Estimation of Uncertainty and Variability for Systems Pharmacology Models Using Monte-Carlo Simulations

1. Estimation of Uncertainty and Variability for Systems Pharmacology Models Using Monte-Carlo Simulations Victor Sokolov, Dmitry Onishchenko, Kirill Zhudenkov Gabriel Helmlinger, Kirill Peskov 02-NOV-2017 BIOMAT 2017

2. Introduction: mathematical modeling in drug development Drug-Disease Modeling Modeling & simulation methodologies are established quantitative tools, which have proven to be critical in supporting the research, development (R&D), regulatory approval, and marketing of novel therapeutics. Relevant question Systems Biology Right target QSP PKPD: Pharmacokinetics and pharmacodynamics PBPK Right tissue PBPK: physiologically-based pharmacokinetic modeling Meta-analyses Right safety Pharmacometrics QSP: quantitative systems pharmacology Right patients Right commercial potential R&D Stage Drug discovery Life cycle management Early-stage development Late-stage development • Integrative quantitative modeling of data and disease based on pharmacology concepts generates knowledge that informs clinical drug development and underpins business decisions

3. Modeling workflow depends on available data Clinical/pre-clinical data Subject-level Study-level mean±SD Methodology Quantitative Systems Pharmacology (QSP) (non)linear fixed effects models Pharmacometrics (PMx) (non)linear mixed effects models Software MATLAB, R NONMEM, Monolix, R

4. Warfarin pharmacokinetics (PK) model One-compartment PK model with first-order absorption and elimination dose Vd absorption elimination Ad Ac Variables: – amount in dosing compartment – amount in central (plasma) compartment Parameters: – absorption constant – clearance – volume of distribution Functions: – plasma drug concentration Available data: change in Cc (plasma drug concentration) over time (subject- and study-level) 3 parameters to estimate: ka, CL and Vd

5. Approaches for PK parameters estimation Subject-level data Study-level data Non-linear fixed effects model Non-linear mixed effects model – plasma concentration for ith subject – time – vector of parameters for ith subject – residual error – ka value for ith subject – fixed value of ka – random effect on ka for ith subject , etc. Software applied: Matlab (IQM Toolbox) Fitting algorithm: Simplex Estimation results:fixed values Software applied: Monolix Fitting algorithm: SAEM Estimation results: fixed values + random effects and uncertainty distribution

6. PK parameters estimation results Subject-level data Study-level data Parameters distribution 1 value per parameter One mean prediction Prediction with confidence intervals Red curve and dots – experimental data (median±SD) Blue curve – model prediction Shaded area – 90% confidence interval

7. Estimating variability/uncertainty for study-level data A set of functions was developed for MATLAB software Averaged values Standard deviations n simulated trials Monte-Carlo (MC) simulations Fitting Variability/uncertainty taken into account Input: typical study-level data • Key assumptions: • distribution of the variable • independency of each observation within a subject • parameter distribution Parameters distribution Confidence intervals

8. PK parameters estimation results with MC method Median parameter values with 95% CI Parameter distribution based on original subject-level data is more narrow compared to Monte-Carlo simulated set

9. Comparison of model predictions Subject-level data Trial-level data with Monte-Carlo simulations Plasma concentration, mg/L Time, hours Red curve and dots – experimental data (median±SD) Blue curve – model prediction Shaded area – 90% confidence interval Both approaches result in similar prediction intervals, with the predictions based on original data having wider intervals compared to the MC-simulated

10. Conclusions A set of functions was developed for MATLAB environment, that allows procedure of parameter estimation and model diagnostics Using Monte-Carlo simulated data we were able to calculate confidence intervals for parameter estimates and prediction intervals for the model simulations A certain level of discrepancy is observed when comparing the results of parameter estimations obtained by different methods, which requires further investigation

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13. PMx workflow Model development “no” Prior Knowledge Structural model System Definition “yes” Covariate model Standardized dataset Problem Definition Base model Random effects Relevant Questions Trial-level data Does the model describe the data adequately? “no” “no” Is covariate significant? “yes” FINAL Model Independent datasets Model validation Model simulations Model analysis

14. QSP workflow (based on study-level data) Model development Prior Knowledge System Definition Standardized dataset Problem Definition QSP model structure nth sub-model 1st sub-model … Relevant Questions Open-source study-level data Does the model describe the data adequately? “no” “no” Parameters are identifiable and sensitive? “yes” “yes” FINAL Model Independent datasets Model validation Model simulations Model analysis

15. The advantages of script-based solver and fitter Time profiles, observed vs. predicted, residuals Opportunities to automate: 1. Model diagnostics Family of curves, tornado plots OFV profiling 2. Sensitivity analysis Monte-Carlo simulations, CI and prediction intervals 3. Identifiability analysis

16. Governance principles Modeling must be fit for purpose and model structure should be selected based on the law of parsimony QSP model is a slice of knowledge and is based on a thorough analysis of experimental data Parameters should have physiological meaning; parameter values should lie in a plausible biology / physiology range Parameters must be identifiable; uncertainty in parameter estimation must be evaluated Free parameters should be fixed only if strong prior understanding of physiology, biology, and/or signaling pathways is available Do not try to predict unpredictable

17. Stages of a PMx workflow and available software “no” Stage 2: NONMEM, Monolix, IQM, Simbiology, AZnlme Stage 1: SAS, R Prior Knowledge Structural model System Definition “yes” Covariate model Standardized dataset Problem Definition Base model Does the model describe the data adequately? Random effects Relevant Questions Trial-level data “no” Is covariate significant? “no” “yes” FINAL Model Independent datasets Stage 3: Monolix, IQM, Xpose, AZRsim Model validation Model simulations

18. PMx workflow Model development “no” Structural model “yes” Covariate model Base model Random effects Does the model describe the data adequately? “no” “no” Is covariate significant? “yes” FINAL Model Model analysis