Modeling Data: Methods and Examples

Arthur G. Roberts

WHAT IS MODELING?

3-6 Years 6-7 Years 0.5-2

Phase I

5,000-10,000

250 51

Phase 2 Phase 3

Find

Tar

gets

Discovery Preclinical Clinical

Volunteers

20-100

100-500

1,000-5,000

FDA Scale-up

Market

Innovation.org and DiMasi, et al. 2003*Inflation Adjusted

$420 million* $585 million* Total= >$1 billion

Drug Development

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] [Drug]

Compartment 1 Compartment 2 Compartment 3

Chain

CPK: Topology

• Closed• Open• Catenary• Cyclic• Mammillary • Reducible

[Drug][Drug]in [Drug]out

[Drug] [Drug]

Compartment 1 Compartment 2 Compartment 3

CPK: Topology

• Closed• Open• Catenary• Cyclic• Mammillary • Reducible

[Drug]

[Drug]

[Drug]

Central Compartment

PeripheralCompartment

1

PeripheralCompartment

2

CPK: Topology

• Closed• Open• Catenary• Cyclic• Mammillary • Reducible

[Drug] [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• Emax-model=

Concentration-effect (Pharmacodynamic Emax-model)

Example

Opioid Receptor Agonist

PD Models for non-steady state

Dose-concentration-effect relationship to be modeled

Direct Linkvs.

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][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

[dru

g]P

Lym

phoc

ytes

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 (1702-1761)– 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

• http://www.lixoft.eu/products/monolix/product-monolix-overview/

– Excel• Open Source or Free– http://www.pharmpk.com/soft.html

• 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