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Adaptive Designs for Dose Ranging Trials:

ADRS WG Simulation study

Vlad Dragalin Quintiles Innovation

RTP, NC, U.S.A.

KOL Lecture Series on Adaptive Designs July 9th 2010

V. Dragalin | Adaptive Designs for Dose Ranging Trials

Outline

–Dose-ranging studies

–Adaptive model-based designs

–Statistical Operational Characteristics

–Conclusion

2

Simulation Study: Complete Summary

3


To appear in: Statistics in Biopharmaceutical Research, 2010

Dose-Ranging Studies

– The overall goal of dose-ranging studies is to establish the existence, nature and extent of dose effect: • Detecting DR: evaluate if there is evidence of activity associated with the

drug, represented by a change in clinical response resulting from a change in dose (PoC);

• Identifying clinical relevance: if PoC is established, determine if a pre-defined clinically relevant response (compared to the placebo response) can be obtained within the observed dose range;

• Selecting a target dose: when the previous goal is met, select the dose to be brought into the confirmatory phase, the so-called target dose;

• Estimating the dose response: finally, estimate the dose-response profile within the observed dose range.

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New Adaptive Designs

– AMCP-Mod – Adaptive MCP-Mod approach combining multiple comparisons

and modeling (Bornkamp, Bretz, Pinheiro)

– DcoD – D-optimal followed by a c-optimal design based on sigmoid Emax

model (Dragalin, Padmanabhan)

– IntR – Bayesian design minimizing average variance of all LS-estimates for

“interesting part” of dose-response curve (Miller)

– MultObj – Multi-objective optimal design incorporating 2nd order moments and

based on inverse quadratic model (Smith)

– T-Stat – Dose-adaptive design based on t-statistics (Patel, Perevozskaya)

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AMCP-Mod Design

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Adaptive MCP-Mod Design

– Extension to a response-adaptive version of the MCP-Mod methodology using • optimal design theory to allocate new cohorts of patients

• posterior model probabilities and posterior parameter estimates to update initial guesses

– AMCP-Mod Before Trial Start

1. Select the candidate models (two logistic and one beta models)

2. Select “best guesses” for , m = 1, . . . ,M

3. Choose prior model probabilities p(Mm)

4. Choose prior for

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Adaptive MCP-Mod Design at IA

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Adaptive MCP-Mod Design at Trial End

1. Calculate optimal contrasts and critical value using MCP

2. Select one of the significant models for dose-response

and MED estimation

3. Fit dose-response model and estimate MED

– Bayesian model is only used for updating the design;

the classical MCP-Mod procedure is wrapped around this.

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DcoD: Adaptive Dc-optimal Design

– Working Model Sigmoid Emax model (4 parameter logistic)

dose

Mea

n R

espo

nse

0 2 4 6 8

-1.5

-1.0

-0.5

0.0

0 2 4 6 8

-1.5

-1.0

-0.5

0.0

t4=1t4=2t4=4t4=10

Dragalin et al

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V. Dragalin | To adapt or to confirm: what is the question?|

St. Petersburg, Russia

Sigmoid Emax Fit

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D- and c-optimal Designs

A design is locally D-optimal (LDoD) if and only if

A design is locally c-optimal (LcoD) if it minimizes

is the Fisher information matrix at dose x

is the normalized information

matrix for design

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D- and c-Optimal Designs

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Dc-Optimal Designs

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Adaptive Dc-optimal Design

–For 2 adaptations:

• 1/3rd of the subjects allocated according to a fixed 5-

dose design

• Parameters are estimated –> next 1/3rd allocated

according to augmented LDoD

• Parameters are re-estimated –> final 1/3rd allocated

according to augmented LcoD

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IntR Design

– Estimation of the interesting part of the

dose-response curve

– Working model: sigmoid Emax

– Inference based on LS estimates from

this sigmoid Emax model

– Minimize average variance of all LS-

estimates for

f(x) - f(0) with xδ<x<8.

xδ is dose with effect 1 compared to

placebo

– “Detecting Dose-Response”:

trend test used to test null hypothesis

of flat dose-response

xδ

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IntR Design

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MULTOBJ Design

– Primary focus within MULTOBJ criterion is MED estimation

– Lower weighted components also included related to POC and EDp

(for a range of p’s)

– Weights chosen to reflect importance of component criteria

– MULTOBJ criterion is essentially an extended form of S-optimality

but incorporating 2nd order moments and with MSE in place of

variances

– Working Model: Non-Monotonic 4 parameter Inverse Quadratic

model

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T-statistic design

– Non-parametric design adaptive approach

– Concentrates dose allocations around the dose with target (pbo-adjusted) response level

– Patients are randomized sequentially in cohorts of fixed size; all assigned to the same dose or pbo (e.g. 3:1)

– Dose selection is adaptive and driven by the value of t-statistic at the last dose studied (Ti):

• Escalate to xi+1 if Ti ≥∆ • Stay at xi if -∆<Ti≤∆ • De-escalate to xi-1 if Ti ≤-∆ • Ti is standardized pbo-adjusted mean response at dose xi • ∆ is a design parameter

Ivanova A., Bolognese JA, Perevozskaya I. Adaptive dose-finding based on t-statistic in dose-response trial. Stat in Medicine, 2008; 27:1581-1592 19


Simulation Study: Assumptions

– Doses:

• 9 doses: {0,1,2,3,4,5,6,7,8}

• 5 doses: {0,2,4,6,8}

– Endpoint: change from baseline in VAS score

– Clinically meaningful difference: –1.3

– Variance: 4.5

– Sample Size: 250

– Number of adaptations: 0,1,2,4,9

– Total of 56 combinations

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Simulation Scenarios

1. Linear: y = -(1.65/8) d + ε

2. Umbrella: y = -(1.65/3)d + (1.65/36)d2 + ε

3. Sigmoid Emax: y = -1.70 d5/(45 + d5) + ε

4. Emax: y = -1.81 d/(0.79 + d) + ε

5. Emax low: y = -1.14 d/(0.79 + d) + ε

6. Explicit: y = {0, -1.29, -1.35, -1.42, -1.5, -1.6, -1.63, -1.65, -1.65} + ε

7. Flat: y = ε.

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Simulation Scenarios

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Performance metrics

– Statistical significance level

– Probability of detecting dose response: Pr(DR)

– Probability of identifying clinically relevant dose: Pr(dose)

– Target Dose selection • Distribution of selected doses

• Summary statistics (mean and standard deviation) for percentage difference from target

• pDiff = 100( d - dtarg)/dtarg

– Dose Response estimation: • summary statistics for absolute prediction error

– Subject Allocation pattern

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ANOVA

aMCPMod

DcoD

IntR

t-test

MULTOB

0 1 2 3 4 5 6

0 IAs5 doses

1 IAs5 doses

0 1 2 3 4 5 6

2 IAs5 doses

4 IAs5 doses

0 1 2 3 4 5 6

9 IAs5 doses

ANOVA

aMCPMod

DcoD

IntR

t-test

MULTOB

0 IAs9 doses

0 1 2 3 4 5 6

1 IAs9 doses

2 IAs9 doses

0 1 2 3 4 5 6

4 IAs9 doses

9 IAs9 doses

Significance level

Detecting Dose-Response: type I error

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ANOVA

aMCPMod

DcoD

IntR

t-test

MULTOB

95 96 97 98 99 100

explicit

94 96 98 100

umbrella

85 90 95 100

linear

ANOVA

aMCPMod

DcoD

IntR

t-test

MULTOB

94 95 96 97 98 99 100

Emax

90 92 94 96 98 100

Sig Emax

65 70 75 80 85 90

Emax low

Pr(DR) (%)

9 doses0 IAs 1 IAs 2 IAs 4 IAs 9 IAs

Detecting D-R: power for 9 doses

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ANOVA

aMCPMod

DcoD

IntR

t-test

MULTOB

0.1 0.3

0 IAs5 doses

0.1 0.3

1 IAs5 doses

0.2 0.4

2 IAs5 doses

0.1 0.3

4 IAs5 doses

0.1 0.3

9 IAs5 doses

ANOVA

aMCPMod

DcoD

IntR

t-test

MULTOB

0 1 2 3 4

0 IAs9 doses

0 1 2 3 4

1 IAs9 doses

0 1 2 3 4

2 IAs9 doses

0 1 2 3 4

4 IAs9 doses

0 1 2 3 4

9 IAs9 doses

Pr(dose | flat DR) (%)

Identifying clinically-relevant dose: flat D-R

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ANOVA

aMCPMod

DcoD

IntR

t-test

MULTOB

84 86 88 90 92 94

explicit

80 85 90

umbrella

75 80 85 90

linear

ANOVA

aMCPMod

DcoD

IntR

t-test

MULTOB

86 88 90 92 94

Emax

88 90 92 94 96 98

Sig Emax

30 40 50 60

Emax low

Pr(dose) (%)

9 doses0 IAs 1 IAs 2 IAs 4 IAs 9 IAs

Identifying clinically-relevant dose

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Selecting Target Dose: 9 doses

ANOVA

aMCPMod

DcoD

IntR

t-test

MULTOB

65 70 75 80

explicit

30 35 40 45 50

umbrella

30 35 40 45

linear

ANOVA

aMCPMod

DcoD

IntR

t-test

MULTOB

35 40 45 50

Emax

50 55 60 65 70

Sig Emax

Correct target interval probability (%)

0 IAs1 IAs2 IAs4 IAs9 IAs

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0

10

20

30

40

2 4 6 8

ANOVA0 IAs

aMCPMod0 IAs

2 4 6 8

DcoD0 IAs

IntR0 IAs

2 4 6 8

t-test0 IAs

MULTOB0 IAs

ANOVA1 IAs

aMCPMod1 IAs

DcoD1 IAs

IntR1 IAs

t-test1 IAs

0

10

20

30

40

MULTOB1 IAs

0

10

20

30

40

ANOVA2 IAs

aMCPMod2 IAs

DcoD2 IAs

IntR2 IAs

t-test2 IAs

MULTOB2 IAs

ANOVA4 IAs

aMCPMod4 IAs

DcoD4 IAs

IntR4 IAs

t-test4 IAs

0

10

20

30

40

MULTOB4 IAs

0

10

20

30

40

ANOVA9 IAs

2 4 6 8

aMCPMod9 IAs

DcoD9 IAs

2 4 6 8

IntR9 IAs

t-test9 IAs

2 4 6 8

MULTOB9 IAs

Dose selected

% T

rials

Sig Emax, 9 dosesSelecting a target dose: distribution

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-2.0

-1.5

-1.0

-0.5

0.0

0.5

0 2 4 6 8

ANOVA aMCPMod

0 2 4 6 8

DcoD

IntR

0 2 4 6 8

t-test

-2.0

-1.5

-1.0

-0.5

0.0

0.5

MULTOB

Dose

Ave

rage

pre

dict

ion

erro

r

Sig Emax, nIA = 9, 9 doses

5%, 95% 25%, 75% 50%

Estimating D-R curve

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Summary and Conclusions

–Detecting DR is considerably easier than estimating it

–Current sample sizes used for D-R studies are inadequate for dose selection and D-R estimation

–Adaptive methods lead to gain in power to detect DR + precision of target dose selection + DR estimation compared to traditional ANOVA design

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– None of the designs was uniformly superior to the others • All 5 designs performed well with respect to achieving specific

objective they were designed for:

– IntR, did well for DR estimation

– AMCPMod, t-test: did well for dose selection

– MULTOB and DcoD: did well for both objectives

– The appeal of a particular design will depend on • the specific goal of the trial

• and the set of plausible DR scenarios, because the latter affects relative performance of the designs

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– Due to complexity of the designs, operating characteristics can be assessed only via simulations during the DR trial planning stage

– Need software which is sufficiently flexible, comprehensive and extensible to allow in-depth exploration of various methods to determine design most appropriate for the study

– We investigated impact of only one component of AD: allocation rule and adaptation based on efficacy endpoint only

– The approach can be extended to examine other sources of “adaptivity”: • sampling rule,

• early stopping for futility/efficacy,

• information-driven SS determination,

• using early data through longitudinal modeling

• incorporating safety endpoint 33


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