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Pharmacometrics Introduction

Pharmacometrics Introduction . Yaning Wang, Ph.D. Team Leader, Pharmacometrics Office of Clinical Pharmacology Center for Drug Evaluation and Research Food and Drug Administration yaning.wang@fda.hhs.gov. Disclaimer: My remarks today do not necessarily reflect the official views of FDA.

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Pharmacometrics Introduction

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  1. Pharmacometrics Introduction Yaning Wang, Ph.D. Team Leader, Pharmacometrics Office of Clinical Pharmacology Center for Drug Evaluation and Research Food and Drug Administration yaning.wang@fda.hhs.gov Disclaimer: My remarks today do not necessarily reflect the official views of FDA NONMEM Estimation Methods

  2. Outline • Issues and opportunities in drug development • Model-based drug development • Bayesian statistics and its relationship with NONMEM • NONMEM estimation methods NONMEM Estimation Methods

  3. Issues in Drug Development • Low efficiency • NME IND = NDA <20% of time • Reported >50% failure rate in Phase 3 (Carl Peck, CDDS) • Decreased NME NDAs despite increased INDs • Cost per NME approved estimated at $1.7B NONMEM Estimation Methods

  4. Low Success Rate Across Different Diseases Kola I, Landis J.Can the pharmaceutical industry reduce attrition rates? Nat.Rev.Drug.Disc. Aug 2004. NONMEM Estimation Methods

  5. High Failure Rate Even in Late Development Kola I, Landis J.Can the pharmaceutical industry reduce attrition rates? Nat.Rev.Drug.Disc. Aug 2004. NONMEM Estimation Methods

  6. 10-Year Trends of Major Submissions to FDA NONMEM Estimation Methods

  7. Investment Escalation Source: Windhover’s in Vivo: The Business & Medicine Report, Bain drug economics model, 2003 NONMEM Estimation Methods

  8. Various Initiatives • National Institutes of Health (NIH) • Roadmap initiative • National Cancer Institute (NCI) • Specialized Programs of Research Excellence (SPOREs) • European Organization for the Treatment of Cancer (EORTC) • make translational research a part of all cancer clinical trials • National Translational Cancer Research Network • facilitate and enhance translational research in the United Kingdom • FDA • Critical Path Initiative NONMEM Estimation Methods

  9. Application of quantitative disease models to drug development Pharmacogenomics in drug development New imaging technologies may contribute biomarkers in drug development 2004 FDA Critical Path Initiative Application of New Scientific Knowledge to Drug Development： http://www.fda.gov/oc/initiatives/criticalpath/ NONMEM Estimation Methods

  10. 2006 FDA Critical Path Update NONMEM Estimation Methods

  11. Model-Based Drug Development “The concept of model-based drug development, in which pharmaco-statistical models of drug efficacy and safety are developed from preclinical and available clinical data, offers an important approach to improving drug development knowledge management and development decision-making”Adapted from Lewis B. Sheiner, “Learning vs Confirming in Clinical Drug Development”, Clin. Pharmacol. Ther., 1997, 61:275-291. NONMEM Estimation Methods

  12. Terminology • Model-based drug development • Pharmacokinetics/Pharmacodynamics (PK/PD) • Modeling and simulation • Exposure-response • Quantitative clinical pharmacology • Quantitative disease and drug models • Pharmacometrics-Pharmacometricians • Areas involved: clinical pharmacology, statistics, pathophysiology,biology, bioengineering NONMEM Estimation Methods

  13. DRUG MODEL PLACEBO/DISEASE MODEL Morbidity#1 Relative Risk Morbidity#2 Surrogate Toxicity Mortality Surrogate Exposure Disease Drug Trial Models Surrogate Exposure High dose Low dose TIME TIME PATIENT/CLINICAL TRIAL MODEL % Drop-out % Compliance QD TID TIME Surrogate Body Weight Patient Population NONMEM Estimation Methods

  14. Applications in FDA Review • Exposure-response analysis of efficacy and safety data in NDA review for the choice of dosing regimen (s) • Dose adjustment in special populations (hepatic, renal, gender, age and drug interactions) based on intersubject variability and risk assessment • Routine use of population PK and PD data analysis to understand variability and to provide evidence for label claims • Issuing guidance to assist the industry in using these tools • Case studies • Leveraging Prior Quantitative Knowledge to Guide Drug Development Decisions and Regulatory Science Recommendations: Impact of FDA Pharmacometrics During 2004-2006, Journal of Clinical Pharmacology (2008) 48: 146-157 • Impact of Pharmacometric Reviews on New Drug Approval and Labeling Decisions - A Survey of 31 New Drug Applications Submitted Between 2005-2006, Clinical Pharmacology and Therapeutics (2007) 81: 213-221 • Impact of Pharmacometrics on Drug Approval and Labeling Decisions - A Survey of 42 New Drug Applications, The AAPS Journal, 7(3): E503-E512, 2005 NONMEM Estimation Methods

  15. Tools for Modeling and Simulation • NONMEM (UCSF, Globomax) • SAS (SAS Institute Inc) • Splus (Insightful Corporation) or R (Free) • WinBUGS (MRC Biostatistics, Free) • ADAPT II (USC, Free) • WinNonLin/WinNonMix (Pharsight) • Trial Simulator (Pharsight) NONMEM Estimation Methods

  16. 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Basic Statistics 1.0 • Random Variable (Y) • Discrete (gender, pain score) • Continuous (body weight, clearance) • Distribution (histogram) • Binomial • Normal • Lognormal • Probability Function (P(Y=y)) • Probability Mass Function (PMF) • Probability Density Function (PDF) 0.8 0.6 0.4 0.2 0.0 0 1 0.02 0.015 0.010 0.005 0.0 20 40 60 80 100 120 140 1 2 3 4 5 6 7 NONMEM Estimation Methods

  17. Normal Distribution 0.04 0.03 P(y) 0.02 Y~N(100, 102) 0.01 0.0 • 100 120 • Y NONMEM Estimation Methods

  18. Joint, Marginal and Conditional Probabilities P(Y2) P(Y1) Joint probability: P(Y1=0,Y2=0)=0.72 Marginal probability: P(Y1=0)= 0.90 Conditional probability: P(Y2=0|Y1=0)= 0.72/0.90=0.80 NONMEM Estimation Methods

  19. Marginal and Conditional Probabilities P(Y2) P(Y1) Conditional probability: Marginal probability: For continuous variables: Marginal probability: weighted average of conditional probability NONMEM Estimation Methods

  20. Bayes’ Theorem NONMEM Estimation Methods

  21. Parameter • Unknown but fixed (Frequentist) • Unknown and random (Bayesian) • Unknown hyperparameters • Hyperprior (Full Bayesian) • Estimation (Empirical Bayesian) (Prior distribution of ) Hyperparameters NONMEM Estimation Methods

  22. Prior, Likelihood and Posterior Likelihood Posterior Distribution Prior Distribution Marginal Distribution NONMEM Estimation Methods

  23. Prior, Likelihood and Posterior NONMEM Estimation Methods

  24. Posterior Likelihood Prior 2  n Shrinkage   NONMEM Estimation Methods

  25. A Simple Example • Unknown parameter (): long-term systolic blood pressure (SBP) of one particular 60-year-old female • 4 measurements with a mean and a standard deviation =5 • Survey of the same population (60-year-old female): mean SBP =120 and standard deviation =10 NONMEM Estimation Methods

  26. Estimation of  • Frequentist • Point estimate: • Interval estimate (95%CI) • Bayesian • Posterior distribution P(|Y) • Posterior mean • 95% credible interval NONMEM Estimation Methods

  27. Individual parameter (posterior) Individual data (likelihood) Population Distribution (prior) Prior, Likelihood and Posterior Long-term systolic blood pressure (SBP) of 60-year-old woman NONMEM Estimation Methods

  28. Population PK Variability Sheiner, 1992 NONMEM Estimation Methods

  29. NONMEM and Bayesian i: Posthoc estimate (Empirical Bayesian Estimate) because , , 2 are all estimated based on MLE NONMEM Estimation Methods

  30. A Simple Example yij: the jth observation for the ith individual Assume: only k is the unknown parameter to be estimated Goal: search for the estimate, , that can minimize the following objective function where Li(k) is the marginal likelihood of k for ith individual NONMEM Estimation Methods

  31. What Is Marginal Likelihood ? P(i) P(Yi|k) P(Yi|k,i) P(Yi,i|k) This is just the area under the curve (AUC) of h(,k) versus  at a fixed k • Each fixed k leads to different AUC • Assuming only 1 subject, is associated with maximum AUC. is called the maximum likelihood estimator (MLE) of k • Even though AUC is a function of k, it cannot be expressed as a closed-form equation of k (difficulty of nonlinear mixed effect modeling) k=1 h ()  NONMEM Estimation Methods

  32. Grid Search to Find • Imagine we can try every possible k and evaluate AUC with numerical integration (similar to trapezoidal rule with very dense data) k=0.3 k=0.7 k=1.1 h ()    y AUC (k) k=0.3 k=0.7 k=1.1 Time (hr) k NONMEM Estimation Methods

  33. Estimation Methods • NONMEM • Laplacian • First order conditional estimate (FOCE) • First order (FO) • SAS • Adaptive Gaussian Quadrature • Importance sampling • FO • Splus • Lindstrom and Bates Algorithm NONMEM Estimation Methods

  34. What is LAPLACIAN doing? • Approximate h() with another function LAP() so that AUC is a close-form function of k k=0.3 k=0.7 k=1.1 LAP () or h ()    NONMEM Estimation Methods

  35. What is FOCE doing? • After Laplacian approximation, the second derivative, , is further approximated by , a function of the first derivative k=0.3 k=0.7 k=1.1 FOCE () or h ()    NONMEM Estimation Methods

  36. What is FO doing? • Approximate h() with another function FO() and also approximate the second derivative, , with a function of the first derivative k=0.3 k=0.7 k=1.1 FO () or h ()    NONMEM Estimation Methods

  37. Which one is the best? True LAP FOCE FO Marginal Likelihood LAP is the best even though occasionally FOCE, even FO, is closer to the true marginal likelihood NONMEM Estimation Methods

  38. Proportional Residual Error Model yij: the jth observation for the ith individual Assume: only k is the unknown parameter to be estimated NONMEM Estimation Methods

  39. LAPI* FOCEI** LAP FOCE FO k=0.3 k=0.7 k=1.1      *: LAPI, Laplacian with interaction is available in NONMEM VI **: FOCEI, first-order conditional estimate with interaction NONMEM Estimation Methods

  40. Which one is the best? True LAPI FOCEI LAP FOCE FO Marginal Likelihood LAPI is the best and LAP is worse than FOCEI for proportional error model k NONMEM Estimation Methods

  41. A Two-Dimensional Example yij: the jth observation for the ith individual Assume: k and V are the unknown parameters to be estimated Goal: search for the estimates, and , that can minimize the following objective function where Li(k, V) is the marginal likelihood of k and V for ith individual NONMEM Estimation Methods

  42. What Is Marginal Likelihood ? This is just the volume under the surface (VUS) of h(1, 2, , k, V) versus 1 and 2 at a fixed (k,V) k=1 and V=1 • Each fixed pair (k,V) leads to different VUS • If and are associated with maximum VUS. They are the maximum likelihood estimators (MLEs) of k and V • Even though VUS is a function of k and V, it cannot be expressed as a closed-form equation of k and V h (1, 2) 2 1 NONMEM Estimation Methods

  43. LAPLACIAN, FOCE, FO Volumes vs True Volume LAPLACIAN FOCE FO h (1, 2) 1 1 1 2 2 2 h (1, 2) 2 1 2 2 1 1 NONMEM Estimation Methods

  44. Summary for Estimation Methods • The approximation of true marginal likelihood is analogous to approximating an irregular shape with a symmetric shape whose AUC or VUS can be easily calculated • The difference among LAPLACIAN, FOCE and FO is mainly the thinness and height of the symmetric shapes • In general, the shape generated by LAPLACIAN method is the closest to the true shape, but the shape from FOCE is almost equally close • For models with - interaction, taking the interaction into account seems more important than avoiding first-order approximation (FOCEI vs LAP) Reference: Derivation of Various NONMEM Estimation Methods, Yaning Wang, Journal of Pharmacokinetics and Pharmacodynamics, 34: 575-93, 2007 NONMEM Estimation Methods

  45. Full Bayesian for PopPK NONMEM Estimation Methods

  46. Acyclic Structure H R a b MVN W G MVN Dose Model Time N Data NONMEM Estimation Methods

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