Training/BestDose

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2 Training/BestDose

3 How can we optimize individual patient dosing?

4 The parametric approach Population CL Data Posterior CL

5 MAP-Bayesian Parametric model Maximum a posteriori Bayesian probability One version of the patient Shrinkage of variability No probability of success vs. failure

6 Non-Normal Populations Simulated population ( ) Non-parametric estimation of population values ( ) - Size proportional to probability Vol The entire population is accurately and precisely described Kel Neely MN, van Guilder MG, Yamada WM, Schumitzky A, Jelliffe RW. Accurate detection of outliers and subpopulations with Pmetrics, a nonparametric and parametric pharmacometric modeling and simulation package for R. Ther Drug Monit. 2012;34(4):

7 Non-Normal Populations Simulated population ( ) Mean (+) and percentile distributions of parametric population parameter estimates Vol Percentile Missed the outlier completely. Nobody is at the mean! Kel

8 Non-Parametric Model

9 Using the model

10 Multiple Models

11 Multiple Models

12 Very rich data

13 Moderate data

14 Very sparse data

15 Interacting MM (IMM) Useful when one set of parameter estimates does not capture a single patient over time, i.e. the patient is changing For example, development or recovery from septic shock and changes in volume of distribution and/or clearance

16 IMM At each measured serum concentration, with a specified probability (usually 1-3%), the model can be refit to the new data to generate a new Bayesian posterior The points in the model don t change their values, only their probabilities Probabilities will gradually erode after each dose which has no subsequent level, as we know less about the patient

17 No IMM IMM 1 IMM 2 IMM 3

18 Hybrid MAP Bayesian MM MM Hybrid

19 Hybrid MAP Bayesian MM MM Hybrid Much better precision!

20 That s the dose. What about sampling?

21 The problem?

22 D-optimal sampling Sample at times when drug concentrations are most sensitive to small changes in parameter values Maximizes the determinant of the Fisher Matrix [1,2] which is comprised of partial derivatives of the changes in concentration for changes in each parameter value Goal is to estimate parameter values [3] 1. S.D. Silvey, Optimal Design: An Introduction to the Theory for Parameter Estimation. Chapman and Hall, London, V.V. Fedorov, Theory of Optimal Experiments. Academic Press, New York, D Argenio DZ, Optimal Sampling Times for Pharmacokinetic Experiments, J. Pharmacokinetics and Biopharmaceutics, vol. 9, no. 6, 1981:

23 Problems with D-optimal Circular reasoning Number of samples cannot be less than the number of model parameters

24 Improving D-optimal To improve D-optimal design, an expectation is taken with respect to prior information[1-5] ED: max E{ M } EID: min E{ 1/ M } Still need to have a model first ELD (or API): max E{ Optimally, log M } samples parameters 1. K. Chaloner and I. Verdinelli, Bayesian experimental design: A review, Statistical Science, Vol. 10, No. 3, pp , L. Pronzato and E. Walter, Robust experiment design via stochastic approximation, Mathematical Biosciences, Vol. 75, pp , E. Walter and L. Pronzato, Optimal experiment design for nonlinear models subject to large prior uncertainties, American Journal of Physiology Regulatory, Integrative and Comparative Physiology, 253:R530-R534, M. Tod and J-M Rocchisani, Comparison of ED, EID, and API criteria for the robust optimization of sampling times in pharmacokinetics, J. Pharmacokinetics and Biopharmaceutics, Vol. 25, No. 4, D.Z. D Argenio, Incorporating prior parameter uncertainty in the design of sampling schedules for pharmacokinetic parameter estimation experiments, Mathematical Biosciences, Vol. 99, pp , 1990.

25 MMopt Multiple-Model Optimal design Completely new optimal sampling paradigm in the PK world Shift focus from estimating parameters directly to correctly classifying which time-concentration profile among many matches a subject best

26 The NP Model Prior Distribution?

27 Minimize misclassification Model Responses Model 1 Reponse Model 2 Response Two-Model Classification Problem r(t) = response separation r(t) = response separation Time Bayes Risk Choose t

28 2-Model results* Design Metric Sample Time Bayes Risk Bayes Optimal MMopt ED EID API *Previously presented at the Population Optimum Design of Experiments Workshop, Windlesham, England, 15 June, 2013

29 Methods For all analyses and plots we used Pmetrics*, R, and Matlab. Pmetrics is freely available from our lab at *Neely MN, van Guilder MG, Yamada WM, Schumitzky A, Jelliffe RW. Accurate Detection of Outliers and Subpopulations With Pmetrics, a Nonparametric and Parametric Pharmacometric Modeling and Simulation Package for R. Ther Drug Monit 2012; 34:

30 Methods - MMOPT 1 2 Model 141 richly sampled adults and children with MM-clearance, allometric scaling, peripheral compartment (9 parameters, 118 support points). Generate the profile every 30 minutes from each point in the model when given a single oral dose of 7 mg/kg to a 9 year old child weighing 33.5 kg, adding random noise to each simulated observation with mean 0 and SD= *C (voriconazole assay error)

31 Methods - MMOPT All Model Responses with 3-Sample Design=(triangle,square,o) Conc hr Calculate the MMOptimal sample times for 1 (MMopt1), 2 (MMopt2), and 3 (MMopt3) samples

32 Methods - validation Full Peak/Tr Trough Full MMopt3 MMopt2 MMopt1 NCA Bias Imprecision AUC, C1, C12 AUC, C1, C12 AUC, C1, C12 AUC, C1, C12

33 Bias and imprecision High Bias Low Bias High Imprecision Low Imprecision

34 Results: Vori MMopt Background Assay Polynomial sigma= c0 + c1*y + c2*y^2 + c3*y^3 [c0,c1,c2,c3] Optimal Designs One Sample Design (hr) All Model Responses with 3-Sample Design=(triangle,square,o) Two Sample Design (hr) Three Sample Design (hr) Four Sample Design (hr) Bayes Risk 1-Sample: Sample: Sample: Sample: Conc hr

35 Bias (Sampled-True) Sampling AUC C1 C12 TRUE Full PeakTrough -1.62* * Trough -1.09* 0.24* -0.06* MMopt3 (0.5, 1.5, 3.5) MMopt2 (0.5, 2.5) MMopt1 (1.0) -1.63* * * P 0.01 vs. 0 bias

36 Imprecision - AUC

37 Imprecision - C1

38 Imprecision - C12

39 Conclusions (1) MMopt is an optimal sampling scheme based on classification of new subjects relative to previous experience It does not depend on a population model or method (non-parametric vs. parametric) A population model is only required if PK parameter values are desired, and the number of samples may be less than the number of model parameters

40 Conclusions (2) In this analysis, 2 MMoptimally timed voriconazole samples at 0.5 and 2.5 hours after an oral dose in a simulated pediatric population estimated the full 12- hour AUC, peak and trough concentrations with little bias and good precision The number of optimal samples (2) was far less than the number of model parameters (9) Future work will refine MMopt to optimize timing to estimate drug-specific metrics, such as AUC for busulfan

41 Limitations of standalone BestDose Algebraic models only Limited covariate structure No lag, bioavailability parameters Windows only

42 BestDose Server Past Future Busulfan Concentration (mg/l) Dose Measured mg 5.2 mg 7.73 mg 7.23 mg 7.26 mg 7.25 mg 7.25 mg 7.25 mg 7.25 mg 7.25 mg 7.25 mg 7.25 mg 7.26 mg 7.26 mg 7.26 mg 7.41 mg 4:00 10:0016:3022:30 4:30 10:3016:3022:30 4:30 10:3016:3022:30 4:30 10:3016:3022:30 % Probability Wtd Mean Nov 15 6:00 Nov 15 18:00 Nov 16 6:00 Nov 16 Nov 17 Nov 17 Nov 18 18:00 6:00 18:00 6:00 Date and Time Nov 18 18:00 Nov 19 6:00 Nov 19 18:00

43 BestDose Local Past Future Patient folder Busulfan Concentration (mg/l) Past Dose Measured Nov 15 6:00 Nov 15 18:00 Future mg 5.2 mg 7.73 mg 7.23 mg 7.26 mg 7.25 mg 7.25 mg 7.25 mg 7.25 mg 7.25 mg 7.25 mg 7.25 mg 7.26 mg 7.26 mg 7.26 mg 7.41 mg 4:00 10:0016:3022:30 4:30 10:3016:3022:30 4:30 10:3016:3022:30 4:30 10:3016:3022:30 Nov 16 6:00 Nov 16 18:00 Nov 17 6:00 Nov 17 18:00 Nov 18 6:00 Date and Time Nov 18 18:00 Nov 19 6:00 % Probability Nov 19 18:00 Wtd Mean

44 Past data file Same as Pmetrics data file EXCEPT Date column and Times are clock

45 Future data file Same as Pmetrics data file EXCEPT OUT becomes the target

46 Pre-flight check Past and future data files are in patient folder Working directory in R is set to patient folder with setwd() bestdose() command properly entered Laboratory of Applied Pharmacokinetics and Bioinformatics

47 bestdose() bestdose(drug, index = 1, target, dose, optimize = T, cycles = 0, nextdose, past = "pdata.csv", future = "fdata.csv", idelta = 60, biaswt = 0.5, prior = NA, run, overwrite = F, auc = F, MMopt = F, nsamp = 1, gamlam, simonly = F, ylim)

48 bestdose: drug Name of drug cartridge (model), e.g. drug= voriconazole

49 bestdose: index Index of drug cartridge if multiple of the same name E.g. three models for voriconazole, one for children, one for adults, one for adults in intensive care; index=2

50 bestdose: target OUT values in future file are targets Can replace them here The last value will be replicated to replace targets in future file E.g. If future file has targets of 1, 2, 2, target=c(1,2) will achieve the same results

51 bestdose: dose DOSE values in future file are starting doses for optimization if optimize=t, or forecasting doses if optimize=f Can replace them here The last value will be replicated to replace doses in future file E.g. If future file has doses of 100, 200, 200, dose=c(100,200) will achieve the same results; dose=100 will replace all doses in future file with 100

52 bestdose: optimize If true, the most precise and accurate dose to achieve the targets will be returned If false, doses in future file or dose argument will be forecasted using patient s Bayesian posterior

53 bestdose: cycles Allow NPAG to cycle, using population model (cartridge) as prior Default is 0, which uses model to calculate Bayesian posterior only

54 bestdose: nextdose Date and time of next dose to be given Defines the time of TIME=0 in future file Format is mm/dd/yy hh:ss by default Can be changed by setbdpref()

55 bestdose: past Name of the past data file, e.g. pdata.csv If planning a first dose (i.e. no past data), set to NA

56 bestdose: future Name of the future data file, e.g. fdata.csv Must be present

57 bestdose: idelta Frequency of predicted concentrations in minutes Default is 60 E.g. idelta=15

58 bestdose: biaswt Two opposing forces: minimize bias (increase accuracy) or minimize imprecision (increase precision) The most precise response is when no drug is given (everyone has same response profile) Fully maximally precise regimen will tend to underdose with respect to targets Default is biaswt=0.5, balanced between accuracy and precision Increase to 1 to maximize accuracy; decrease to 0 to maximize precision

59 bestdose: prior As in Pmetrics, if you have generated a new prior for a patient by cycling NPAG (cycles > 0), you can reuse by specifying prior as the folder number E.g. prior=3 to use the patient s individual model from run 3

60 bestdose: run, overwrite Same as for Pmetrics

61 bestdose: auc If AUC=T, targets in future data file are interpreted as AUC; if AUC=F, targets are interpreted as concentrations Targets should be specified as cumulative AUC starting at 0 at time 0

62 bestdose: MMopt,nsamp If MMopt=T, BestDose will also calculate nsamp optimal times in the future to sample the patient

63 bestdose: gamlam Allows user to inflate gamma/lambda in the setting of a patient who is initially fitted poorly by the model E.g. gamlam=5

64 bestdose: simonly If simonly=t, use the population prior to (i.e. do not fit model to generate Bayesian posterior) to simulate the profile given dosing history, sampling history, and covariates Can be used to understand how different your patient is from the median Default is false

65 bestdose: ylim Change the y-limits of the plot E.g. ylim=c(0,20)