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

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Response Optimization in Oncology In Vivo Studies: a Multiobjective Modeling Approach 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 MBSW’2009, May 18-20, Muncie, I

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MBSW’2009, May 18-20, Muncie, IN. Response Optimization in Oncology In Vivo Studies: a Multiobjective Modeling Approach. Maksim Pashkevich, PhD (Early Phase Oncology Statistics) Joint work with Philip Iversen, PhD (Pre-Clinical Oncology Statistics) - PowerPoint PPT Presentation

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Page 1: Response Optimization in Oncology In Vivo Studies: a Multiobjective Modeling Approach

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

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

MBSW’2009, May 18-20, Muncie, IN

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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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MotivationIn 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 DataTumor Weight vs Time

(mean +/- SE)

0

500

1000

1500

2000

2500

0 10 20 30 40 50 60Day

Tum

or W

eigh

t, m

g

Vehicle, 0.2 ml, IV, TID7dx4 <n Vehicle, 0.2 ml, IV, TID7dx4Drug A, 15 mg/kg, IV, q7dx4 <n Drug A, 15 mg/kg, IV, q7dx4Drug A, 30 mg/kg, IV, q7dx4 <n Drug A, 30 mg/kg, IV, q7dx4Drug A, 60 mg/kg, IV, q7dx1 <n Drug A, 60 mg/kg, IV, q7dx1Drug A, 15 mg/kg, IV, BID7dx4 <n Drug A, 15 mg/kg, IV, BID7dx4Drug A, 30 mg/kg, IV, BID7dx4 Drug A, 20 mg/kg, IV, TID7dx4

Max wt. Sac, DeadLoss / Total -10 10, 0 / 10 -7 10, 0 / 10 -8 9, 1 / 10 -21 5, 5 / 10 -9 0, 0 / 10 -11 0, 0 / 10 -10 0, 0 / 10

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Example of Toxicity DataBody Weight vs Time

(mean +/- SE)

19

20

21

22

23

24

25

26

27

28

0 10 20 30 40 50 60Day

Bod

y W

eigh

t, g

Vehicle, 0.2 ml, IV, TID7dx4 <n Vehicle, 0.2 ml, IV, TID7dx4Drug A, 15 mg/kg, IV, q7dx4 <n Drug A, 15 mg/kg, IV, q7dx4Drug A, 30 mg/kg, IV, q7dx4 <n Drug A, 30 mg/kg, IV, q7dx4Drug A, 60 mg/kg, IV, q7dx1 <n Drug A, 60 mg/kg, IV, q7dx1Drug A, 15 mg/kg, IV, BID7dx4 <n Drug A, 15 mg/kg, IV, BID7dx4Drug A, 30 mg/kg, IV, BID7dx4 Drug A, 20 mg/kg, IV, TID7dx4

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Simeoni Model

Rocchetti et al., European Journal of Cancer 43 (2007), 1862-1868

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Model Extension

)(2 tck n

P

x1

x2

Nonlineardrug effect

1P

cytotoxic

cytostatic

x5

x3 x41k 1k

1kCell death

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

Cell growth

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Developed Efficacy Model

)()()1()()()()(

)()()(),()()()(

)()()(1)()(

125

4314

3213

21122

121

10101

),(

)(

)( )(

txtckdttdxtxtxk

dttdx

txtxkdttdxtxktxtck

dttdx

txtcktwtxdttdx

n

n

n

),0(~),()()()()()(

0)()()()(),exp()(

254321

05040302001

uNutxtxtxtxtxtw

txtxtxtxuwtx

Dynamic model: system of ordinary differential equations

Initial conditions: with random effect for initial tumor weight

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90 10 20 30 40 50 60

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Time (days)

log(

Tum

or w

eigh

t)

0 10 20 30 40 50 60-2.5

-2

-1.5

-1

-0.5

0

0.5

1

Time (days)

log(

Tum

or w

eigh

t)

5 10 15 20 25 30 35 40-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Time (days)

log(

Tum

or w

eigh

t)

5 10 15 20 25 30 35 40 45-2.5

-2

-1.5

-1

-0.5

0

0.5

1

Time (days)

log(

Tum

or w

eigh

t)

5 10 15 20 25 30 35 40-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Time (days)

log(

Tum

or w

eigh

t)

5 10 15 20 25 30 35 40-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Time (days)

log(

Tum

or w

eigh

t)

5 10 15 20 25 30 35 40-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time (days)

log(

Tum

or w

eigh

t)Modeled vs. Observed for Groups

Model adequacy assessmentIndividual profiles vs. mean modeled tumor growth curves for each group

Control 15 mg/kg QD 30 mg/kg QD

60 mg/kg QD 15 mg/kg BID 30 mg/kg BID

20 mg/kg TID

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Efficacy Model Results

0 10 20 30 40 50 600

0.5

1

1.5

2

2.5

Time (days)

Tum

or w

eigh

t

Control15 mg/kg q7dx430 mg/kg q7dx460 mg/kg q7dx115 mg/kg BID7dx430 mg/kg BID7dx420 mg/kg TID7dx4

Modeled population-average tumor growth curves for each dose group

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115 10 15 20 25 30 35 40

0.96

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1

1.005

1.01

Time (days)

Rel

ativ

e bo

dy w

eigh

tBody Weight Loss

drug

drug

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

Next dose causes more weight loss

Slow recovery phase: body weight growth based on Gompertz model

Maximum body weight lossis roughly 3.25%

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Developed Toxicity Model

)(),(

)(

)()()()()()(

)()()()(

)()()(ln)()(

4314

3213

21122

121101

txtxkdttdxtxtxk

dttdx

txktxtckdttdx

txtcktwtxdttdx

n

n

),0(~),()()()()(

0)()()(),exp()(

24321

040302001

uNutxtxtxtxtw

txtxtxuwtx

Dynamic model: system of ordinary differential equations

Initial conditions: with random effect for initial body weight

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135 10 15 20 25 30 35 40

0.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

Time (days)

Rel

ativ

e bo

dy w

eigh

t

5 10 15 20 25 30 35 400.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

Time (days)

Rel

ativ

e bo

dy w

eigh

t

5 10 15 20 25 30 35 400.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

Time (days)

Rel

ativ

e bo

dy w

eigh

t

5 10 15 20 25 30 35 400.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

Time (days)

Rel

ativ

e bo

dy w

eigh

t

5 10 15 20 25 30 35 400.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

Time (days)

Rel

ativ

e bo

dy w

eigh

t

5 10 15 20 25 30 35 400.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

Time (days)

Rel

ativ

e bo

dy w

eigh

t

5 10 15 20 25 30 35 400.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

Time (days)

Rel

ativ

e bo

dy w

eigh

tModeled vs. Observed for Groups

Model adequacy assessmentIndividual profiles vs. mean modeled body weight curves for each group

Control 15 mg/kg QD 30 mg/kg QD

60 mg/kg QD 15 mg/kg BID 30 mg/kg BID

20 mg/kg TID

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Toxicity Model Results

5 10 15 20 25 30 35 400.75

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

1.25

Time (days)

Mic

e bo

dy w

eigh

t (g)

Control15 mg/kg q7dx430 mg/kg q7dx460 mg/kg q7dx115 mg/kg BID7dx430 mg/kg BID7dx420 mg/kg TID7dx4

Modeled population-average animal weight curves for each dose group

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ML Parameter EstimationComputationally 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 SimulationSimulation 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

0 10 20 30 40 50 600

0.5

1

1.5

2

2.5

Time (days)

Tum

or w

eigh

t, kg

Control60 mg/kg q7dx420 mg/kg TID7dx4

Area under thetumor growth curve

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Efficacy-Toxicity PlotRed – QD, blue – BID, green – TID

0 2 4 6 8 10 12 14 16 18 2050

55

60

65

70

75

80

85

90

95

100

30 mg/kg BID7dx4

20 mg/kg TID7dx4

Toxicity (%)

Effi

cacy

(%)

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Pareto-Optimal SolutionsRed – QD, blue – BID, green – TID

0 2 4 6 8 10 12 14 16 18 2050

55

60

65

70

75

80

85

90

95

100

Toxicity (%)

Effi

cacy

(%)

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200 2 4 6 8 10 12 14 16 18 20

50

55

60

65

70

75

80

85

90

95

100

Toxicity (%)

Effi

cacy

(%)

Pareto-Optimal SolutionsRed – QD, blue – BID, green – TID

Zoomingthis part …

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Pareto-Optimal SolutionsRed – QD, blue – BID, green – TID

0 1 2 3 4 5 680

85

90

95

14,1

15,1

16,1

17,1

18,1

8,1

9,1

10,1

5,1

6,1

7,1

10,2

12,2

Toxicity (%)

Effi

cacy

(%)

Notation: dose in mg/kg, interval in days

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80

85

90

95

14,1

15,1

16,1

17,1

18,1

8,1

9,1

10,1

5,1

6,1

7,1

10,2

12,2

Toxicity (%)

Effi

cacy

(%)

Pareto-Optimal Solutions

Optimal regimens(QD, BID, TID)

Red – QD, blue – BID, green – TID

Notation: dose in mg/kg, interval in days

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Optimal Regimens

0 10 20 30 40 50 60-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time

log(

Tum

or w

eigh

t)

ControlQD 16 mg/kg every dayBID 9 mg/kg every dayTID 6 mg/kg every day

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Prediction Accuracy

Regimen: TID 6 mg/kg every day

0.75 0.80 0.85 0.90 0.95

05

1015

2025

30

Efficacy probability distribution

Efficacy

Den

sity

0.00 0.01 0.02 0.03 0.04

020

4060

80

Toxicity probability distribution

Toxicity

Den

sity

Methodology• Fisher’s information matrix computed numerically • Variance-covariance matrix for ML parameter estimates• Simulations performed to quantify prediction uncertainty

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Closer Look at QD Administration

0 1 2 3 4 5 6 7 8 9 1050

55

60

65

70

75

80

85

90

95

100

10,1

11,1

12,1

13,1

14,1

15,1 16,1

17,1 18,1

18,2

19,1

19,2

20,2

21,2

22,2

23,2

24,2 25,2

26,2 27,2

28,2 29,2 30,2

Toxicity (%)

Effi

cacy

(%)

Notation: dose in mg/kg, interval in days

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In Vivo Study: Dosing Until Day 28

0 10 20 30 40 50 60-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time

log(

Tum

or w

eigh

t)

Control16 mg/kg QD until day 2825 mg/kg Q2D until day 2835 mg/kg Q3D until day 2830 mg/kg BID7D x 4

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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