Download What is Modeling?

Modeling Data: Methods and
Examples
Arthur G. Roberts
WHAT IS MODELING?
Drug Development
Discovery
Find Targets
Phase I
5,000
-10,000
250
Phase 2
Phase 3
FDA
Scale-up
5
1
Volunteers
20
-100
3-6 Years
$420 million*
*Inflation Adjusted
Market
Clinical
Preclinical
100
-500
1,000
-5,000
6-7 Years
$585 million*
0.5-2
Total= >$1 billion
Innovation.org and DiMasi, et al. 2003
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
[Drug]
Open
Catenary
Cyclic
Mammillary
Reducible
[Drug]out
in
[Drug]
CPK: Topology
•
•
•
•
•
•
Closed
Open
Catenary [Drug]
Cyclic
Mammillary
Reducible
Compartment 1
Compartment 2
Compartment 3
[Drug]out
in
[Drug]
[Drug]
Chain
[Drug]
CPK: Topology
•
•
•
•
•
•
Closed
Open
Catenary [Drug]
Cyclic
Mammillary
Reducible
Compartment 1
Compartment 2
Compartment 3
[Drug]out
in
[Drug]
[Drug]
[Drug]
CPK: Topology
•
•
•
•
•
•
Closed
Open
Catenary
Cyclic
Mammillary
Reducible
Peripheral
Compartment
2
Peripheral
Compartment
1
[Drug]
[Drug]
Central
Compartment
[Drug]
CPK: Topology
•
•
•
•
•
•
Closed
Open
Catenary
Cyclic
Mammillary
Reducible
Compartment
2
Compartment
1
[Drug]
[Drug]
Compartment
3
[Drug]
The coupling between the compartments has
vastly different dynamics.
Simplifies modeling
CPK: Topology
•
•
•
•
•
•
Brain
Closed
Open
Catenary
Cyclic
Mammillary
Reducible
[Drug]Receptor
[Drug]
Elimination
Response
Liver
CPK: Topology
•
•
•
•
•
•
Brain
Closed
[Drug]
Open
Catenary
[Drug]
Cyclic
Mammillary Liver
Reducible
[Drug]Receptor
Elimination
Response
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
Attributes of PK/PD-models to be considered.
Direct Link
vs.
Indirect Link
Direct
Response vs.
Indirect
Response
Hard Link vs.
Soft Link
Selected PK/PD-approach
Time
invariant vs.
Time variant
Direct link versus indirect link
Direct Link
Brain
Plasma
Elimination
[Drug]
[Drug]
Relative concentrations between the the plasma and the brain remain
relatively constant despite the system not being in steady-state.
Indirect Link
Exhibit hysteresis
Distribution delay
Indirect Link: Hysteresis
Counter-clockwise
Clockwise
Potential Causes
• Distribution Delay
• Active metabolite
• Sensitization
Potential Causes
• FunctioTolerance
Cocaine and Functional Tolerance
Cocaine
Other examples: Capsaicin
S-Ibuprofen and time delay
S-ibuprofen
Definition
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.
Direct Response versus Indirect
Response
• Direct Response
– no time lag like indirect link (hysteresis?)
• Indirect Response (hysteresis?)
Drug
Effect
Indirect Response
Lymphocytes
[drug]P
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
dose 3
dose 2
dose 1
[Drug]
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-monolixoverview/
– 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