1. Modeling Data: Methods and Examples Arthur G. Roberts

2. WHAT IS MODELING?

3. 3-6 Years 6-7 Years 0.5-2 Phase I 5,000 -10,000 250 5 1 Phase 2 Phase 3 Find Targets DiscoveryPreclinical Clinical Volunteers 20 -100 100 -500 1,000 -5,000 FDAScale-up Market Innovation.org and DiMasi, et al. 2003 *Inflation Adjusted $420 million* $585 million* Total= >$1 billion Drug Development

5. Outline Model Types – PK – PK/PD – Disease Progression – Meta-models and Bayesian Averaging – Population Estimating Parameters Simulation Methods Regulatory Aspects

6. PK models [drug] versus time types – compartment PK modeling (CPK) – physiology-based PK modeling (PBPK)

7. PK models: Topology Closed Open Catenary Cyclic Mammillary Reducible

8. PK models: Topology Closed Open Catenary Cyclic Mammillary Reducible [Drug]

9. CPK: Topology Closed Open Catenary Cyclic Mammillary Reducible [Drug] [Drug] in [Drug] out

10. CPK: Topology Closed Open Catenary Cyclic Mammillary Reducible [Drug] [Drug] in [Drug] out [Drug] Compartment 1 Compartment 2 Compartment 3 Chain

11. CPK: Topology Closed Open Catenary Cyclic Mammillary Reducible [Drug] [Drug] in [Drug] out [Drug] Compartment 1 Compartment 2 Compartment 3

12. CPK: Topology Closed Open Catenary Cyclic Mammillary Reducible [Drug] Central Compartment Peripheral Compartment 1 Peripheral Compartment 2

13. CPK: Topology Closed Open Catenary Cyclic Mammillary Reducible [Drug] Compartment 1 Compartment 2 [Drug] Compartment 3 The coupling between the compartments has vastly different dynamics. Simplifies modeling

14. CPK: Topology Closed Open Catenary Cyclic Mammillary Reducible [Drug]- Receptor [Drug] Brain Liver Elimination Response

15. CPK: Topology Closed Open Catenary Cyclic Mammillary Reducible [Drug]- Receptor [Drug] Brain Liver Elimination Response [Drug]

16. Physiology-Based PK

17. PBPK modeling strategy

18. Examples of Drug Candidate Optimization Areas via PBPK

19. Common Parameters Required

20. ADME Parameters that affect PBPK

21. Where PBPK add value or fail

22. all-trans-retinoic acid (Tretinoin)

23. Pharmacokinetic/Pharmacodynamic (PKPD) PK + Dose Response

24. Pharmacokinetic/Pharmacodynamic Modelling Procedure – Estimate exposure – Correlate exposure to PD or other endpoints (e.g. excretion rates) – Use mechanistic models – Model excretion rate as a function of exposure Purpose – Estimate therapeutic window – Dose selection – Mechanism

25. PD Models Steady-state Non-steady state

26. PD models for Steady-State Situations Fixed effect =Response constant – ototoxicity and gentamycin Linear model=[drug] proportional to Response Log-linear model=log[drug] proportional to Response E max -model=

27. Concentration-effect (Pharmacodynamic E max -model)

28. Example Opioid Receptor Agonist

29. PD Models for non-steady state Dose-concentration-effect relationship to be modeled Direct Link vs. Indirect Link Direct Link vs. Indirect Link Direct Response vs. Indirect Response Hard Link vs. Soft Link Time invariant vs. Time variant Attributes of PK/PD-models to be considered. Selected PK/PD-approach

30. Direct link versus indirect link Plasma [Drug] Brain Elimination Direct Link Indirect Link Relative concentrations between the the plasma and the brain remain relatively constant despite the system not being in steady-state. Distribution delay Exhibit hysteresis

31. Indirect Link: Hysteresis Counter-clockwise Potential Causes Distribution Delay Active metabolite Sensitization Clockwise Potential Causes FunctioTolerance

32. Cocaine and Functional Tolerance Cocaine Other examples: Capsaicin

33. S-Ibuprofen and time delay S-ibuprofen EP=Evoked Potential An evoked potential or evoked response is an electrical potential recorded from the nervous system of a human or other animal following presentation of a stimulus, as distinct from spontaneous potentials as detected by electroencephalography (EEG), electromyography (EMG), or other electrophysiological recording method. Definition

34. Direct Response versus Indirect Response Direct Response – no time lag like indirect link (hysteresis?) Indirect Response (hysteresis?) Drug Effect

35. Indirect Response [drug] P Lymphocytes fluticasone

36. Soft link versus Hard Link Soft link – PK+PD data – temporal delay – Indirect link models are soft link because they must be characterized using PK and PD data. Hard link – PK data + in vitro studies (e.g. binding affinities)

37. Time variant versus time invariant Tolerance – Functional or PD tolerance (Hysteresis?) Sensitization (Hysteresis)

38. Disease Progression Models 1992 – Alzheimer’s via Alzheimer Disease Assessment Scale (ADASC) Characteristics – Subject variability – Correlated to PK model – Drug effects

39. Meta-models and Bayesian averaging Meta-analyses means “the analysis of analyses” Bayesian averaging – Thomas Bayes (1702-1761) – Biased averaged based on other information – Method to average several different models

40. Population Models Data and database preparation Structural models – algebraic equations – differential equations Linearity and superposition Stochastic models for random effects Covariate models for fixed effects

41. Population Models: Data and database preparation only good as the data in them accuracy (remove errors) data consistency remove significant outliers

42. Population Models: Structural Models Structural model = Structural equation modeling (SEM) Algebraic and Differential

43. Population Models: Linearity and superposition Linearity – Linear with respect to parameters (i.e. directly correlated) – Equation doesn’t have to be linear Superposition – additive – dose 1 + dose 2 = doses together [Drug] dose 1 dose 2 dose 3

44. Population Models: Stochastic Models for Random Effects Variability – low therapeutic index  high probability of subtherapeutic and toxic exposure – Residual unexplained variability (RUV) Observation value – Model predicted value – Between subject variability (BSV) – 1 level-linear regressiion – Multi-level-hierarchies

45. Population Models: Covariate models for fixed effects Covariates- Something that causes variation. Fixed effect- parameter estimated from an average or an equation and not estimated from data (no BSV)

46. Variability and Covariates

47. Estimating Parameters Least Squares – slope and intercept values – residues=Value-Average Value – least squares= Sum of (Value-Average Value)^2 Weights – least squares weighted toward high data points Objective Function Value (OFV) – negative log sum of likelihoods – minimum value = best fit Parameter Optimization – used because PK has too many variables

48. Parameter Optimization Examples Evolutionary Programming Genetic Algorithm Simulated Annealing Random Searching

49. Simulation Methods Validation – internal – subset of the data – external – new data set Extrapolation – simulating data outside the observed data set Limitations and Assumptions Non-Stochastic Simulations (simple fitting) Stochastic Simulations – Random-effect parameters (e.g. Population Variability) simulated with a random number generator based on a distribution – Model simulated repeatedly

50. Stochastic Simulations: Simulated doses to different groups

51. Simulation Software Proprietary – PK-Sim 5 – Pheonix WinNonlin Freeish – Monolix http://www.lixoft.eu/products/monolix/product-monolix- overview/ http://www.lixoft.eu/products/monolix/product-monolix- overview/ – Excel Open Source or Free – http://www.pharmpk.com/soft.html http://www.pharmpk.com/soft.html JavaPK for Desktop

52. Regulatory Aspects FDA Modernization Act of 1997 – exposure-response with a single clinical trial = effectiveness – Population modeling identify sources of variability  safety and efficacy Personalized Medicine – Cost effective – Modeling critical Optimize doses – Pharmacogenetics Warfarin exposure and response dependent on CYP2C9 genotrype

53. END OF MODELING DATA AND EXAMPLES