modeling data: methods and examples arthur g. roberts
TRANSCRIPT
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