Modeling Data: Methods and Examples Arthur G. Roberts

WHAT IS MODELING?

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

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

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

PK models: Topology Closed Open Catenary Cyclic Mammillary Reducible

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

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

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

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

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

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

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

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

Physiology-Based PK

PBPK modeling strategy

Examples of Drug Candidate Optimization Areas via PBPK

Common Parameters Required

ADME Parameters that affect PBPK

Where PBPK add value or fail

all-trans-retinoic acid (Tretinoin)

Pharmacokinetic/Pharmacodynamic (PKPD) PK + Dose Response

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

PD Models Steady-state Non-steady state

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=

Concentration-effect (Pharmacodynamic E max -model)

Example Opioid Receptor Agonist

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

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

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

Cocaine and Functional Tolerance Cocaine Other examples: Capsaicin

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

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

Indirect Response [drug] P Lymphocytes fluticasone

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)

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

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

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

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

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

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

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

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

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)

Variability and Covariates

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

Parameter Optimization Examples Evolutionary Programming Genetic Algorithm Simulated Annealing Random Searching

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

Stochastic Simulations: Simulated doses to different groups

Simulation Software Proprietary – PK-Sim 5 – Pheonix WinNonlin Freeish – Monolix overview/ overview/ – Excel Open Source or Free – JavaPK for Desktop

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

END OF MODELING DATA AND EXAMPLES