Response Optimization in Oncology In Vivo Studies: a Multiobjective Modeling Approach

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Response Optimization in Oncology In Vivo
Studiesa Multiobjective Modeling Approach
MBSW2009, May 18-20, Muncie, IN

• Maksim Pashkevich, PhD(Early Phase Oncology
  Statistics)
• Joint work with
• Philip Iversen, PhD(Pre-Clinical Oncology
  Statistics)
• Harold Brooks, PhD(Growth and Translational
  Genetics)
• Eli Lilly and Company

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Outline

• Problem overview
• In vivo studies in oncology drug development
• Efficacy and toxicity measures for in vivo
  studies
• Optimal regimen as balance between efficacy /
  toxicity
• Models for efficacy and toxicity
• Modified Simeoni model of tumor growth inhibition
• Animal body weight loss model to describe
  toxicity
• Statistical estimation of model parameters in
  Matlab
• Optimal regimen simulation
• Multiobjective representation of simulation
  results
• Pareto-optimal set of optimal dosing regimens

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Motivation

• In vivo studies in oncology
• Typical way to assess cancer compound activity
• Cancer tumors are implanted in mice or rats
• Tumor size and animal weight are measured over
  time
• Efficacy and toxicity measures
• Tumor growth delay is a standard efficacy measure
• Body weight loss is a typical surrogate for
  toxicity
• Optimal dosing regimen is unknown
• Goal is to achieve balance between efficacy and
  toxicity
• Number of possible dosing regimens is very
  significant
• Modeling should help to select promising regimens

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Example of Efficacy Data
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Example of Toxicity Data
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Simeoni Model
Rocchetti et al., European Journal of Cancer 43
(2007), 1862-1868
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Model Extension
Nonlineardrug effect
cytotoxic
cytostatic
Cell death
Cell growth

• Modifications to get adequate model
• Drug effect depends on exposure in a non-linear
  way
• Drug has both cytotoxic and cytostatic effect
• Rationale is based on cell-cycle effect of the
  compound

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Developed Efficacy Model
Dynamic model system of ordinary differential
equations
Initial conditions with random effect for
initial tumor weight
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Modeled vs. Observed for Groups
Control
15 mg/kg QD
30 mg/kg QD
60 mg/kg QD
15 mg/kg BID
30 mg/kg BID
Model adequacy assessment Individual profiles vs.
mean modeled tumor growth curves for each group
20 mg/kg TID
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Efficacy Model Results
Modeled population-average tumor growth curves
for each dose group
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Body Weight Loss
Hypothetical example two dosing cycles at days 7
and 17
Body weight is initially in steady state
Drug exposure causes weight loss
Body weights starts to recover
drug
Next dose causes more weight loss
Slow recovery phase body weight growth based on
Gompertz model
drug
Maximum body weight lossis roughly 3.25
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Developed Toxicity Model
Dynamic model system of ordinary differential
equations
Initial conditions with random effect for
initial body weight
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Modeled vs. Observed for Groups
Control
15 mg/kg QD
30 mg/kg QD
60 mg/kg QD
15 mg/kg BID
30 mg/kg BID
Model adequacy assessment Individual profiles vs.
mean modeled body weight curves for each group
20 mg/kg TID
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Toxicity Model Results
Modeled population-average animal weight curves
for each dose group
1.25

Control
1.2
15 mg/kg q7dx4
30 mg/kg q7dx4
1.15
60 mg/kg q7dx1
15 mg/kg BID7dx4
1.1
30 mg/kg BID7dx4
20 mg/kg TID7dx4
1.05
1
Mice body weight (g)
0.95
0.9
0.85
0.8
0.75

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10
15
20
25
30
35
40
Time (days)
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ML Parameter Estimation

• Computationally hard problem
• Numerical solution of system of differential
  equations
• Numerical integration due to random effects
• Numerical optimization of resulting likelihood
  function
• Three heavy numerical problems nested in one
  another
• Implementation in Matlab
• Relying on standard functions is unacceptably
  slow
• Special problem-specific method was developed for
  ODE system solution and random effects
  integration
• Numerical optimization was done by Matlab function

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Regimens Simulation

• Simulation settings
• Dosing was performed until day 28 as in original
  study
• Doses from 1 to 30 mg/kg (QD, BID, TID) were used
• Dosing interval was varied between 1 and 14 days
• Regimen evaluation
• Efficacy and toxicity were computed for each
  regimen
• Efficacy was defined as overall tumor burden
  reduction
• Toxicity was defined as maximum relative weight
  loss
• Efficacy was plotted vs. toxicity for each
  simulation run
• Pareto-optimal solutions were identified for QD,
  BID, TID

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Tumor Burden
Area under thetumor growth curve
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Efficacy-Toxicity Plot
Red QD, blue BID, green TID
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Pareto-Optimal Solutions
Red QD, blue BID, green TID
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Pareto-Optimal Solutions
Red QD, blue BID, green TID
Zooming this part
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Pareto-Optimal Solutions
Red QD, blue BID, green TID
Notation dose in mg/kg, interval in days
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Pareto-Optimal Solutions
Red QD, blue BID, green TID
Optimal regimens(QD, BID, TID)
Notation dose in mg/kg, interval in days
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Optimal Regimens
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Prediction Accuracy

• Methodology
• Fishers information matrix computed numerically
  ?
• Variance-covariance matrix for ML parameter
  estimates
• Simulations performed to quantify prediction
  uncertainty

Regimen TID 6 mg/kg every day
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Closer Look at QD Administration
Notation dose in mg/kg, interval in days
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In Vivo Study Dosing Until Day 28
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Summary

• Methodological contribution
• New multiobjective method for optimal regimen
  selection
• Novel dynamic model for cancer tumor growth
  inhibition
• Novel dynamic model for animal body weight loss
• Practical contribution
• More efficacious and less toxic in vivo dosing
  regimens
• Better understanding of compound potential
  pre-clinically
• Validation
• Application of modeling results to in vivo study
  in progress

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Acknowledgements

• Project collaborators
• Philip Iversen
• Harold Brooks
• Data generation
• Robert Foreman
• Charles Spencer