An Adaptive Design for Survival Studies with Subgroup Selection - - PowerPoint PPT Presentation

An Adaptive Design for Survival Studies with Subgroup Selection based on Predictive Biomarkers

RSS / MRC HTMR Workshop on Stratified Medicine Thomas Hamborg

t.hamborg@warwick.ac.uk

Warwick Medical School The University of Warwick Funded by AstraZeneca

30 June 2010

Introduction Adaptive Design Framework Survival Studies Discussion

Outline

1

Introduction

2

Adaptive Design Framework

Thomas Hamborg 2

Introduction Adaptive Design Framework Survival Studies Discussion

Outline

1

Introduction

2

Adaptive Design Framework

3

Survival Studies

Thomas Hamborg 2

Introduction Adaptive Design Framework Survival Studies Discussion

Outline

1

Introduction

2

Adaptive Design Framework

3

Survival Studies

4

Discussion

Thomas Hamborg 2

Introduction Adaptive Design Framework Survival Studies Discussion

Outline

1

Introduction

2

Adaptive Design Framework

3

Survival Studies

4

Discussion

Thomas Hamborg 2

Introduction Adaptive Design Framework Survival Studies Discussion

Problem Definition

Targeted Therapies in Oncology Tumours are heterogeneous ⇒ Only some patients may benefit Recruit patients with a certain type of cancer Might draw wrong conclusion or even miss an effective agent! Idea Presumption (uncertainty!) about a most beneficial subgroup Subgroup defined by biomarker: +ve patients vs. -ve patients Compare treatment effect in subgroups and adapt recruitment and efficacy claim

Thomas Hamborg 1

Introduction Adaptive Design Framework Survival Studies Discussion

Problem Definition

Targeted Therapies in Oncology Tumours are heterogeneous ⇒ Only some patients may benefit Recruit patients with a certain type of cancer Might draw wrong conclusion or even miss an effective agent! Idea Presumption (uncertainty!) about a most beneficial subgroup Subgroup defined by biomarker: +ve patients vs. -ve patients Compare treatment effect in subgroups and adapt recruitment and efficacy claim Method Seamless phase IIb/III clinical trial design

Thomas Hamborg 1

Introduction Adaptive Design Framework Survival Studies Discussion

Problem Definition

Targeted Therapies in Oncology Tumours are heterogeneous ⇒ Only some patients may benefit Recruit patients with a certain type of cancer Might draw wrong conclusion or even miss an effective agent! Idea Presumption (uncertainty!) about a most beneficial subgroup Subgroup defined by biomarker: +ve patients vs. -ve patients Compare treatment effect in subgroups and adapt recruitment and efficacy claim Method Seamless phase IIb/III clinical trial design

Thomas Hamborg 1

Introduction Adaptive Design Framework Survival Studies Discussion

Illustration: KRAS Biomarker

Panitumumab Metastatic colorectal cancer Monoclonal antibody directed at EGFR Subgroups KRAS mutant & wild-type [Amado et al., 2008]

Figure: Outcome for KRAS mutant tumour patients - Amado et al (2008) JCO, 26

Thomas Hamborg 2

Introduction Adaptive Design Framework Survival Studies Discussion

Illustration: KRAS Biomarker

Panitumumab Metastatic colorectal cancer Monoclonal antibody directed at EGFR Subgroups KRAS mutant & wild-type [Amado et al., 2008]

Figure: Outcome for KRAS wild-type tumour patients - Amado et al (2008) JCO, 26

Thomas Hamborg 2

Introduction Adaptive Design Framework Survival Studies Discussion

General Design Framework

Test Statistics Efficient score Z = ∂ℓ(0)

∂θ : cumulative measure of advantage of

experimental treatment E over control C (Observed) Fisher’s information V = −∂2ℓ(0)

∂θ2 : amount of

information on treatment difference contained in Z θ = Z

V - Measure of treatment difference

Under H0:

Z √ V ∼ N(0, 1)

(Score test) Here:

+ve patients: Z+,1, -ve patients: Z−,1, all patients: ZB,1 Final analysis ZS V correspondingly

Thomas Hamborg 3

Introduction Adaptive Design Framework Survival Studies Discussion

General Design Framework

Test Statistics Efficient score Z = ∂ℓ(0)

∂θ : cumulative measure of advantage of

experimental treatment E over control C (Observed) Fisher’s information V = −∂2ℓ(0)

∂θ2 : amount of

information on treatment difference contained in Z θ = Z

V - Measure of treatment difference

Under H0:

Z √ V ∼ N(0, 1)

(Score test) Here:

+ve patients: Z+,1, -ve patients: Z−,1, all patients: ZB,1 Final analysis ZS V correspondingly

Thomas Hamborg 3

Introduction Adaptive Design Framework Survival Studies Discussion

Design Illustration

Interim

+ v e

• ve

+ v e

select +ve no sel.

• ve

+ v e

Pr(Z>=c & no sel.) Pr(Z>=c & sel. +ve) V1 V2 V1 Thomas Hamborg 4

Introduction Adaptive Design Framework Survival Studies Discussion

Design Illustration

Interim

+ v e

• ve

+ v e

select +ve no sel.

• ve

+ v e

Pr(Z>=c & no sel.) Pr(Z>=c & sel. +ve) V1 V2 V1 Thomas Hamborg 4

Introduction Adaptive Design Framework Survival Studies Discussion

Design Illustration

Interim

+ v e

• ve

+ v e

select +ve no sel.

• ve

+ v e

Pr(Z>=c & no sel.) Pr(Z>=c & sel. +ve) V1 V2 V1

Cochran’s Q test Q =

m

• i=1

(ˆ θi − ˆ θ)2ωi In terms of Z and V: Q = Z+,1V−,1 − Z−,1V+,1

• V+,1 + V−,1
• V+,1V−,1

Subgroup selection if: Q ∼ N(0, 1) ≥ k

Thomas Hamborg 4

Introduction Adaptive Design Framework Survival Studies Discussion

Design Illustration

Interim

+ v e

• ve

+ v e

select +ve no sel.

• ve

+ v e

Pr(Z>=c & no sel.) Pr(Z>=c & sel. +ve) V1 V2 V1

Cochran’s Q test Q =

m

• i=1

(ˆ θi − ˆ θ)2ωi In terms of Z and V: Q = Z+,1V−,1 − Z−,1V+,1

• V+,1 + V−,1
• V+,1V−,1

Subgroup selection if: Q ∼ N(0, 1) ≥ k

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Introduction Adaptive Design Framework Survival Studies Discussion

Interim Analysis in Detail

Futility Stopping Criterion

• Cond. power (CP) approach

CP stopping unlikely if early in study ⇒ stop if: CPθR(V) ≤ 1 − βCP

• r

Zi,1 ≤ 0, i ∈ {+, B} for respective interim decision Upper Selection Limit Criterion Undesireable to select if drug has certain effect in -ve patients Do not select +ve patients if: ˆ θ−,1 ≥ τθR, 0 < τ ≤ λ Natural choice τ = 1

continue +ve no selection

Z Z

+ , 1

• ,1

futility stop

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Introduction Adaptive Design Framework Survival Studies Discussion

Interim Analysis in Detail

Futility Stopping Criterion

• Cond. power (CP) approach

CP stopping unlikely if early in study ⇒ stop if: CPθR(V) ≤ 1 − βCP

• r

Zi,1 ≤ 0, i ∈ {+, B} for respective interim decision Upper Selection Limit Criterion Undesireable to select if drug has certain effect in -ve patients Do not select +ve patients if: ˆ θ−,1 ≥ τθR, 0 < τ ≤ λ Natural choice τ = 1

continue -ve continue +ve no selection

Z Z

+ , 1

• ,1

futility stop

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Introduction Adaptive Design Framework Survival Studies Discussion

Power Requirements

Power Requirement I Study-wise type-I error rate Pr(ZS ≥ c | θ+ = θ− = 0) = α Power Requirement II Pr(ZS ≥ c ∩ no sel. | θ+ = θ− = θR) = 1 − βB = PowerB θR reference improvement

Interim

+ v e

• ve

+ v e

select +ve no sel.

• ve

+ v e

Pr(Z>=c) = type-I error rate V1 V2 V1

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Introduction Adaptive Design Framework Survival Studies Discussion

Power Requirements

Power Requirement I Study-wise type-I error rate Pr(ZS ≥ c | θ+ = θ− = 0) = α Power Requirement II Pr(ZS ≥ c ∩ no sel. | θ+ = θ− = θR) = 1 − βB = PowerB θR reference improvement Power Requirement III Pr(ZS ≥ c ∩ sel +ve | θ+ = λθR, θ− = 0) = 1 − β+ = Power+ λ ≥ 1 ⇒ demand larger effect for selection

Interim

+ v e

• ve

+ v e

select +ve no sel.

• ve

+ v e

Pr(Z>=c & no sel.)=Power V1 V2 V1

B

Thomas Hamborg 6

Introduction Adaptive Design Framework Survival Studies Discussion

Power Requirements

Power Requirement I Study-wise type-I error rate Pr(ZS ≥ c | θ+ = θ− = 0) = α Power Requirement II Pr(ZS ≥ c ∩ no sel. | θ+ = θ− = θR) = 1 − βB = PowerB θR reference improvement Power Requirement III Pr(ZS ≥ c ∩ sel +ve | θ+ = λθR, θ− = 0) = 1 − β+ = Power+ λ ≥ 1 ⇒ demand larger effect for selection

Interim

+ v e

• ve

+ v e

select +ve no sel.

• ve

+ v e

Pr(Z>=c & sel. +ve)=Power V1 V2 V1

+

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Introduction Adaptive Design Framework Survival Studies Discussion

Calculation of Design Variables

Score function properties:

1

Approximately Z ∼ N(θV, V)

2

Independent increment structure Numerical root finding procedure For each Power Requirement:

Pr(ZS ≥ c) = X

i u−

i

Z

l−

i

u+

i

Z

l+

i

 1 − Φ `c − (z·) − θj(VS − V·,1) √VS − V·,1 ´ff f(z+)f(z−)dz+dz−, where f(z) =

1 √ V φ

“

z−θV √ V

”

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Introduction Adaptive Design Framework Survival Studies Discussion

Design Framework for Survival Outcome

Superiority Trial Outcome: time to unfavourable event SE(t), SC(t) survival probabilities H0 : θ = 0 vs H1 : θ > 0 Proportional Hazard Model Assumption: hE(t) = ψhC(t), t > 0 Parameterisation: θ = − log (hE(t)/hC(t))

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Introduction Adaptive Design Framework Survival Studies Discussion

Design Framework for Survival Outcome

Superiority Trial Outcome: time to unfavourable event SE(t), SC(t) survival probabilities H0 : θ = 0 vs H1 : θ > 0 Proportional Hazard Model Assumption: hE(t) = ψhC(t), t > 0 Parameterisation: θ = − log (hE(t)/hC(t)) Exponential assumption Survival times Weib(γi, 1) ≡ EXP(γi) distributed Loss to follow-up EXP(τ) distributed Analysis: log-rank test: Z2/V or Z/ √ V ∼ N(0, 1)

Thomas Hamborg 8

Introduction Adaptive Design Framework Survival Studies Discussion

Design Framework for Survival Outcome

Superiority Trial Outcome: time to unfavourable event SE(t), SC(t) survival probabilities H0 : θ = 0 vs H1 : θ > 0 Proportional Hazard Model Assumption: hE(t) = ψhC(t), t > 0 Parameterisation: θ = − log (hE(t)/hC(t)) Exponential assumption Survival times Weib(γi, 1) ≡ EXP(γi) distributed Loss to follow-up EXP(τ) distributed Analysis: log-rank test: Z2/V or Z/ √ V ∼ N(0, 1)

Thomas Hamborg 8

Introduction Adaptive Design Framework Survival Studies Discussion

Design Framework for Survival Outcome II

Design specification Specify trial in terms of time units (weeks) and no. patients Conduct trial in terms of V Recruit +ve and -ve patients according to population proportion At the design stage calculate: V ≈ e/4 (1:1 allocation ratio) Expected no. of events e = aGpe ⇒ determine pe expected prop. deaths

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Introduction Adaptive Design Framework Survival Studies Discussion

Example KRAS study

Pre-specified values: Power req.: α = 0.025, 1 − βB = 0.9, 1 − β+ = 0.9 Study duration: recruit 75 weeks, follow up 50 weeks, interim at week 50

• Treat. effect: SC(t0) = 0.10, SE(t0) = 0.20, t0 = 20, λ = 2.6

Search procedure results:

S+

E (t0)

a n n+ k c V1,+ V1,− VS 0.407 4.9 368 243 1.988 2.233 20.05 18.73 58.250

Table: Calculation of design variables for KRAS biomarker study

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Introduction Adaptive Design Framework Survival Studies Discussion

Example KRAS study

Pre-specified values: Power req.: α = 0.025, 1 − βB = 0.9, 1 − β+ = 0.9 Study duration: recruit 75 weeks, follow up 50 weeks, interim at week 50

• Treat. effect: SC(t0) = 0.10, SE(t0) = 0.20, t0 = 20, λ = 2.6

Search procedure results:

S+

E (t0)

a n n+ k c V1,+ V1,− VS 0.407 4.9 368 243 1.988 2.233 20.05 18.73 58.250

Table: Calculation of design variables for KRAS biomarker study

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Introduction Adaptive Design Framework Survival Studies Discussion

Example: KRAS study

4 8 12 16 20 24 28 32 36 40 44 48 10 20 30 40 50 60 70 80 90 100 Time (weeks) Proportion Event Free (%)

|||| | | || | | | | | | || | || | | | | | |

BSC alone

• Panit. + BSC

Figure: Interim outcome for mutant type

4 8 12 16 20 24 28 32 36 40 44 10 20 30 40 50 60 70 80 90 100 Time (weeks) Proportion Event Free (%)

||| | | | | | | | | | | | | | || | | | || | ||| | | || | | | | | | | |

BSC alone

• Panit. + BSC

Figure: Interim outcome for wild type

252 patients recruited at interim: Q = 2.958 ⇒ select wild-type Recruit remaining patients: ZS = Z+,1 + Z2 = 38.9, VS = V1,+ + V2 = 47.947 p-value 0.000237 ⇒ Panitumumab significantly better for wild-type patients

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Introduction Adaptive Design Framework Survival Studies Discussion

Simulation study

+ve adaptive design S+

E (t0)

S−

E (t0)

SC(t0) n selection EPO EPB EP+ 0.25 0.25 0.25 358 3.13% 0.049 0.043 0.006 0.40 0.40 0.25 358 3.5% 0.9329 0.8989 0.034 0.671 0.25 0.25 358 87.68% 0.9886 0.1119 0.8767

Table: Simulation results for the adaptive method. EP denotes the estimated power

based on 20,000 simulated trials.

2 parallel trials S+

E (t0)

S−

E (t0)

EPO EPB EP+ EP− 0.25 0.25 0.048 0.001 0.025 0.023 0.40 0.40 0.839 0.360 0.600 0.599 0.671 0.25 0.999 0.025 0.999 0.025

Table: Simulation results for 2 separate trials for +ve and -ve patients.

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Introduction Adaptive Design Framework Survival Studies Discussion

Simulation study

+ve adaptive design S+

E (t0)

S−

E (t0)

SC(t0) n selection EPO EPB EP+ 0.25 0.25 0.25 358 3.13% 0.049 0.043 0.006 0.40 0.40 0.25 358 3.5% 0.9329 0.8989 0.034 0.671 0.25 0.25 358 87.68% 0.9886 0.1119 0.8767

Table: Simulation results for the adaptive method. EP denotes the estimated power

based on 20,000 simulated trials.

2 parallel trials S+

E (t0)

S−

E (t0)

EPO EPB EP+ EP− 0.25 0.25 0.048 0.001 0.025 0.023 0.40 0.40 0.839 0.360 0.600 0.599 0.671 0.25 0.999 0.025 0.999 0.025

Table: Simulation results for 2 separate trials for +ve and -ve patients.

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Introduction Adaptive Design Framework Survival Studies Discussion

Simulation study

+ve adaptive design S+

E (t0)

S−

E (t0)

SC(t0) n selection EPO EPB EP+ 0.25 0.25 0.25 358 3.13% 0.049 0.043 0.006 0.40 0.40 0.25 358 3.5% 0.9329 0.8989 0.034 0.671 0.25 0.25 358 87.68% 0.9886 0.1119 0.8767

Table: Simulation results for the adaptive method. EP denotes the estimated power

based on 20,000 simulated trials.

2 parallel trials S+

E (t0)

S−

E (t0)

EPO EPB EP+ EP− 0.25 0.25 0.048 0.001 0.025 0.023 0.40 0.40 0.839 0.360 0.600 0.599 0.671 0.25 0.999 0.025 0.999 0.025

Table: Simulation results for 2 separate trials for +ve and -ve patients.

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Introduction Adaptive Design Framework Survival Studies Discussion

Simulation study

+ve adaptive design S+

E (t0)

S−

E (t0)

SC(t0) n selection EPO EPB EP+ 0.25 0.25 0.25 358 3.13% 0.049 0.043 0.006 0.40 0.40 0.25 358 3.5% 0.9329 0.8989 0.034 0.671 0.25 0.25 358 87.68% 0.9886 0.1119 0.8767

Table: Simulation results for the adaptive method. EP denotes the estimated power

based on 20,000 simulated trials.

2 parallel trials S+

E (t0)

S−

E (t0)

EPO EPB EP+ EP− 0.25 0.25 0.048 0.001 0.025 0.023 0.40 0.40 0.839 0.360 0.600 0.599 0.671 0.25 0.999 0.025 0.999 0.025

Table: Simulation results for 2 separate trials for +ve and -ve patients.

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Introduction Adaptive Design Framework Survival Studies Discussion

Simulation study

+ve adaptive design S+

E (t0)

S−

E (t0)

SC(t0) n selection EPO EPB EP+ 0.25 0.25 0.25 358 3.13% 0.049 0.043 0.006 0.40 0.40 0.25 358 3.5% 0.9329 0.8989 0.034 0.671 0.25 0.25 358 87.68% 0.9886 0.1119 0.8767

Table: Simulation results for the adaptive method. EP denotes the estimated power

based on 20,000 simulated trials.

2 parallel trials S+

E (t0)

S−

E (t0)

EPO EPB EP+ EP− 0.25 0.25 0.048 0.001 0.025 0.023 0.40 0.40 0.839 0.360 0.600 0.599 0.671 0.25 0.999 0.025 0.999 0.025

Table: Simulation results for 2 separate trials for +ve and -ve patients.

Thomas Hamborg 12

Introduction Adaptive Design Framework Survival Studies Discussion

Simulation study

+ve adaptive design S+

E (t0)

S−

E (t0)

SC(t0) n selection EPO EPB EP+ 0.25 0.25 0.25 358 3.13% 0.049 0.043 0.006 0.40 0.40 0.25 358 3.5% 0.9329 0.8989 0.034 0.671 0.25 0.25 358 87.68% 0.9886 0.1119 0.8767

Table: Simulation results for the adaptive method. EP denotes the estimated power

based on 20,000 simulated trials.

2 parallel trials S+

E (t0)

S−

E (t0)

EPO EPB EP+ EP− 0.25 0.25 0.048 0.001 0.025 0.023 0.40 0.40 0.839 0.360 0.600 0.599 0.671 0.25 0.999 0.025 0.999 0.025

Table: Simulation results for 2 separate trials for +ve and -ve patients.

Thomas Hamborg 12

Introduction Adaptive Design Framework Survival Studies Discussion

Impact of Design Changes I

Analysis type τ λ n k c No futility stop

• 3

352 1.8442 1.6980 Futility stop

• 3

358 1.8667 1.6849 Fut stop & upper lim 3 3 358 1.8667 1.6836 Fut stop & upper lim 1 3 372 1.7646 1.6934 Fut stop & upper lim 0.70 3 468 1.3638 1.7304

Table: Impact of interim decision rules on design parameter - standard scenario

Futility stopping rule is cheap Upper selection limit can be cheap Lower bound τ ≈ 0.60

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Introduction Adaptive Design Framework Survival Studies Discussion

Impact of Design Changes I

Analysis type τ λ n k c No futility stop

• 3

352 1.8442 1.6980 Futility stop

• 3

358 1.8667 1.6849 Fut stop & upper lim 3 3 358 1.8667 1.6836 Fut stop & upper lim 1 3 372 1.7646 1.6934 Fut stop & upper lim 0.70 3 468 1.3638 1.7304

Table: Impact of interim decision rules on design parameter - standard scenario

Futility stopping rule is cheap Upper selection limit can be cheap Lower bound τ ≈ 0.60

Thomas Hamborg 13

Introduction Adaptive Design Framework Survival Studies Discussion

Impact of Design Changes I

Analysis type τ λ n k c No futility stop

• 3

352 1.8442 1.6980 Futility stop

• 3

358 1.8667 1.6849 Fut stop & upper lim 3 3 358 1.8667 1.6836 Fut stop & upper lim 1 3 372 1.7646 1.6934 Fut stop & upper lim 0.70 3 468 1.3638 1.7304

Table: Impact of interim decision rules on design parameter - standard scenario

Futility stopping rule is cheap Upper selection limit can be cheap Lower bound τ ≈ 0.60

Thomas Hamborg 13

Introduction Adaptive Design Framework Survival Studies Discussion

Impact of Design Changes I

Analysis type τ λ n k c No futility stop

• 3

352 1.8442 1.6980 Futility stop

• 3

358 1.8667 1.6849 Fut stop & upper lim 3 3 358 1.8667 1.6836 Fut stop & upper lim 1 3 372 1.7646 1.6934 Fut stop & upper lim 0.70 3 468 1.3638 1.7304

Table: Impact of interim decision rules on design parameter - standard scenario

Futility stopping rule is cheap Upper selection limit can be cheap Lower bound τ ≈ 0.60

Thomas Hamborg 13

Introduction Adaptive Design Framework Survival Studies Discussion

Impact of Design Changes II

*** * * * * * * * 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1.0 1.2 1.4 1.6 1.8 2.0

c, k for varying upper selection boundaries

τ c + + + + + + + + + +

*

+

c k

• 0.75

0.80 0.85 0.90 0.95 300 350 400 450 500 550

Varying one Power requirement respectively

• req. Power

n

• 1 − βB

1 − βve

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Introduction Adaptive Design Framework Survival Studies Discussion

Comments

Multiple interim analyses Can be incorporated at design stage Impose linear relationship on c1, . . . , cn Family-wise error rate Method controls FWER in strong sense

Thomas Hamborg 15

Introduction Adaptive Design Framework Survival Studies Discussion

Comments

Multiple interim analyses Can be incorporated at design stage Impose linear relationship on c1, . . . , cn Family-wise error rate Method controls FWER in strong sense Discrete approximation Anticipate SC(ti), i = 1, . . . , G + F SE(ti) found from θR and proportional hazards

Thomas Hamborg 15

Introduction Adaptive Design Framework Survival Studies Discussion

Comments

Multiple interim analyses Can be incorporated at design stage Impose linear relationship on c1, . . . , cn Family-wise error rate Method controls FWER in strong sense Discrete approximation Anticipate SC(ti), i = 1, . . . , G + F SE(ti) found from θR and proportional hazards Non uniform recruitment rate Optimal recruitment pattern is u-shaped

Thomas Hamborg 15

Introduction Adaptive Design Framework Survival Studies Discussion

Comments

Multiple interim analyses Can be incorporated at design stage Impose linear relationship on c1, . . . , cn Family-wise error rate Method controls FWER in strong sense Discrete approximation Anticipate SC(ti), i = 1, . . . , G + F SE(ti) found from θR and proportional hazards Non uniform recruitment rate Optimal recruitment pattern is u-shaped

Thomas Hamborg 15

Introduction Adaptive Design Framework Survival Studies Discussion

Summary

1

Developed a method that allows to draw inference for all patients in the trial or a subgroup

2

Flexible approach that is useful if uncertainty exists about target population in late stage trial

3

Greater power than fixed sample trial designs in appropriate scenario and allows to draw more accurate conclusion

4

Phase IIb/III design?

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Introduction Adaptive Design Framework Survival Studies Discussion

References

Amado, R. et al. (2008). Wild-type kras is required for panitumumab efficacy in patients with metastatic colorectal cancer. Journal of Clinical Oncology, 26(10):1626–1634. Stallard, N. and Todd, S. (2003). Sequential designs for phase iii clinical trials incorporating treatment selection. Stat Med, 22(5):689–703. Whitehead, J. (1997). The Design and Analysis of Sequential Clinical Trials. Statistics in Practice. Wiley, Chichester, revised 2nd edition.

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