml min 1 73M2 0 005 0 005 hrl and Vs the apparent central volume of distribution 0 6 0 6 I kg The nonrenal intercept of the elimination rate constant Ki was held fixed at 0 00693 15 hrl so that the elimination rate constant Ki Ks x creatinine clearance The IT2B program converged in this analysis on the 8th iteration The population mean values for the parameters Ka Ks and Vs found were 1 45 hr 0 0033 hrl and 0 257 L kg respectively The medians were 1 42 hr 0 0035hr and 0 252 L kg respectively The population standard deviations were 0 341 hrl 0 000693 hr and 0 0479 L kg respectively yielding coefficients of variation of 24 21 and 19 percent respectively The empirical distributions of Ka Ks and Vs are shown in Figures through 3 The joint distribution of Ks and Vs in shown in Figure 4 which shows a visible positive correlation between the two parameters consistent with t
46. chosen or not One can choose a different goal if needed and once again one can compute the dosage regimen to achieve it In this way the model can be individualized and dosage can continue to be adjusted to the patient s body weight renal function and available serum concentrations for example to achieve the desired target goal usually with increasing precision CRITIQUE OF THE MAP BAYESIAN APPROACH The weakness of the MAP Bayesian procedure is that the models it uses have only single point estimates of the various pharmacokinetic parameters Because of that there is only one version of either the individualized model or of the population model itself The regimen developed to achieve the target goal is simply assumed to do so exactly THE SEPARATION PRINCIPLE The separation or heuristic certainty equivalence principle 4 states that whenever control of a system is separated first into obtaining single point parameter estimates for the model and second of using those single point estimates to control the system the task is often achieved in a suboptimal manner This is a significant problem with MAP Bayesian fitting and dosage design The way around this problem is by incorporating improved nonparametric approaches to population pharmacokinetic modeling and in using them specifically to design maximally precise dosage regimens USE OF POPULATION MODELS IN CLINICAL THERAPEUTICS When a parametric population model 1s used as the Bay
47. cribed as process noise 16 The problem is that it is difficult to estimate process noise as it requires stochastic differential equations and no software for this exists at present in the pharmacokinetic field to our knowledge Furthermore the IT2B program can also be used to search for estimates of the various assay error pattern coefficients if one has absolutely no idea what the assay error pattern is or if the measurement is one which it is impossible to replicate In this case gamma is not determined but is implied in all the various other coefficients The following results are taken from a representative run of the IT2B program The original patient data files were made using the USC PACK clinical software The program like the NPEM program reads those files and writes out working copies of them in another format The following illustrative results are taken from a subset of data obtained by Dr Dmiter Terziivanov in Sofia Bulgaria 17 on 10 patients who received intramuscular Amikacin 1000 mg every 24 hours for 5 or 6 days In each patient two clusters of serum levels were measured one on the first day and one on the Sth or 6th day approximately 5 levels in each cluster Creatinine clearance was estimated from data of age gender serum creatinine height and weight as described in another paper in this issue Serum concentrations were measured by a bioassay method The assay error pattern was described by a polynomial in whi
48. d dose interval amp gt D a om si San D gt xf 30 40 50 Dose interval hours The best dose interval based on the average deviation is 24 hours You may alter the dose interval 24 hours Cancel The dots in the graph indicate that a cost has been computed for that dosage interval The graph shows that the optimal dose interval is 24 hours Select OK to continue The new regimen is now computed an operation that will take a few seconds When completed RightDose will switch to the Report tab USCPACK for Windows Beta 1 0 alan forrests Gentamicin ae Oj x File Edit View Window Patient Popmodel Task Plot Advanced Help hed lt a p gt pe Lastname alan forrests Firstname patient rs Date of birth 11 2141936 Age 65 BSA 1 84 Gender Male Height 70 00 in Weight 68 00 kg Drugname Gentamicin Provider LAPK SDSC Hame Mean Median Mode D Min Max KA 0 069148 1 306860 0 00e 000 0 164049 0 946229 1 768180 KS1 0 000110 0 003099 0 00e 000 0 000259 0 002099 0 004059 S1 0 009727 0 242018 0 00e 000 0 023233 0 169692 0 329628 KI 0 006932 0 006932 0 006932 0 0 0 006932 0 006932 Route I Option 1 Control Peak and Trough Select Dose Interval Goal 1 12 00 Goal 2 1 00 Time 1 1 00 Time 2 1 00 Cost 0 347280 AUC 322 872901 Dose Date Time Dose mg mg kg mq msq 1 04 03 80 16 00 00 39 22 0 58 21 33 2 04 04 80 16 00 00 63 92 1 31 43 36 3 04 05 80 16 00 00 88 96 1 31 48 38 4 04 06 80 16 00 00 92 9
49. desired number of processors A differential equation solver is employed The results are then sent back to the user s PC where they are examined just as in the various figures shown above Thus one can now make large and nonlinear models of a drug with multiple responses such as serum concentrations and various drug effects 18 This resource is now in use by researchers Strengths and Weaknesses of Parametric Population Modeling The major strength of the parametric population modeling approaches is their ability to separate interindividual variability in the population from intraindividual variability in the individual subjects gamma for example and from variability due to the assay error Because of this it seems best for the present to begin making a population model by using a parametric method such as the IT2B First one should estimate the assay error pattern explicitly obtaining the assay error polynomial as described in an earlier paper in this collection and elsewhere 14 15 Then having that assay error polynomial one can use a parametric method such as IT2B to find gamma and to determine the overall intraindividual variability and to know what fraction of that is due to the assay itself Then one is in a position to overcome the weaknesses of these approaches by using this information in making a nonparametric population model see below One weakness of the parametric methods 1s that they generally lack the desirable
50. duced as a random Gaussian error having the SD of the Abbott TDx assay used in our laboratory to make the original population model This heteroschedastic random Gaussian assay error see 6 had an SD represented by the polynomial SD 0 30752 0 024864C 0 00027637C2 where C is the true serum level of a simulated true patient randomly chosen as support point number 15 of the 28 in the model set drawn at the various sampled times Thus two things were going on in this scenario On the one hand the MM stochastic controller was designing the MM stepwise infusion regimen to most precisely achieve the goal of 15 ug ml at 2 4 6 12 18 and 24 hours during the first day of therapy On the other hand this ideal dosage regimen was being corrupted by the Monte Carlo simulator incorporating the clinical errors stated above The MM controller also takes these stated errors into account in designing the dosage regimen Figure 4 shows the computed 99 most probable trajectories of the serum levels for Day 1 of MM therapy before any feedback The variability is close to that shown in Figure 3 The solid lines represent the 95 most probable trajectories and the dotted lines represent the next most probable 4 This represents the clinical situation as much as it is knowable to the clinician until the serum level results come back Further in a way that is never knowable clinically the time course of the computed serum concentrations for a si
51. e central compartment select the absorptive compartment and see what happens The plot now changed showing the events in the absorptive compartment If you selected Alan Forrest s patient you will see one spike at 18 hours 18 25 to be exact This is the time when the IM dose was given It might be a good time to spend some time looking at the patient the population model and the posterior fit views Are the Dose ticks shown at the right times Why are there no spikes in the absorptive compartment when doses are given IV How many trajectories should there be in the plot In the above example the default posterior plot looks decent This may not always be the case If you have many diverse trajectories the plot may look cluttered and the information shown may need to be reduced If you want to only see the estimated Weighted average of all the trajectories select the Extractions submenu and select Weighted average only You can also set a threshold level showing you the trajectories making up a percent of the probabilities Examine this by selecting Set subsets instead of Weighted average only Enter 40 into the dialog that pops up and you will get the two first trajectories the first one has a probability of 24 97 the second 12 63 making it a total of 37 6 and the weighted average The subset selection will be active until you make a new selection or perform another fit Selecting the absorptive compartment the plot will show the
52. e clearance will have a coefficient of variation of 11 The resulting 95 confidence limit is therefore 22 This error closely corresponds to the scatter found between the estimated and measured CCr values shown in Figure 1 Because of this it is likely that this method of estimating CCr has a precision about equal to the classical measurement of it It addition it is practical in clinical situations It is also probably better at sensing changes in renal function in response to sudden changes in serum creatinine than are the more simple formulas of Jadrny 1 Jelliffe 3 or Cockcroft and Gault 4 which were designed only for use when serum creatinine 1s stable as serum creatinine usually requires about one week to stabilize following a change in renal function The Question of Ideal Body Weight It would seem logical to correct the estimate of creatinine production and muscle mass by using some estimate of ideal body weight However in anecdotal examinations of this question in several morbidly obese patients somewhat more precise estimates of CCr were actually obtained using total body weight than with various estimates of ideal body weight Because of this we have continued to use total body weight in preference to an estimate of ideal body weight It would be interesting to study this question further in another study Conclusion The method described here for estimating CCr in acutely ill and unstable patients provides a useful to
53. e data grid portion of this view will contain statistical information about the population model and the matrix containing the parameter description support points and their corresponding probabilities The controls Selecting Pop model on the menu bar will automatically switch the view to the Pop model data The sub options for this menu are limited to one Load population model Select this option and you will get a dialog box asking you to select a drug population model Models in directory G winUSCPACK popmodels No description for this population model ikacin seca Date generated 11 20 2001 entamicin mm j Generated by LAPK SDSC trimethoprim mm iino lalla Drugname Tobermycin Checksum NOT IMPLEMENTED X Cancel UW Select Select the correct drug population model and press OK If you selected Vancomycin the Pop model data view should look like the one below Take a look at the window frame at the top Patient name USCPACK for Windows Beta 1 0 Hansen vanco 80Kpts File Edit View Window Patient Popmodel Task hd lt lt gt p Advanced Help Population model It now contains both the Patient name we entered FRank Hansen and the name of the Population name vanco 80kpts The names shown in this frame are always up to date so you can always take a look at it if you are uncertain about which patient or population model you are working on Statistical informat
54. e data making up the population model in more detail It will display the plots when you have selected a drug population model The display This is the first in a series of plots When a population model is loaded and you switch to this tab the default display 1s a 3D plot showing the parameters KS and VS if they are present in your population model If they are not the two first parameters will be selected and displayed Plot view Plot selector Parameter selector USCPACK for Windows Beta 1 Hansen vanco 80Kpts model Tash Plot Advanced Help KO KPC V KS Probability Patient data For Help press F1 Scrollbar Value display The Plot view is the main window in this view all the plots will be displayed in this window The plotting routines used in RightDose are quite extensive giving you a multiple options You can export the plot or the data making up the plot to your clipboard or printer You can add a grid change axis and lots more A detailed explanation of your options is given in Appendix A Use the Parameter selector to select the parameters to be plotted You must select two parameters if you want the 3D plot or the 2D scatter plot If present KS and VS will be selected by default The Plot selector allows you to switch between the different plots mode A 2D plot showing all parameters and the 2D scatter plot showing KS and VS is shown below Parameter If you move the arrow over
55. e probability matrix PROBABILITY KA KS1 vs1l FA 0 3078591 0 3361750 0 0010866 1 0126800 0 9998090 0 2048287 0 8304400 0 0014187 1 0063800 0 9998580 0 0865280 0 0762225 0 0006258 1 2360500 0 8043380 0 0729067 0 8320020 0 0014187 1 0073500 0 9998580 0 0667204 0 5291610 0 0021567 0 6420140 0 9998340 0 0550678 0 0966272 0 0009847 0 8849330 0 8272260 0 0374097 0 0962025 0 0005925 1 4900300 0 9265490 0 0336980 0 3529200 0 0014854 0 6441420 0 8660140 0 0324623 1 9477200 0 0002237 3 1675500 0 9999600 0 0303316 0 0002172 0 0000721 3 5082600 0 0000668 0 0289079 3 5189700 0 0011616 1 7157800 0 9102320 0 0285714 0 0003410 0 0081684 0 7570980 0 2779230 0 0147084 0 0962025 0 0005925 1 4910000 0 9273300 The support point matrix END FILE 43597657865846357819 An end of file indicator and the checksum for the whole file An example of a population model file The file shown below is the population model for Amikacin BEGIN F I LE 3 L it USCPACK for Windows population model file File revision 1 0 it BEGIN LOCKED SECT ION 3 it The drug modeled Amikacin Date file was generated gt 11 14 2001 File genererated by program gt bignpem v4 3 Location where file was generated LAPK SDSC File authorized by Roger Jelliffe LAPK File lock code ao END LOCKED SECTION 15937389753495 File update list 11 14 2001 Andrea
56. e regimen for a patient who needs only a gentle touch and a more aggressive one for a patient who really needs his dosage pushed 100 50 PERCENT RESPONSE OR EXPECTATION OF EFFECT O THERAP EFFECTS 8 TOXIC EFFECTS 20 SERUM CONC ARBITRARY UNITS Figure 1 General relationships usually found between serum drug concentrations and the incidence of therapeutic and toxic effects The eye is drawn to the bends in the curves and the therapeutic range is classified in relation to these bends This qualitative procedure of classification discards the important quantitative relationship of the incidence of toxic effects versus serum concentration Another approach is one in which the clinician evaluates each patient s individual clinical need for the drug in question and selects an estimated risk of toxicity which is felt on clinical grounds to be justified by the patient s need One then selects a target serum concentration goal to be achieved One does not want the patient to run any greater risk of toxicity than is justified by the patient s clinical need Within that constraint however one wants to give the patient as much drug as possible to get the maximum benefit This approach provides the rationale for selecting a specific target serum concentration goal rather than a wider window and then to attempt to achieve that target goal with the greatest possible precision just as if one were shooting at any other t
57. e selected dose is also outside the not to exceed range the user will get a warning The ranges for the peripheral compartment peak and trough use the value 1 if this selection is not valid for this model Usual ranges peak min peak max trough min trough max 1 0 1 0 1 0 1 0 Not to exceede ranges peak min peak max trough min trough max 1 0 1 0 1 0 1 0 The same as above but for the peripheral compartment The assay polynomial asl as2 as3 as4 0 322720 0 0183650 0 00120510 0 0 The coefficients in the assay polynomial where as1 is the zero order coefficient as2 the first order and so on The assay polynomial will in general depend on both the population model and the apparatus used to measure the serum level The process noise wsqrt del de2 de3 de4 terr 0 000010 0 0 0 000010 0 0 0 0 0 000010 TBD The number of random parameters 4 The number of random parameters in the model The random parameters used was KA KS1 vs1l FA 3 7 16 20 The names of the random parameters and their corresponding coefficients The number of fixed parameters 1 The number of fixed parameters in the model The fixed parameters used was KI 6 The names of the fixed parameters and their corresponding coefficients The values of the fixed parameters 0 115500E 01 The values of the fixed parameters The number of probability points 13 The number of support points for this model Th
58. ecting Print from the File menu The Future plot view Please complete the steps outlined for the Report view above or develop your own future regimen The display Computing a new regimen takes you to the Report view Then select the Future plot tab to see more detailed information about your new regimen Old regimen New regimen USCPACK for Window Beta 1 0 alan forrests AMIKACIN TERZ pu D me del Tash Plot Adyari ed Help Ss a C ent 12 63 percent 9 62 percent 8 12 Mercent VWigtAvaq gi N QO ak gi ahi O D t 0 A 5 OO w C D O C 5 D oO a O For Help press F1 Borderline Because we have based this new regimen on the fitted data this view will also show the results on the Old regimen The Old regimen has the diamonds indicating serum level measurement and both plots have the blue lines showing where a dose was or will be given The controls The controls for this view are the same as with the Posterior plot accessible from the Plot menu option Note that you now have more options available for this menu selection You can remove the past plot by selecting Toggle past and future Try it and watch the past disappear Turn it back on using the same selection To get a completely different view select the Concentration vs probability This will bring up the following display Arrow buttons Goal indicator USCPAL for Windows Beta
59. esian prior to design an initial dosage regimen for the next patient one encounters one usually has only a single estimated value for each parameter Because of this only one prediction of future al Ii A a Se aikcrogeany 5 Luu 159 DIU ESO Tima Mine concentrations can be made The dosage regimen is simply assumed to achieve the target goal exactly as shown in Figure 2 Figure 2 Using lidocaine population mean parameter values an infusion regimen designed to achieve and maintain a target goal of 3 ug ml does so exactly when the patient as here has exactly the mean population parameter values Figure 2 shows the results of an infusion regimen of lidocaine based on the mean population parameter values for that drug which was designed to achieve and maintain a target serum concentration of 3 ug ml As shown this regimen based on the single mean population parameter values hits the target exactly but only when the patient has parameter values which are exactly the population mean values However as shown in Figure 3 when the regimen used in Figure 2 was given to the combination of the actual 81 diverse nonparametric population support points from which the mean values were obtained an extremely wide distribution of predicted serum concentrations was seen due to the diversity in the nonparametric population support points from which the mean parameter values were obtained The predicted serum concentrations actua
60. etric method such as IT2B the parametric EM or NONMEM is used to study the population shown in Figure 8 The second order density in the figure 1s the one obtained by a parametric method Note that the mean 1s actually where there are no subjects at all Parametric methods cannot discover subpopulations without additional aid They give an entirely different impression of the population behavior of the drug Figure 10 also gives an impression of much greater variability within the population than actually existed among the two fairly tightly grouped subpopulations as shown in Figures 8 and 9 Figure 11 describes an NPEM population model of Vancomycin made by Hurst et al 25 It shows the relationship between the volume of distribution VS in L kg and the slope K7 of the elimination rate constant hr per unit of creatinine clearance The many discrete spikes are seen in this now unsmoothed plot of this pair of parameters The multiple spikes and their various probabilities provide a much more optimal Bayesian prior permitting multiple model design of a dosage regimen to achieve a selected target goal with optimal precision 26 31 Some representative results from the NPEM program are shown below from the same data set as in the IT2B analysis of the 10 patients receiving intramuscular Amikacin 1000 mg every 24 hours for 5 or 6 days 17 It obtains somewhat similar but more likely results than IT2B A total of 10 007 possible p
61. f the central serum compartment in L kg K7 elimination constant per unit of creatinine clearance increment of APPROAIMATE MARGINAL DENSITY AL ou aar Ghd gal died ede lceh ee ee ots mm sco SHAH Ro D M a A oo ta T oo r re KA Figure 12 NPEM marginal distribution for the rate constant Ka Note that there are 10 major points here each with its own estimated probability Another quite minor point is also shown In this plot there are 100 divisions in which such points can exist APPROAIMATE MARGINAL DENSITY 0 P 20 E i 15 3 10 AS AB HAA AAI HA2 HA3 B84 8851 bel A71 002l HHI KS Figure 13 NPEM marginal distribution for the rate constant Ks1 the increment of elimination rate constant per unit of creatinine clearance Note that there are 9 major points here each with its own estimated probability One point corresponds to approximately two subjects Two points correspond to approximately two subjects each In this plot there are 100 divisions in which points can exist APPROAIMATE MARGINAL DENSITY 4 wee a 18 16 14 cae 18 AB AB a4 We AL 8 12 1 24 1 36 98 61 f3 1 85 aa 61 89 aS SHAH Reo D M a A T Jsi Figure 14 NPEM marginal distribution for the apparent volume of distribution per unit of body weight Vs1 Note that there are 10 major points here each with its own estimated probability In this plot there are 100 divisions in which points can ex
62. for a particular support point set of parameter values such as the means will inevitably be incorrect for all other parameter values in the population and develops the regimen which minimizes the overall error in the failure to achieve the desired target goal It thus does a simulated clinical trial in which the most precise dosage regimen is found If the regimen based on the mean parameter values is given to each of the 28 support points or multiple models of the patient each model will have its own predicted trajectory of serum levels over time and each of these will contribute its increment of weighted squared error in the overall failure of the regimen to achieve the target goal Figure 2 shows the multiple predicted serum concentration trajectories when the regimen based on the population mean parameter values was given to all the individual 28 support points or models of the patient that generated those mean values Many predicted serum concentrations were very high as the distribution of the Vd was not at all Gaussian but was skewed to the right As shown in Table 1 the mean Vd was actually close to the 75th percentile Due to all the variability in the various combinations of population parameter values the variability in the serum level response was great In contrast the MM regimen was specifically designed to minimize the expected value of the total weighted squared error in achievement of the goal taking into account all t
63. ght to bear to describe pharmacokinetic models parametrically in this way Much of this is described in an excellent review 1 On the other hand if each individual subject s pharmacokinetic parameter values in a given population could somehow be truly and exactly known and if we were examining two typical parameters such as volume of distribution V in L or Vslope in L kg and elimination rate constant K in hr l or Kslope in hr I unit of its descriptor such as creatinine clearance then the truly optimal joint population distribution of these parameter values would actually be the entire collection of each patient s individual parameter values All subpopulations and those in between would be truly known as well not merely classified but truly quantified However these values can never be known exactly but must be estimated from data of doses given and serum concentrations measured and in a setting of environmental uncertainty with errors in preparation and administration of the doses and errors in recording the times when doses are given and serum samples obtained In the nonparametric approach one obtains discrete spikes approximately one per subject The location of each spike reflects its set of estimated values usually for a given subject data set The height represents the estimated probability of that individual parameter set No other summary parameters such as mean or SD will be any more likely given t
64. he data of dosage and serum concentrations than the actual estimated collection of all the individual discrete points each one having certain parameter values such as Vd and Kel for example and the estimated probability associated with each combined point of Vd and Kel This is what is meant by the word nonparametric in this sense No specific parameters such as means and SD s are used or needed to describe the distribution of parameter values within a population The shape of the discrete distribution is totally determined only by the raw data of the individual subjects studied in the population Many patient populations actually are made up of clusters of unsuspected subpopulations For example there may be fast and slow metabolizers of a drug and those in between The relative proportions of fast in between and slow subjects may vary from one population Caucasian people for example to another Asian people for example 22 Describing such a distribution of clusters optimally is not possible with any parametric method Since one obviously cannot know each patient s values exactly in real life we must study a sample of patients requiring therapy with a drug by giving it to them and measuring the serum levels and or other responses Lindsay 23 and Mallet 19 were the first to show that the optimal solution to the population modeling problem 1s actually a discrete not continuous spiky not smooth probability distribution in which n
65. he individual predicted 28 MM trajectories each of which was weighted by its probability Figure 3 shows the results achieved using the MM regimen The trajectories are much less variable and are much better centered about the chosen goal of 15 ug ml INCORPORATION OF CLINICAL ENVIRONMENTAL NOISE TERMS AND MM SERUM LEVEL FEEDBACK The MM therapeutic scenario has now been carried further incorporating serum level feedback with Bayesian posterior updating of the probabilities but not the parameter values of the 28 population model support points The capabilities of this control strategy were evaluated by a Monte Carlo simulation of a realistic clinical scenario which also contained stated sources of simulated clinical environmental errors in the preparation of the doses and the timing of their administration as well as in the laboratory assay error Each ideal computed dose was assumed to be prepared with a random Gaussian error having a standard deviation SD of 10 of the dose That erroneous dose was then what was given Further the times of switching from one IV infusion rate to another were assumed to have a random Gaussian error having a SD of 6 min for the start of the first 2 hr infusion step and of 12 min for the switch to each of the other infusion steps Three days of such simulated therapy were analyzed Serum levels were assumed to be drawn exactly at 2 4 and 8 hours into the regimen for each day Their assay error was intro
66. he parameters that best fit the patient s data are assumed to be fixed and unchanging throughout the period of data analysis This is a very conventional assumption It underlies all our conventional practices of fitting data to find the best fit to it In this case the probabilities of the population parameter support points in the nonparametric joint density are recomputed using Bayes theorem Those support points that predict the patient s measured serum concentrations well become more probable and those that do not become less probable In this way the patient s individual Bayesian posterior joint parameter density is found Past fits NolMM Alpha parameter IMM Future regimens weight factor 2 Absolute error Percent error eaten ey ear fo Minimize variance Minimize bias For all computations OK Plot points O00 Integer 50 300 Cancel Note in the present version it is the numbers given that are used The radio buttons have no effect Select OK to continue using the selected settings These settings will be valid until they are changed or until RightDose is restarted Start the fitting process by selecting Fit model from the Task menu bar After a few seconds the new Posterior plot will be displayed as shown below USCPACK for Windows Beta 1 0 alan forrests Gentamicin File Edit view Window Patient Popmodel Task Plot Advanced Help
67. heir population correlation coefficient of 0 671 The entropy a measure of randomness was 3 57 This value is 81 6 of the distance from the high initial entropy associated with the uninformed initial grid in which all possible parameter values had equal probability to the theoretical least possible entropy which would result if each subject s parameter values could be known exactly The value of the scaled information of 81 6 indicates that a good deal of information was obtained from this analysis Figures 5 and 6 are scattergrams of predicted versus measured serum concentrations Figure 5 shows the predictions based on the population parameter medians and the doses each subject received In contrast Figure 6 shows the predictions made using each subject s individual MAP Bayesian posterior parameter values to predict only his her own measured serum concentrations The improved predictions in Figure 6 are due to the removal of the population interindividual variability as perceived by the IT2B program The remaining smaller scatter is due to the intraindividual variability resulting not only from the assay error but also to the other sources of noise in the system such as the errors in preparation and administration of the various doses errors in recording the times the doses were given and the serum samples drawn and the mis specification of the pharmacokinetic model used The results shown in Figure 6 show that the study was done with reas
68. igure 1 3D plot of a Vancomycin population marginal joint density Vs slope of volume with respect to body weight K7 Slope of Kel with respect to creatinine clearance The other parameters Kcp and Kpc which describe exchange out to and back from the peripheral nonserum compartment are not shown here but can be similarly displayed as can any selected pair of parameters Hodel Responses Unreer Palk koriz 84 19 Io nae Time houri Figure 2 Serum concentration trajectories predicted when the regimen to control the mean value of each parameter in the Vancomycin nonparametric population model is given to all many support points which constitute the model The horizontal dashed line is the 15 ug ml therapeutic goal Great diversity in predicted serum concentrations 1s seen due to the diversity of patients in the population model Model Responses Mrider MPa Horie 34 Time hours Figure 3 Serum level trajectories predicted when the MM regimen is given to all support points in the nonparametric population model The horizontal dashed line is the 15 ug ml therapeutic goal Much less diversity in predicted serum concentrations 1s seen due to the fact that the MM regimen is specifically designed to achieve the desired goal with the least possible weighted squared error over the course of that day vanco Came MML carneol 99 prob Horie 1 Time hours i Figure 4 Trajectories of the 99 most probable
69. ill show the dates as day month year Note that the Ethnicity field is not used at the moment This field will be used when our model will take into account the ethnic group of the patient The data grid is filled with data if and only if the patient has a past history of drug doses and measured serum concentrations The grid will be empty if the patient file contains no information The patient we have loaded SANCH MB has a past history Dose Route Date Time Time Weight Descriptor IV inf Time Dose Interv IVRate Amount _ cr cl _ Hours Hours mg Hour mg Ge n E a 08 01 85 00 00 00 0 500 19 33 200 00 100 0 z X 0801 85 19 20 00 0100 3 00 ooo 0 00 3 Iv 08 01 85 22 20 00 0 100 1 00 0 00 000 4 Iv 08 01 85 23 20 00 0 500 72 00 100 00 50 00 5 Iv 08 04 85 23 20 00 0 500 14 77 220 00 110 0 6 Iv 08 05 85 14 06 00 110 10 7030 53 00 0 100 3 00 0 00 0 00 7 Iv 08 05 85 17 06 00 11310 70 30 3 00 0 100 550 0 00 0 00 8 Iv 08 05 85 22 36 00 118 60 7030 3 00 0 500 35 50 160 oo 80 00 g Iv 08 07 85 10 06 00 15410 7030 53 00 0 100 3 00 0 00 0 00 10 Iv 08 07 85 13 06 00 15710 70 30 3 00 0100 500 000 000 11 v 08 07 85 18 06 00 162 10 70 30 3 00 0 500 38 00 200 00 100 0 12 Iv 08 09 85 08 06 00 200 10 7030 3 00 0 500 52 90 200 00 100 0 13 Iv 08 11 85 13 00 00 253 00 70 30 53
70. imen in unstable and critically ill patients A number of years ago several methods were developed to estimate CCr without a urine specimen 1 4 However those approaches only considered the situation where serum creatinine was stable To overcome this problem a dynamic approach to the problem was developed A Model of Creatinine Kinetics The dynamic model 5 first used the relationship that the daily change in the total amount of creatinine in a patient s body is the difference between creatinine production P and excretion E during that day This was described by V C2 C1 P E 1 where V is the apparent volume of distribution of serum creatinine in hundreds of ml C1 and C are the first and second serum creatinine values taken typically one day apart in mg dL and P and E are production and excretion in mg Since V 1s somewhat less than total body water it was empirically approximated as 40 of the patient s total body weight in hundreds of grams Calculation of Daily Creatinine Production The Effect of Age The data of Siersbaek Nielsen et al 2 of the effect of age upon the carefully measured 24 hour urinary creatinine excretion in hospitalized patients who were clini cally free of any renal disease was shown to be described by E 29 305 0 203A 2 where E is the measured urinary creatinine excretion in mg kg day and A is the age in years Since the patients were all quite stable and in a steady st
71. ing to collect a traditional timed urine specimen Method The daily change in the total amount of creatinine is the difference between its production and excretion Production is estimated based on studies by others employing many carefully timed urine specimens It is related both to age and to the degree of chronic uremia Urinary excretion of creatinine is equal to creatinine clearance times the average of a pair of timed serum creatinine concentrations times the duration of the collection usually 24 hours Results Good correlation was found between measured creatinine clearance and the estimated values with precision essentially equal to that of the traditional method Conclusions In this way one can estimate the creatinine clearance which makes serum creatinine change from an initial concentration at one stated time to another one at another stated time for a patient of a stated age gender height and weight This method has been incorporated into software to perform the calculations easily and rapidly and has been integrated into the USC PACK PC programs for planning monitoring and adjusting individualized dosage regimens of drugs Introduction Especially for purposes of providing guidance for dosage with renally excreted drugs that are potentially toxic estimation of creatinine clearance CCr has long been a problem in sick and unstable patients largely because of difficulty in collecting a carefully timed urine spec
72. ion USCPACK for Windows Beta 1 0 Hai en vanco 80Kpts File Edit View Window Patient Pop moe Task Plot Advanced Help Usual ranges Peak Central 20 00 100 00 Trough Centra 7 00 20 00 Peak Peripheral 5 00 50 00 Trough Peripheral 200 15 00 Medion Apdo So mn ma OE raeo 69e 001 4 41e 001 re 001 2 86e 001 0 00e 000 1 40e 000 4 38e 003 3 71e 003 1 42e 003 3 03e 003 0 00e 000 1 50e 002 2 66e 001 2 17e 001 1 35e 001 1 92e 001 0 00e 000 1 00e 000 K 204e 003 204e 003 __2 04e 003 O4e 003 2 04e 003 aT 2 04e 003 2 04e 003 aes Propet 93e 002 Ae 30e 001 4 ee By 10e 003 1 ae As 04e 003 3 61e 002 1 69e 001 2 19e 001 6 02e 004 7 87e 001 204e 003 04e 003 3 40e 002 2 92e 001 1 10e 001 1 36e 003 3 27e 001 ee 04e 003 2 63e 001 9 99e 4 56e 001 2 04e 003 eae 3 35e 002 5 13e 001 2 72e 001 3 34e 002 1 65e 001 2 7 4 93e 001 2 04e 003 3 33e 002 335e 000 8 92e 002 2 04e 003 Sneon ameo zaseo 2an zeen amena 3 33e 002 5 63e 001 2 31 e 001 L 4 2 45e 001 2 04e 003 3 33e 002 1 45e 000 6 01e 001 1 35e 001 Lee 04e 003 bi Full matrix As mentioned the data grid for the Pop model data can be separated into two parts one for the Statistical information and one for the Full matrix The Pop model plots view This view is used to examine th
73. ion models coupled with multiple model dosage design 9 11 niregun o Tiras Ailes Figure 4 Predicted response of the 81 support points models when the regimen obtained by multiple model dosage design is given The target is achieved with visibly greater and optimal precision As shown in Figure 4 the multiple model MM dosage regimen based on the same nonparametric population model with its 81 support points obtained a much more precise achievement of the target goal because it was specially designed to do so The error in the achievement of the therapeutic target goal is much less and the dispersion of predicted serum concentrations about the target goal is much less Other cost functions can also be used 13 14 OBTAINING MULTIPLE MODEL BAYESIAN POSTERIOR JOINT DENSITIES With the MAP Bayesian approach to posterior parameter values the single most likely value for each parameter is obtained when they altogether minimize the objective function shown in equation 1 In contrast the MM Bayesian approach using the nonparametric joint densities preserves the multiple sets of population parameter values but specifically recomputes their Bayesian posterior probability based upon the serum concentrations obtained Those combinations of parameter values that predicted the measured concentrations well become more probable Those that predicted them less well become less so In this way the probabilities of all the nonparamet
74. ions of subjects such as fast intermediate and slow metabolizers without recourse to other descriptors or covariates and without recourse to individual Bayesian posterior parameter estimates 19 That cannot be dons with parametric methods A nonparametric EM NPEM method has been developed by Schumitzky 20 24 Like the NPML method it also can work with only one sample per patient and does not have to make any approximating parametric assumptions about the shape of the joint probability distribution It also obtains the entire discrete joint density or distribution of points In contrast to the NPML method though the NPEM method obtains a continuous although very spiky distribution which then becomes discrete in the limit after an infinite number of iterations With each iteration the NPEM method examines the patient data and develops a more and more spiky joint distribution The spikes eventually become the approximately N discrete support points for the population distribution of parameter values just as with the NPML method Both the NPML and the NPEM methods converge to essentially the same results 11 Both the NPML and the NPEM methods are proven under suitable hypotheses to have the desirable property of mathematical consistency 7 9 Figures 7 through 9 illustrate the ability of the nonparametric approach as shown by the NPEM algorithm to discover unsuspected subpopulations 20 The NPML method of Mallet has similar capa
75. ist WS 1 REAA EARE R RR REARRIR EEAO o RRR C EERIE LETTE SOME EEEE EEEIEE EEEIEE EEE P ECCOCI CME MOM M ME M M M aE M a ME ME M E E aE M M a ME M CC e E aE M E E M M EEEE A A a A A A a A A REAR ERRER HR ALU batt By iy A A A A E A A A EA A RARER HHR AAR RR EKK KEAK KKHH KKK KAKAK K KAKEL RRR RRR R JOINT DENSITY ine CERRY ronan RERE RAK RR HCH OK KURRA ie oe eit ELEC ET RETEE EEEE het tit A AA NRI N AIORA IANO KANAAN AIONE f pee niit j EAKR AKAK KEE AKEKE FAA AAI amen OSI gO OGG EKRAR RRR E ae H PRERESI ref te ome Ta iit amb eetey RAR REEERE ERE RIA ELERTE RETTES VRRRRR KY S KS ED OLE a E E WOLDS Op ee t of incremen bution for the parameters Ks1 the istri t marginal d t per unit of creat join e NPEM Figure 15 learance and Vs1 the apparent volume inine c of distribution per unit of body weight There are actually 10 major points here each with imination rate constan el d probability but some are difficult to see One can check this by looking at Figures 13 and 14 which show each single marginal density in better detail In this frequency plot there are 50 x 50 divisions in which points can exist its own estimate POINTS L S LINE AND Y LINE ENTIRE POPULATION omz amama NZzFoHADAAZMOFZoON Figure 16 38 45 44 ad 38 fie H i f t H4 t t t t 4 tt t t wo oy t to f
76. ith an estimate of the probability for that parameter set The collection of all such points 28 in the present case constitutes the nonparametric estimate of the discrete joint probability density for the population It is made without using any parametric assumptions normal lognormal etc about the overall shape of that distribution The nonparametric population model 1s thus represented not simply by a single best parameter estimate such as mean or standard deviation SD but rather by a matrix of rows and columns The 5 columns here represent the discrete values of the 4 parameters Vd Kslope Kcp and Kpc and of the probability associated with that set of parameter values which constitute each support point In the present model there were 28 rows of 5 columns each The 28 rows provided 28 possible versions of the next patient for whom the population model might serve as the Bayesian prior for the optimal design of the initial dosage regimen to achieve a clinically selected individualized target goal The selection of such individualized target goals has been discussed in another paper in this collection These multiple discrete support points are shown graphically in Figure 1 for the parameters of Vd and Kslope A similar 3D plot can be made for Kcp and Kpc and for any desired pair of parameters This report further describes a comparison of the results achieved using the nonparametric population model versus results obtained using the t
77. lly covered much more than the usual therapeutic range of 2 to 6 ug ml In contrast if one has a nonparametric population model 5 8 with its multiple sets of model parameter values 81 in this case one can make multiple predictions instead of only one forward into the future from any candidate dosage regimen which is given to all the models in the population discrete joint density The richer and more likely population parameter joint density reflects better the actual diversity among the subjects studied in the past population Based on these multiple models in the population the discrete joint density one can compute microgram mi Time Mins Figure 3 Result when the above lidocaine infusion based on population mean parameter values is given to the 81 diverse support points from which the population mean values were obtained Great diversity in the predicted responses is seen the weighted squared error with which any candidate regimen 1s predicted to fail to achieve the desired target goal at a target time Other regimens can then be considered and the optimal regimen can be found which is specifically designed to achieve the desired target goal with the least weighted squared error 9 11 This approach using the multiple models of the patient provided by the nonparametric population model avoids much of the limitations of the separation principle This is the real strength of the combination of nonparametric populat
78. m However the entropy was less 2 2998 versus 3 57 and the scaled information was 100 04 versus 81 6 The fact that this information value was greater than 100 suggests that more grid points than the 10 007 used might be considered if the run was to be repeated Usually the more grid points the better up to the current maximum of 80 000 on the PC Larger and Nonlinear Nonparametric Population Models Large and nonlinear nonparametric population modeling software has now been implemented on the Cray T3E parallel machine at the San Diego Supercomputer Center SDSC as a research resource for such work The user specifies the structural model and pathways using PC software now in the USC PACK collection The model file the patient data files and the instructions are sent to the SDSC machine the analysis is done using the desired number of processors and the results are sent back to the user s PC where they are examined just as with the NPEM program described herein 18 For these larger models up to several million grid points may be used to define the parameter space This resource 1s now available and in use by researchers to make such models Weaknesses and Strengths of Nonparametric Methods The main weakness of the nonparametric population modeling approach 1s that there 1s no feature to separate the various sources of variability into their respective components the interindividual variability due to the diversity among
79. made more precise in the newer version 100 00 Read muscle mass as percent of normal F7 2 0 Read Flag for Dialysis Patient status 1 digit integer if Flag equal to 1 then this is a DIALYSIS PATIENT If Flag equal to 0 then this is NOT A DIALYSIS PATIENT 1 Read MIC Flag 1 digit integer MIC Flag 0 no MIC MIC Flag 1 with MIC Flag is initialized as 0 here it is set to be 1 in the drug initialization routine where it is needed e g Ginit for Gentamicin 1 Read SC CCr Flag SC CCR Flag 1 for SC entries followed by calculation of CCr SC CCR Flag 2 for direct entry of CCr in the PASTRX EXE program 8 00000 if MIC Flag is equal to 1 MIC Flag conc of MIC entered 0 150 Read MIC F10 5 else do not read anything here but simply go directly to the next line 1 Read CCr Flag ikpccr 1 digit integer If ikpccr 0 recompute CCr 1f ikpccr 1 keep current CCr This is used in the edit portion of PASTRX EXE If the second digit of General File Flag see first line is equal to 1 Then read these two age and weight unit flags 2 digit integer 2 spaces 2 digit integer An example of a population model file The file shown below is the patient data file GENT2 MB 1 alan forrests patient 123 ok 650000 00M 70 00 70 001 4 1 80 CCR ML MIN 0 20 0 150 00 HOURS MG MG HR MCG ML KG MG DL 60 00 6 IV 1 480 80 00000000 1 00000000 80 00000000 56 46828000 IV 1 990 80 00000000 1 00000000 80 00000000 41 34090000 IM 2 gt
80. mod is the model estimate of each serum concentration at the time it was obtained Similarly Ppop is the collection of the various population model parameter values Var Ppop is the collection of their respective variances and Pmod is the collection of the Bayesian posterior model parameter values Each data point is given a weight according to its Fisher information the reciprocal of its variance Population models in which there is greater diversity and therefore greater variance contribute less to the individualized model than do more uniform models having smaller variances Similarly a precise assay will draw the fitting procedure more closely to the observed concentrations and a less precise assay will do the opposite The more serum data are obtained the more that information dominates the determination of the MAP Bayesian posterior parameter values Pmod in the patient s individualized pharmacokinetic model Having made the patient s individualized model one then uses it to reconstruct the past behavior of the drug in the patient during his therapy to date One can examine a plot of the behavior of this model over the duration of the past therapy One can thus evaluate the clinical sensitivity of the patient to the drug by looking at the patient clinically and comparing the patient s clinical behavior with that of the patient s individualized pharmacokinetic model In that way one can evaluate whether the initial target goal was well
81. more with respect to developing the next dosage regimen than if all the data in that cluster were fitted simultaneously The procedure is still looking for a hypothetical single model support point set of parameter values which best describes all the data When this fails to be the case combinations of support points are found which fit best Still the procedure 1s looking for a fixed and unchanging single model or combination of models which best fit the data even though the posteriors are fitted sequentially A third approach is the interacting multiple model IMM approach 12 This method permits the true patient being sought for actually to jump from one model or support point to another during the sequential Bayesian analysis Because of this the IMM method originally designed to track missiles and aircraft taking evasive action permits detection of changing pharmacokinetic parameter densities during the sequential analysis procedure It thus provides an improved method to track the changing parameter densities and behavior of a patient during the evolution of his clinical therapy For example it permits an improved ability to detect and to quantify changes in the volume of distribution of aminoglycoside drugs during changes in a patient s clinical status which are not captured by the use of conventional clinical descriptors Using carefully simulated models in which the true parameter values changed during the data collection the integ
82. most recent probabilities The controls There are no menu options associated with this view The Report view Moving from left to right the next option should be the future plot but we will do the Report view first The reason for this will become apparent in a few lines If you have followed this from top to bottom you will now have a patient that has been fitted in your program If not please perform the steps lined out at the start of the Posterior plot section You will now compute a future regimen for your patient Start off by selecting Future regimen via the Task menu option A dialog box will pop up asking you to select the route and sub option The process of computing a new or future regimen will be explained in detail later Accept the default route IV option 1 Control peak and trough by clicking on the OK button Select Continue when asked to use your fitted data with this regimen and select OK to accept the body weight and creatinine clearance The values suggested for body weight and creatinine clearance are the last known values recorded for your patient You must now select the target level goals for your patient Enter values so that your dialog box looks like the one below a fom z 2 am z i fo a fixe November 21 2001 09 ae iad Select OK The program now starts to compute this dosage regimen for several dose intervals When it completed you will see a dialog box with a plot Accep
83. mulated true patient here represented by support point 15 chosen randomly is shown in Figure 5 Clearly there was visible error in the initial achievement of the therapeutic goals as the true patient had parameter values different from those of the population means The true patient s serum level results at 2 4 and 8 hrs into the regimen corrupted by their assay errors were made available at the end of Day 1 Based on these results Bayesian updating of the multiple models was done revising their probabilities given the observed serum concentration data using Bayes theorem Instead of the 28 original support points only four support points now had significant probabilities The rest had negligible ones The simulated events of therapy days 2 and 3 repeated the same format as in Day 1 The goals again were 15 ug ml to be achieved at 2 4 6 12 18 and 24 hrs into each day s regimen The same continuous infusion format of 3 steps of 2 hrs followed by 3 steps of 6 hrs was used Serum levels were again obtained at 2 4 and 8 hrs into each day with results available at the end of each day for revising the model probabilities and planning the next day s regimen Based on this the regimen for day 2 was then computed and with the corrupting clinical environmental errors was given Figure 6 shows the 99 most probable serum level trajectories predicted for day 2 horizon 2 As shown by the much narrower bandwidth of predicted ser
84. n weighted squared error for example with which a candidate dosage regimen will hit a desired target serum concentration or other response at a desired time The nonparametric population models thus permit multiple model design of dosage regimens to optimize a specific performance criterion 26 31 The development of such optimally precise dosage regimens using such nonparametric population models will be discussed in a separate paper Other Methods of Population Modeling Besides the nonparametric approaches there are the hierarchical Bayesian or Gibbs sampling approaches of Wakefield et al 32 and the Semi Nonparametric approach of Davidian and Gallant 33 The first method describes another Bayesian strategy of sampling and Bayesian inference The second method is nonparametric but with certain restraints to smooth the distributions These approaches are active and interesting areas of further investigation at the present time Optimal Strategies in Population Modeling The optimal strategy for making clinically useful population PK PD models currently appears to be Determine the assay error pattern explicitly and obtain the assay error polynomial Use a parametric population modeling program such as IT2B Obtain gamma Having both of the above then use a nonparametric population modeling program to obtain the entire discrete joint parameter distribution This sequence of steps currently appears to make optimal use of
85. ncorporating realistic simulated uncertainties in the clinical environment such as those in the preparation and administration of doses INTRODUCTION Previous work from this laboratory has shown the utility of nonparametric population pharmacokinetic modeling resulting in a discrete number of support points for the entire population joint probability density function compared to that using conventional single point parameter estimates such as means and variances as are obtained from parametric population models 1 These multiple discrete support points become multiple contending population parameter estimates instead of the conventional single point summary parameter estimates to use in planing the initial dosage regimen for a new patient who appears to belong to that population Figure 1 shows an example of the multiple support points for the joint probability density for a population pharmacokinetic model of Vancomycin There are a total of 28 such support points derived from the population of 30 patients studied Each support point has a discrete value for each of the 4 pharmacokinetic parameter values the central compartment apparent volume of distribution Vd the increment of elimination rate constant per unit of creatinine clearance Kslope and the rate constants from the central to the peripheral compartment Kcp and back from it Kpc Each discrete support point is a collection of the estimated values for each parameter along w
86. ni G Foo K Jelliffe R and Harrison E Application ofa Bayesian Method to Monitor and Adjust Vancomycin Dosage Regimens Antimicrob Agents and Chemotherap 34 1165 1171 1990 26 Bayard D Milman M and Schumitzky A Design of Dosage Regimens A Multiple Model Stochastic Approach Int J Biomed Comput 36 103 115 1994 2T Bayard D Jelliffe R Schumitzky A Milman M and Van Guilder M Precision Drug Dosage Regimens using Multiple Model Adaptive Control Theory and Application to Simulated Vancomycin Therapy in Selected Topics in Mathematical Physics Professor R Vasudevan Memorial Volume ed by Sridhar R Srinavasa Rao K and Vasudevan Lakshminarayanan Allied Publishers Inc Madras 1995 pp 407 426 28 Mallet A Mentre F Giles J Kelman A Thompson A Bryson S and Whiting B Handling Covariates in Population Pharmacokinetics with an Application to Gentamicin Biomed Meas Infor Contr 2 138 146 1988 29 Taright N Mentre F Mallet A and Jouvent R Nonparametric Estimation of Population Characteristics of the Kinetics of Lithium from Observational and Experimental Data Individualization of Chronic Dosing Regimen Using a New Bayesian Approach Therap Drug Monit 16 258 269 1994 30 Jerling M Population Kinetics of Antidepressant and Neuroleptic Drugs Studies of Therapeutic Drug Monitoring data to Evaluate Kinetic Variability Drug Interactions Nonlinear Kinetics and the Influence of Genetic Factors Ph D Thesis
87. nt using the NPEM population model and the many different predicted serum concentrations one from each support point as shown below in Figures 2 and 3 instead of making only one prediction using a population model having only the single most likely value for each parameter 2 Later on as data of serum concentrations become available for feedback Bayes theorem is used to appropriately increase the probability of those support points or models that predicted the patient s measured levels well and to decrease the probability of those that did not The revised Bayesian posterior joint distribution usually consisting of fewer significant support points is then used to reconstruct the family of serum level trajectories taking place during the past 3 4 The bandwidth or diversity of these predicted trajectories reflects the confidence with which the joint distribution 1s known and the degree of learning about the patient provided by feedback from any serum levels obtained As always the plot based on the past trajectories of serum levels 1s compared with the clinical behavior of the patient the patient s sensitivity to the serum drug concentrations is reassessed the target goal is re evaluated and a new regimen is again computed to achieve the goal always with the greatest possible precision for all the information in the population model and the individual patient data which is available up to that time THE POPULATION PHARMACOKINETI
88. nt 12 63 percent 9 62 percent 8 12 percent VWoatAva _ on i N Lea _ ie E D pm a Q i par Z v Q ho 4v D O O 25 30 35 Time hours Serum level measurement Dose tick This plot shows all the trajectories produced by the fitting process There will be one trajectory for each of the parameter probabilities sets The Top 4 probability trajectories will be shown in color All others will be shown by dotted black lines The probabilities of the 4 most probable trajectories and their corresponding color are shown at the top of the plot The Weighted average computed by adding up all trajectories and multiplying them by their corresponding probability is shown in solid black The red diamonds show the measured Serum concentrations In this case the trajectories are close to the measured values a good thing There are also some short blue bars just above the time axis These Dose tick lines show when a dose was given by any route The controls This view can be altered using the Plot menu Peripheral compartment Central compartment Absorptive compartment Extractions gt Overlays b If you selected the amikacin population model your Plot menu will look like this The Peripheral compartment will be dimmed because there is no peripheral compartment for this particular population model The default plot for posterior fits is th
89. o preconceived parametric assumptions such as Gaussian lognormal multimodal or other are made about its shape 19 20 24 The nonparametric maximum likelihood NPML estimate of the population joint density or distribution is analogous to the entire collection of each patient s exactly known parameter values described above Whatever its shape or distribution turns out to be it does not matter The distribution is determined and supported by up to N discrete points for the N patients in the population studied Each point consists of the estimated single numbered parameter values one for each parameter such as Vd Kel etc along with an estimate of the associated probability of each of these discrete points The NPML method of Mallet 19 like the parametric NONMEM method can also function with only one sample per patient In contrast to parametric methods however no parametric assumptions about the shape of the parameter distributions Gaussian etc need to be made The distribution 1s totally flexible and depends only on the actual subject data The mean SD and other common statistical summary parameters can easily be obtained later from the entire discrete distribution 1f desired The only assumption made about the shape of the discrete parameter distribution 1s that the shape whatever it is is the same for all subjects studied in the population The method therefore can discover in the population itself unsuspected subpopulat
90. oals with visibly greater precision than did the regimen based on traditional single point mean population pharmacokinetic parameter values Further the MM controller appeared to learn well from the feedback provided by the serum levels and to achieve the target goals for the simulated patient with increasing precision as therapy progressed from one feedback cycle therapy day or event horizon to another The MM regimen thus permits visibly greater precision in achievement of desired therapeutic target goals compared to conventional control based on single mean pharmacokinetic parameter values which is employed today by all maximum aposteriori probability MAP Bayesian software in current wide use A user friendly clinical version of the MM program is now in development ACKNOWLEDGMENTS Supported by US Government grants LM 05401 RR 11526 and RR 01629 and by the Stella Slutzky Kunin Research Fund REFERENCES l Schumitzky A Nonparametric EM Algorithms for Estimating Prior Distributions App Math and Computation 45 143 158 1991 2 Bayard D Milman M and Schumitzky A Design of Dosage Regimens A Multiple Model Stochastic Control Approach Int J Bio Med Comput 36 103 115 1994 3 Schumitzky A Bayard D Milman M and Jelliffe R Design of Dosage Regimens a Multiple Model Stochastic Control Approach Clin Pharmacol Therap 53 170 1993 4 Bayard D Jelliffe R Schumitzky A Milman M and Van Guilder M Precisi
91. oints for the overall parameter space constituted the grid of available discrete points There are two methods by which the NPEM iterative analysis is accelerated One is that whenever the estimated probability of a grid point in the parameter space is less than 10 10 it never returns as an active or significant point again For this reason such points can be omitted from further analysis This is why the number of active grid points gets less with almost every cycle Another acceleration technique consists of jumping forward 10 50 or 70 cycles into the future based on the change in probability for each grid point in the present cycle from the cycle before Based on such a change in probability per cycle the new density 1s found the subject data is then analyzed and the new density and its likelihood is found It is more likely than the one before then further extrapolations are performed to 50 or 70 cycles in the future These two acceleration techniques have increased the speed of NPEM analysis by 30 to 50 times over previous versions of NPEM The results of this analysis which converged on Cycle 39 are shown in Table 1 and in the figures below The population mean parameter values for Ka Ks and Vs were 1 53 hr 1 0 0033 hr 1 and 0 255 L kg respectively very similar to the values obtained by the IT2B program in the previous paper The correlation coefficient between Ks and Vs was 0 513 similar to 0 671 obtained with the IT2B progra
92. ol for evaluation of a patient s renal function in a practical manner when serum creatinine concentrations are unstable changing from day to day It also permits linkage of this information about rapidly changing renal function in patients to track the pharmacokinetic and dynamic behavior of drugs in such patients thus permitting improved understanding of drug behavior and improved individualization of drug dosage regimens in such patients ACKNOWLEDGMENTS Supported by US Government grants LM 05401 and RR 01629 and by the Stella Slutzky Kunin Research Fund References l Jadrny L Odhad Glomerularni Filtrace z Kreatinimie Cas Lek Cesk 1965 104 947 949 2 Siersbaek Nielsen K Moholm Hansen J Kampmann J and Kristensen M Rapid Evaluation of Creatinine Clearance Lancet 1971 1 1133 1136 3 Jelliffe R Creatinine Clearance Bedside Estimate Ann Int Med 1973 79 604 605 4 Cockroft D and Gault H Prediction of Creatinine Clearance from Serum Creatinine Nephron 1976 16 33 41 5 Jelliffe R and Jelliffe S A Computer Program for Estimation of Creatinine Clearance from Unstable Serum Creatinine Levels Age Sex and Weight Math Biosci 1972 14 17 24 6 Goldman R Creatinine Excretion in Renal Failure Proc Soc Exp Biol Med 1954 85 446 448 Figure legend Figure 1 Comparison of Estimated CCr as described herein with measured CCr 116 8 91 8 O O 676 a L or 5 i ax 434 LL gt 19 1
93. on Drug Dosage Regimens using Multiple Model Adaptive Control Theory and Application to Simulated Vancomycin Therapy in Selected Topics in Mathematical Physics Professor R Vasudevan Memorial Volume ed by R Sridhar K Srinavasa Rao and Vasudevan Lakshminarayanan Allied Publishers Ltd Madras pp 407 426 1995 5 Jelliffe R Hurst A and Tahani B A 2 Compartment Population Model of Vancomycin made with the new Multicompartment NPEM2 Computer Program Clin Pharmacol Therap 55 160 1994 6 Jelliffe R and Tahani B Pharmacoinformatics Equations for Serum Drug Assay Error Patterns Implications for Therapeutic Drug Monitoring and Dosage Proceedings of the 17th Annual Symposium on Computer Applications in Medical Care 1994 pp 517 521 TABLE 1 SUMMARY of VANCOMYCIN POPULATION PARAMETER VALUES Attribute Vc L kg Kcp Kpc Kslope MEAN 0 2278 2 2332 0 8147 0 0063 MODE 0 1275 2 425 0 8775 0 0051 25th ile 0 0946 1 0832 0 5487 0 0023 MEDIAN 0 1427 2 1594 0 8743 0 0051 75th ile 0 2348 3 3032 1 0467 0 0105 Kint was held fixed at 0 002043 hr throughout all in units of hr FIGURES AND FIGURE LEGENDS JOINT DENSITY Ao Ke oe m ARAIA ED danane AUXIN RUDI ARAL re Ae AMALIA Ace A NARS at ay WA AAAA ih a A OONTY i Ny I tits i ONY are a TTY AANA B AN o a if i C IE Ot E eE e A a 40 4 4 tt SE E WS F
94. onable precision The IT2B method of population modeling is a useful one and is based on the widely used and robust strategy of MAP Bayesian individualization of pharmacokinetic models Its weaknesses like those of any parametric method are that it only perceives population parameter values in terms of their means medians variances and correlations The actual parameter distributions are usually not of this type Lognormal assumptions have often been made but the actual parameter distributions are frequently not of that form either Larger and Nonlinear IT2B Population Models Similar software for IT2B population modeling of large and nonlinear PK PD models has now been implemented on the Cray T3E parallel computer at the San Diego Supercomputer Center SDSC as a research resource for such work The user uses a PC program in the USC PACK collection to specify the data files to be analyzed and the instructions for the analysis One also either writes the differential equations for the structural PK PD model to be used or employs the BOXES program in the USC PACK collection placing boxes on the screen for the compartments and connecting them with arrows to represent the various types of pathways involved The model equations are then generated automatically and stored in a model file These two files are then sent to the SDSC Cray by a secure protocol The model source code file is compiled and linked The analysis is performed using the
95. or IV int Time Dose Interu IV Rate Amount M iavieo locale hh mm ss Hours kg CCCI Hours Hours mgttiour mg _ a m omeo o oo esoo ses7 1o aso eooo 8000 o wv omea eow eso eeo nas 100 75 eooo 6000 a m omo oso me eeo na ooo so oo 1000 a wv omo oeo as eoo na noo eso 1000 1000 s v cameo teasoo a275 eoo a10 1o 1525 10000 1000 cs omo soo esoo 210 10o aoo eooo 6000 E a Level Dee Time Time AfterDose AfterDose 0 ooo Ium Tlocale h zmm ss Hours Humber Hours Smeg 1 oma 0 aa O ao aas o oo f oo o oma sso re o s o T T G o f omw eo an o a o T T SO a omw eaw aa o s o o y a s omo oro a7e7 S Stet o o y Cpo T S T T e T e T To 4 ld 4 gt Patient data Pop model data A Pop model plots A Posterior Plot A Fitted Probabilities A Future Plot For Help press F1 Note that the frame header displays the name of the patient and the name of the population model The header display will be the same for all tabs making is easy to keep track of the current simulation Fitting without IMM You will now fit the patient data to the population model first without IMM The settings controlling the use of IMM as well as other options can be found in the Advanced gt Compute options menu option Turn IMM off by setting the Alpha parameter to 1 In this mode t
96. ose will consider this population model to be invalid and it will not be used File update list 11 14 2001 Andreas Botnen Manually converted from old file The file update list where updates to the file is entered Note that altering a file with file lock code of 3 or higher without updating the checksums will invalidate the file START DESCRIPTION No description for this population model END DESCRIPTION A general description of the population model can be entered between the lines START DESCRIPTION and END DESCRIPTION The drug used in this analysis was Trimethoprim The drug modeled The units to be used with this drug is mg The most common units for the drug The molecular weight is 1 0 The molecular weight of the drug The active salt fraction is 0 90 The active salt fraction The bioavailability is 1 0 The bioavailability The valid routes are IV PO The routes that can be used with this population model The ranges for the central compartment peak and trough use the value 1 if this selection is not valid for this model Usual ranges peak min peak max trough min trough max 8 0 12 0 4 0 7 0 Not to exceede ranges peak min peak max trough min trough max 4 0 18 0 1 0 9 0 RightDose operates with two sets of ranges When computing future or initial regimens the usual ranges are displayed The users can select to give a dose outside these ranges if th
97. p 334 336 8 Spieler G and Schumitzky A Asymptotic Properties of Extended Least Squares Estimators with Approximate Models Technical Report 92 4 Laboratory of Applied Pharmacokinetics University of Southern California School of Medicine 1992 9 Spieler G and Schumitzky A Asymptotic Properties of Extended Least Squares Estimates with Application to Population Pharmacokinetics Proceedings of the American Statistical Society Biopharmaceutical Section 1993 pp 177 182 10 Rodman J and Silverstein K Comparison of Two Stage TS and First Order FO Methods for Estimation of Population Parameters in an Intensive Pharmacokinetic PK Study Clin Pharmacol Therap 47 151 1990 11 Maire P Barbaut X Girard P Mallet A Jelliffe R and Berod T Preliminary results of three methods for population pharmacokinetic analysis NONMEM NPML NPEM of amikacin in geriatric and general medicine patients Int J Biomed Comput 36 139 141 1994 2 Lindstrom M and Bates D Nonlinear Mixed Effects Models for Repeated Measures Data Biometrics 46 673 687 1990 13 Vonesh E and Carter R Mixed Effects Nonlinear Regressions for Unbalanced Repeated Measures Biometrics 48 1 17 1992 14 Jelliffe R Explicit Determination of laboratory assay error patterns a useful aid in therapeutic drug monitoring No DM 89 4 DM56 Drug Monit Toxicol 10 4 1 6 1989 15 Jelliffe R Schumitzky A Van Guilder M Liu M Hu L Maire P Gomis P
98. predicted serum level responses during Day 1 of therapy before feedback Solid lines the 95 most probable trajectories Dotted lines the next most likely 4 for the total of 99 The horizontal dashed line 1s the 15 ug ml therapeutic goal True Subject Levels koriz 87 a 10 qa ma oa Time houwrs3 Figure 5 Serum level response of the true patient during therapy day horizon 1 Horizontal dashed line the desired goal of 15 ug ml at 2 4 6 12 18 and 24 hrs Solid line true serum concentrations in the simulated true patient vanco Come MMLe Comirak 99 prolio Horie He A 10 15 mae iol Time hours Figure 6 The 99 most probable serum level trajectories predicted for Day 2 of therapy event horizon 2 The horizontal dashed line is the 15 ug ml therapeutic goal True Subject lLeyels Horiz tHe A 10 qn mae iol Time hours Figure 7 Serum level responses of the true patient during therapy day event horizon 2 The horizontal dashed line is the 15 ug ml therapeutic goal Vanco Come MML Comtrak 99 proh Horie 84 qt ool Sie k a 0 ees K k i rae K Pa il Tis l 1 ti 0 i h 1 d5 ae ae Time hours Figure 8 The 99 most probable serum level trajectories predicted for Day 3 of therapy event horizon 3 The horizontal dashed line is the 15 ug ml therapeutic goal True Subject levels Moriz Hi A 10 qn mae iol Time hours Figure 9
99. raditional method based on the mean Vancomycin population parameter values with respect to the ability of each regimen to achieve and maintain the chosen serum level goal s precisely Note that the MM regimen is specifically computed to minimize the expected value of the total weighted squared error in the achievement of the goal s while the traditional regimen using single point parameter estimates cannot do this The MM software has now been extended to incorporate feedback as well This report describes a realistic simulation of vancomycin therapy in which common errors are present in the preparation of the doses and in their timing as well as in the measurement of the serum levels These mean clinical error values are also known to the MM controller for designing the dosage regimen with appropriate skepticism The natural link between nonparametric population modeling and optimal maximally precise drug therapy is MM dosage design In contrast the limiting factor in parametric population modeling is that there is only one single possible value for each parameter Using parametric population models after the therapeutic goal is clinically selected there is only one regimen to compute that which achieves the target goal for the single chosen version or model of the patient using the mean median or modal parameter values exactly There is no opportunity to consider the fact that the patient actually might not have that exact model of the
100. rated total error in tracking a simulated patient was very similar with the sequential MAP and sequential MM Bayesian procedures However the integrated total error of the sequential IMM procedure was only about one half that of the other two 12 CLINICAL APPLICATIONS Nonparametric population parameter joint densities MM dosage design and IMM Bayesian posterior joint densities appear to offer significant improvements 1n the ability to track the behavior of drugs in patients during their care especially when the patients are unstable and have changing parameter values These approaches also develop dosage regimens which are specifically designed to achieve target goals with maximum precision These methods make optimal use of all information contained in the past population data coupled with whatever current data of feedback may be available about a particular patient up to that point to develop that patient s most precise dosage regimen A clinical version of this software which runs on PC s in Windows is now in development Acknowledgements Supported by NIH grants LM 05401 and RR 11526 References l Reuning R Sams R and Notari R Role of Pharmacokinetics in Drug Dosage Adjustment 1 Pharmacologic effects Kinetics and apparent volume of distribution of Digoxin J Clin Pharmacol 13 127 141 1973 2 Jelliffe R Schumitzky A Van Guilder M et al Individualizing Drug Dosage Regimens Roles of Population Pharmacokinetic Model
101. ric population support points become revised using Bayes theorem 10 11 A smaller number of significant points or perhaps even only one 1s usually obtained When the regimen for the next cycle is developed these revised models containing their revised MM Bayesian posterior probabilities are used to develop it The regimen is again specifically designed to achieve the desired target goal with maximum precision minimum weighted squared error OTHER BAYESIAN APPROACHES Three other Bayesian approaches have been used by us to incorporate feedback from measured serum concentration data The first 1s the sequential MAP Bayesian approach in which the MAP posterior parameter values are sequentially updated after each serum concentration data point is obtained This procedure improves the tracking of the behavior of the drug through each data set However at the end of each full feedback cycle after each new full cluster of data points at the time the next regimen is to be developed this method has learned no more with respect to developing the next new dosage regimen than if it had fitted all the data together at once even though it tracks the changing MAP Bayesian parameter values better sequentially The second approach is the sequential MM Bayesian one 9 11 Here the MM Bayesian posterior joint density is also sequentially updated after each data point Still at the end of each feedback cycle this procedure similarly has learned no
102. rmittent IV infusion and to select a trough goal of 10 ug ml with peaks about 35 to 45 ug ml the stable goal of 15 ug ml was selected here as a reasonable alternative goal to be achieved at the end of an initial 2 hr loading infusion again at the end of 2 subsequent 2 hr infusions during the distribution phase of this 2 compartment drug and at the end of 3 further infusions of 6 hrs each to complete Day 1 of therapy Thus the vancomycin was given by continuous IV in 3 infusion steps of 2 hrs each followed by 3 steps of 6 hrs each to achieve the goal of 15 ug ml at the end of each infusion step during Day 1 of therapy THE TWO INITIAL REGIMENS COMPARED Two types of dosage regimen to achieve a target goal of 15 ug ml were developed and compared One the traditional regimen was developed using the single point mean population NPEM parameter values shown in Table 1 It was designed to achieve the goal exactly as there was only one exact value for each parameter to consider No consideration of any therapeutic error is possible with this current widely used method of dosage design The other regimen the MM regimen used all the 28 support points of the NPEM Vancomycin population model in designing the regimen It therefore took into account all these different models of the patient each with its probability of being the new patient to receive the initial regimen The MM dosage designer thus faces the fact that what may be a correct regimen
103. rum compartment or 1n various effect compartments These cannot be seen or inferred at all without such models By comparing the clinical behavior of the patient with the behavior of the patient s model one can evaluate the patient s clinical sensitivity to the drug and can adjust the target goal appropriately For digoxin for example the inotropic effect of the drug correlates best with the behavior of the drug in the peripheral compartment rather than with the serum concentrations The excellent model made by Reuning and colleagues for digoxin 1 has been highly useful clinically 2 CURRENT BAYESIAN INDIVIDUALIZATION OF DRUG DOSAGE REGIMENS The Maximum Aposteriori Probability MAP Bayesian approach to individualization of drug dosage regimens was introduced to the pharmacokinetic community by Sheiner et al 3 In this approach parametric population models are used as the Bayesian priors The credibility of these population models their parameter variances is then evaluated in relationship to those of the measured serum concentrations as they are obtained The contribution of these two types of data and their variances to the MAP Bayesian posterior individualized patient model is shown in the objective function used as shown below 1 Cobs C mod Ppop Pmod 1 Var Cobs Var Ppop where Cobs is the collection of observed serum concentrations Var Cobs is the collection of their respective variances and C
104. s Bayesian Fitting and Adaptive Control Ther Drug Monit 15 380 393 1993 3 Sheiner L Beal S Rosenberg B et al Forecasting Individual Pharmacokinetics Clin Pharmacol Therap 26 294 305 1979 4 Bertsekas D Dynamic Programming Deterministic and Stochastic Models Prentice Hall Englewood NJ 1987 pp 144 146 5 Lindsay B The Geometry of Mixture Likelihoods a General Theory Ann Statist 11 86 94 1983 6 Mallet A A Maximum Likelihood Estimation Method for Random Coefficient Regression Models Biometrika 73 645 656 1986 7 Schumitzky A Nonparametric EM Algorithms for Estimating Prior Distributions App Math Comput 45 143 157 1991 10 11 12 13 14 Schumitzky A The Nonparametric Maximum Likelihood Approach to Pharmacokinetic Population Analysis Proceedings of the 1993 Western Simulation Multiconference Simulation for Health Care San Diego Society for Computer Simulation pp 95 100 1993 Bayard D Milman M and Schumitzky A Design of Dosage Regimens a Multiple Model Stochastic Control Approach Int J Biomed Comput 36 103 115 1994 Bayard D Jelliffe R Schumitzky A Milman M and Van Guilder M Precision Drug Dosage Regimens using Multiple Model Adaptiva Control Theory and Application to Simulated Vancomycin Therapy in Selected Topics in Mathematical Physics Professor R Vasudevan Memorial Issue ed By Sridhar R Srinavasa Rao K and Lakshminarayanan V Allied Publishers Ltd M
105. s Move the mouse pointer into a plot right click and select the Export Dialog You will then see the following dialog box Export mode Export Metafile C BMP C Text Data Only Export lt destination Export Destination ClipBoard C Fie Browse C Printer Object Size Export Cancel No Specific Size Millimeters Inches Points Width 1000 619 Units Help The Export mode section allows you to export the plot image or the data making up the plot Selecting MetaFile or BMP will export the plot Text Data Only will export the plot as floating point data If you export as an image or as data you have several options about where you would like to export the data to BMP cannot be exported to a printer This can be determined using the Export destination section To copy a plot into a Microsoft Word document simply select MetaFile in the Export mode panel ClipBoard as Export destination and press or click Export Go to the location in Word where your would like to have the plot and press Ctrl v Paste Exporting the actual data requires one more step Select Text Data Only in the Export mode ClipBoard in the Export destination and click on Export At this point a new dialog box pops up giving you an option to select which subset to export Select Subsets and Points r Export What AllData C Data Data and Labels Selected Data Data to Export Subsets to Export fe X Avi
106. s Botnen Manually converted from old file it START DESCRIPTION No description for this population model END DESCRIPTION The drug used in this analysis was Amikacin The units to be used with this drug is mg The molecular weight is sikel The active salt fraction is 1 0 The bioavailability is T The valid routes are IV The ranges for the central compartment IM peak and trough use the value 1 if this selection is not valid for this model trough min Usual ranges peak min peak max trough max trough Min trough max peak and trough de4 trough max trough min terr trough max Zoe 8 0 20 Za 10 0 Not to exceede ranges peak min peak max Loe 90 0 Ite 20 0 The ranges for the peripheral compartment use the value 1 if this selection is not valid for this model Usual ranges peak min peak max trough min 4 0 LOD ie S20 Not to exceede ranges peak min peak max ONS 20 0 MERS 12 0 The assay polynomial asl as2 as3 as4 Os 522120 2 OL Co 6a0 Ont OL OSLO 1 020 The process noise wsgrt del de2 de3 OOOO OO WOR OF T0000 0S0 Oe 0 OOOO The number of random parameters 3 The random parameters used was KA KS1 Noel 3 7 16 The number of fixed parameters il The fixed parameters used was KI 6 The values of the fixed parameters Deba T0 E 02 The number of probability points 23 The probabilit
107. s Value Y Avis Value Export Style List C Table Delimited Row vs Column Tab Subsets Paints Paints to Export Comma gt Points Subsets Numeric Precision Current Precision Export Maximum Precision Emot Help You can make multiple selections in the Subsets to Export and Points to Export by the keeping the Ctrl key pressed while selecting subsets or individual points To export the whole dataset into Microsoft Excel select Table in the Export Style frame and press Export Select the cell in Excel where you want the upper left element of the table and press Ctrl v Paste Removing the annotations Annotations are used in three places for the diamonds showing the serum concentration measurements for the blue lines showing when the doses were or will be given and for the red line separating the past and the future You can toggle annotations on and off by selecting and deselecting the Show Annotations option The data points You have two options to get more information about the data points Selecting the Mark Data Points option and the trajectories will have small black dots showing the locations of the actual data computed points To get even more information about these points select the Include Data Labels option The plot will now display the X and Y values of the data plots This option is usually only useful when
108. s of parametric population models that when their single point parameter estimates are used to design dosage regimens that the target goals are inevitably achieved with a precision that 1s not specifically evaluated and which is suboptimal One may ask why we make models to simply report such single point estimates or to take some useful action based on the information obtained from the modeling process That is why it is useful to supplement the knowledge of the assay error empirically determined before starting the modeling with information about the intraindividual variability obtained from a parametric population model Having this information one can then proceed to make a nonparametric population model which can overcome the difficulties presented by the separation principle stated above Nonparametric Methods for Population Modeling Until recently we have become accustomed to obtaining certain types of statistical summaries of past experience We know there is great variability among patients with regard to their pharmacokinetic parameter values Nevertheless we have become accustomed to using selected single numbers to describe such diverse behavior For example we have usually used the population mean or median parameter values as the best single number to describe the central tendencies of their distributions and the standard deviation SD to describe the dispersion of values about such a central tendency It has been customary
109. t of body weight in the population FINAL CYCLE JMINT HISTOGRAM y WS As Hina Ao 4 AN ARA AAN EEEE ES ARAA RRND A ARERR A Oe ies ANA ARIANA ee Haat wo ERRAND ANAM A AAA AR ARAMA AMA AANA RRA o AULA tg Am RANI MAN MANUKA RKKRK RD ARERR ESO EDD DURAN mail GON SANS RURKI oh MAE REECE ARMANI AAR KAS i ARORA AOR T AAA AR ARR AAR ARAN AKA AA RXR ROS RO arn RR ARR AR AAR AR AR AAR UALS aoe ECE CERTER ETE CECELET ERECT CRT RAY AXA Seo GBS esos EEEREN GOR GA HAGA ARAL is KARAN RRR SOOO ROO ROO ON om SO RNA OR ERENER SS Ee NRA KH RD SRR Aa TR LR OS RR A EE ECELEEELTCECLELCECLELEEECCEELELCRELELERELEE EEE PEREAT EEL ERAGE ACER LEE E LEME A LEME URMEHEE AAA AAA AR AR A AAARAAAAAAAAARAARAARARAAAR ARAL LENCEELTREEEESTHSTEENSTESTEETERSTETE TENS CHS AAA AAAAAR AMAR ARARAAAAAAAARARAARARARAR AAS UTEEEECEEESTHSTEEREREREST ETHER TRee tits E RAMANA KY i RERCRT CERT RRLCRTRRTERTRIT AAAA YN K NONN ENK RN ENEE A A AAY BRE a ARAA S n K S a A oman EEEE t AEN AIH aes Henne ttt Meee i ste KRAAN RENREN PEN HUNN OTOI ENTET OAT CARI RAK AKREAN AAAA ANH eet Bae BD RUN AAR BR SY eea AAR ERA MANN MAN A EARRA RRAK RRIRA CD OPO AMAIA RRR RR set OR mo C El El KS WM W st a ea a e a A a E T ce 4 A Showing the joint values of the Ks and Vs in the population Figure 4 POINTS L S LINE AND Y LINE ENTIRE POPULATION m B J4 S t E 43 R t
110. t the selected dose interval of 24 hours by clicking on OK The display Voila the doses for your patient have been computed and the Report view is displayed Patient information Population model information alan rrests AMIKACIN TERZ J een ee er ee USCP K for Windows Beta 1 0 View Window Patient Pop mod Task alan forrests Firstname patie Date of birth 10 29 1936 Gender Male Mean 1 37 e 000 3 27e 003 2 58e 001 6 93e 003 Dose Date 1 04 03 80 2 04 04 80 3 04 05 80 4 04 06 80 Age Median 1 31e 000 3 23e 003 2 49e 001 6 93e 003 16 00 00 16 00 00 16 00 00 16 00 00 3 62e 003 2 40e 001 6 93e 003 Plot Advanced Help Weight 2 48e 001 5 18e 004 4 36e 002 0 00e 000 68 00 kg mq msq 81 01 99 70 99 70 164 79 New regimen Max 1 78e 000 6 64e 003 5 08e 001 6 93e 003 4 laf 4 gt bi Patient data A Pop model data A Pop model plots A Posterior Plot A Fitted Probabilities A Future Plot A Report For Help press F1 This view consists of three sections Patient information at the top then Population model information the route and the goals and the New suggested dosage regimen You may switch to the Report view at any time The information displayed will be based on your selected patient and population model If you have no patient loaded no patient information will be displayed and so on The controls You can print this report by sel
111. tes is from 70 to 130 percent of normal Calculation of Daily Creatinine Excretion In the traditional calculation of creatinine clearance C UVP 9 where U is the urinary creatinine concentration V is the 24 hour urine volume P is the plasma or serum creatinine concentration and C 1s creatinine clearance This can be rearranged to show that what comes out of the body is equal to what was cleared from the body Thus PC UV 10 Because they are numerically equal PC can therefore be substituted for UV the measured 24 hour excretion Thus E UV PC and E PC Cayg x CCr 100 x 1440 11 where E is expressed in mg day Cayg 1s in mg dL CCr is in ml min and 1440 represents the number of minutes in one day The Final Overall Algorithm The final overall algorithm to calculate creatinine clearance from unstable serum creatinine values and without requiring a urine specimen may now be written as 0 4W C2 C1 Padj Cavg x CCr 100 x 1440 12 Where W is body weight in hundreds of grams and C4 and C gt are serum creatinine in grams 100 ml One can simply rearrange the equation and solve it for CCr After this the raw creatinine clearance above can be corrected for body surface area to that of an average patient having a body surface area of 1 73 square meters The above equation thus represents a dynamic model of creatinine kinetics and permits estimation of CCr from routine clinical data of age gender height
112. the corresponding view Some views may also have a Data grid The grid is used to display time dependent data detailed information about the population model and the suggested doses Some data entry forms also use a Data grid The grid can best be thought of as a spreadsheet The fields in the Data grid can also easily be copied to the clipboard and into programs like Microsoft Excel Simply select the desired fields and use Copy in the Edit menu The Patient data view The display This view has two distinct parts the fixed fields and a data grid Go ahead and load a patient by selecting Patient and Load patient from the menu The information displayed is either read directly from the file or it is computed based on data read from the file If you load the patient SANCH MB for example the fixed fields of your patient view will look like this Filename C winUSCPACK Patients SANCHMB 00 Time of first dose 08 01 85 00 00 00 Chart Number 123 Height 69 00in Gender Male Ethnicity Notin use First Name ed Last Name sanch Weight 70 30 kg Dialysis patient NO Birth Date 10 29 28 57 years MostrecentCCr 4 00 Time of next dose 08 23 85 10 00 00 The field label to the left of each field tells you what information is shown in each field All dates will be shown in the format you have selected when installing your operating system This means that if you selected the US locale dates will be given month day year a European locale w
113. the information about the assay error often 1 3 to 1 2 of the overall intraindividual variability and the raw data present in the population studied to obtain the most probable parameter distribution It appears to provide optimal tools to develop dosage regimens which achieve desired target goals with maximum precision ACKNOWLEDGMENTS Supported by US Government grants LM 05401 RR11526 and RR 01629 and by the Stella Slutsky Kunin Research Fund References I Variability in Drug Therapy Description Estimation and Control Ed by Rowland M Sheiner L and Steimer JL Raven Press New York 1985 Di Sheiner L Beal S Rosenberg B and Marathe V Forecasting Individual Pharmacokinetics Clin Pharmacol Therap 26 294 305 1979 3 Aarons L The Estimation of Population Pharmacokinetic Parameters using an EM Algorithm Comput Methods and Programs in Biomed 41 9 16 1993 4 Beal S and Sheiner L NONMEM User s Guide I Users Basic Guide Division of Clinical Pharmacology University of California San Francisco 1979 5 Sheiner L The population Approach to Pharmacokinetic Data Analysis Rationale and Standard Data Analysis Methods Drug Metab Rev 15 153 171 1984 6 Beal S Population Pharmacokinetic Data and Parameter Estimation Based on their First Two Statistical Moments Drug Metab Rev 15 173 193 1984 J De Groot M Probability and Statistics 2nd edition 1986 reprinted 1989 Addison Wesley Reading MA p
114. the subjects in the ways they handle the drug and the intraindividual variability due to the errors in preparing and giving the doses recording the times at which responses such as serum concentrations were obtained structural model misspecification changing parameter values during the study period and the assay error itself Nonparametric methods do not resolve these things That however is what the parametric methods do very well as described earlier The strengths of nonparametric approaches are many First they have the desirable property of mathematical consistency as described 7 9 Second no assumptions about the shape of the parameter distributions need to be made Because of this nonparametric methods can detect without additional aid from covariates or descriptors previously unsuspected subpopulations of patients as shown in Figures 7 through 9 Third instead of obtaining only single point parameter estimates one gets multiple estimates basically one for each subject studied This is why the nonparametric approach is mathematically optimal as 1t comes the closest to the ideal of the best that can ever be done namely to obtain the collection of each subject s exactly known parameter values without bothering with other parametric statistical summaries though these are easily obtained as well Fourth the multiple sets of parameter values provide a tool to circumvent the separation principle 21 and to predict the precisio
115. tional likelihood to obtain a set of parameter values which are more likely than in the previous iteration The process continues until a convergence criterion is met The results are given in terms of the parameter means SD s and correlations or means variances and covariances 3 4 The nonlinear mixed effect modeling NONMEM method developed by Beal and Sheiner 4 6 was the first true population modeling program The method can function with as few samples as one per patient However this very popular algorithm lacks the desirable property of mathematical consistency 7 9 Early versions of it have at times given results which differed considerably from other approaches 10 11 Later improvements have shown more consistent behavior Other variations on this approach are those of Lindsdtrom and Bates 12 and Vonesh and Carter 13 In analyzing any data set it is usually optimal to assign a measure of credibility to each data point In the IT2B program of the USC PACK collection for example one is encouraged to determine the error pattern of the assay quite specifically before beginning the analysis by determining several representative data points in at least quadruplicate and to find the standard deviation SD of each of these points One can measure in at least quadruplicate a blank sample a low one an intermediate one a high one and a very high one One can then find the relationship between the serum concentration
116. two most probable trajectories Return to the default display by selecting Show all subsets The Fitted probabilities view This view will give you useful information about a fitted model It will only have data after you have fitted a model The display This display is very similar to the Pop model data view and it does essentially provide the same information but this time the probabilities are time dependent Parameter Time slider Average plot selector Time into regimen U CPACK for Windows Beta 1 0 alan forrests AMIKA IN TERZ TS 1 So bp ________________ 4 Time 0 00 hours Ry ka M KSI lV VSI Probability og plots A Posterior Plot EE Probabilities Future Plot A Rg ort For Help press F1 EDE ay Plot view Plot selector Value display The main difference in this view is the weighted Average plot and the Time slider The average plot is the plot shown in the Posterior plot view when only the weighted average is plotted The solid diamonds represent the serum level measurements The blue ticks represent the doses given Select a time into the regimen passing one or more of the serum level measurements By dragging the Time slider to the right See how the probabilities in the Plot view changes with each new sequential Bayesian posterior New probabilities are computed each time there is a serum level measurements Select the Raw data button in the Plot selector to see the
117. uential MM or MAP Bayesian approaches Conclusions the IMM approach can detect and quantify changing parameter values in unstable patients and should permit more informed dosage regimens especially for drugs having narrow margins of safety Supported in part by NIH grants LM 05401 and RR 11526 Appendix C A description of the mb patient file format The description comments are given below the patient file sample The file description 110 or 11 This is a General File Flag If the first digit 1s not equal to the minus sign then the file is of much older format If the 4th character is 1 there is a steady state input John Doe 2989 Last name 20 characters first name 20 characters and chart number 10 characters 20 76 000000F 64 17163 002 If the second character of File flag is not equal to 1 then read ward 10 characters patient age Floating point F5 1 patient sex 1 character M or F patient height in inches F5 1 height in cm F5 1 flag for displaying height in other units usually in cm Integer 1 digit where height flag 1 height input in inches height flag 2 height in cm If the second digit of File flag equal l Then read 10 characters patient age Floating point F10 6 patient sex 1 character M or F patient height in inches F6 2 height in cm F6 2 flag for displaying height in other units usually cm Integer 1 digit where height flag 1 height input in inches height
118. um concentrations for Day 2 one has learned a lot about the patient from the first set of serum levels In addition the response of the true patient was predicted to be quite precisely controlled for Day 2 as shown in Figure 7 At the end of Day 2 when the 3 new serum levels came back during Day 2 the model probabilities were further updated Only three significant support points now were present These revised probabilities were used to plan the regimen for Day 3 which was computed and given Figure 8 shows the 99 most probable predicted serum level trajectories The controller and thus the clinician thinks it is doing just great However life is never quite so kind Because of the stated errors in the clinical environment the response of the true patient departed slightly from the predicted response on this day as shown in Figure 9 Finally after the three new simulated measured serum levels came back from Day 3 the true patient was found Furthermore in other preliminary as yet unpublished studies in which the true patient was not a member of the original model set the MM controller was also able to perform its MM adaptive control function quite acceptably DISCUSSION AND CONCLUSION The MM dosage designer developed regimens which were the result of many simulated clinical trials with each virtual subject who was studied to make the population model used as the Bayesian prior Its dosage regimen achieved the therapeutic g
119. y matrix PROBABILITY KA KS1 VS1 02490909 LeLy95Z200 O 0056028 O 2560060 Owl nosoto Taod L200 OOO 9S25 in 82 3 50 0 Q0 962309 dsb 597200 Oe0030496 0 2056 5 10 O OCLI Leobeys00 OeOOS12 7S O6 3296260 O207Z9027 Ae 66S000 02007268 L0r 302 94200 006979360 128926007 00030204 042336460 OOpa TeUGlesou 0020986 Htoo GI20 GOLLIT LTI G2200 0370033970 30 263l7s0 O20469556 0s9462290 020033766 Os 22530620 0 0434977 1 2468700 0 0030408 0 2502980 04 0S92361 DTeS365300 000248605 0 22606 0 0 0350195 1 4554400 0 0031884 0 3242060 CO OLSA O 9678660 O2003Z170 Oa25725450 Us00OS54h 160929700 0 0025439 Os22335010 OPOOLLS43 1 54 75700 Os 0024506 0 2277910 O0 0010446 1 0119700 0 0031067 0 2394870 0 0009267 176091800 0 0040594 0 2567400 O0004389S 1 05 78300 070030989 024201850 OxrJOOLUS6 whoOlesooO sUSO0S RISO U2 S 65600 OOO BND PILE 43597657865646357619 00006 36 0000819 0000073 0000022 merere 33 L6000 0049000 s 1392600 3062600 OOO s003 0331 003 L339 20030335 00 30058 Oooo 29349090 32503430 Z40L6Z20 s29 LQ OLO

User manual - Laboratory of Applied Pharmacokinetics

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