Efficiency of Promising Zone Designs

Cyrus Mehta

Joint with Sam Hsiao & Lingyun Liu

Cytel Inc

FDA and Industry Workshop 2017FDA and Industry, 9/26/17 1

Outline

• Motivating example from oncology trial

• Proposed promising zone adaptive design

• Efficiency comparisons with:

• Optimal adaptive design (Jennison & Turnbull 2015)

• Constrained optimal design

• Conclusions

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Pivotal Trial in Oncology at a Small Biotech

• Indication - Advanced pancreatic cancer

• Endpoint – Progression free survival

• Effect size – HR from 0.67 (expected) to 0.75 (still clinically meaningful)

• Power

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𝜽 = 𝟎. 𝟐𝟗 𝜽 = 𝟎. 𝟒

N = 280 68% 92%

N = 500 90% 99%

HR = 0.75

𝜽 = -ln(HR)=0.29

HR = 0.67

𝜽 = -ln(HR)=0.4

Considerations for Adaptive Design (AD)

• Difficult to get up-front investment to ensure 90% power at 𝜽 = 𝟎. 𝟐𝟗 (requires 500 PFS events)

• Stakeholders expressing conditional utility:

o Initial investment sufficient for 𝜽 = 𝟎.4 (HR=0.67)

o Additional investment linked to interim milestone

o Must attain ≥ 80% conditional power at 𝜽 = 𝟎. 𝟐𝟗(HR=0.75) to justify additional investment

• Early efficacy stopping not of much interest, need adequate drug profile and credibility

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Promising Zone Adaptive Design (AD)

• Plan 𝑛2 = 𝟐𝟖𝟎; interim at 𝑛1 = 𝟏𝟒𝟎; maximum 𝑛𝑚𝑎𝑥 = 𝟒𝟐𝟎

• Construct a SSR rule consisting of a promising zone and a sample size 𝒏𝟐

∗ (𝒛𝟏) for every z1 inside the promising zone:

Maximize 𝐶𝑃0.29 𝑧1, 𝑛2∗ in promising zone subject to

Constraint 1: 𝑛2 ≤ 𝑛2∗ ≤ 𝑛𝑚𝑎𝑥 = 420

Constraint 2: 𝐶𝑃0.29 𝑧1, 𝑛2∗ ≥ 80%

Constraint 3: 𝐶𝑃0.29 𝑧1, 𝑛2∗ ≤ 90%

• No sample size modification outside of promising zone

• Testing uses CHW combination statistic

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Conditional Power if no SSR

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Promising

Zone

Conditional Power if SSR up to nmax=420

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Conditional Power and Prob(zone): nmax=420

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Prob(zone)=43%Prob(zone)=30% Prob(zone)=27%

Conditional Power and Prob(zone): nmax=500

Prob(zone)=20% Prob(zone)=26%

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• Sponsor likes this SSR rule

• Even in the pessimistic case, where q=0.29:

• If SSR is invoked, ≥ 80% power is guaranteed

• But how does this rule compare with the “Optimal” SSR rule as defined by J&T?

Optimal SSR Rule: Has the best unconditional power among

all SSR rules with the same average sample size

But is this SSR rule optimal?

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• SSR Rule: Sample size rule 𝑛2∗(𝑧1) satisfies:

Objective: Maximize 𝐶𝑃𝜃 𝑧1, 𝑛2∗ − 𝛾𝑛2

∗ for every z1

Constraint: 𝑛2 ≤ 𝑛2∗ ≤ 𝑛𝑚𝑎𝑥

where 𝛾 is a constant “exchange rate” between CP and N

• Optimality property: By integrating the objective with respect to fq(z1):

• = Pwr(q) – gE(N) is maximized

• Highest possible unconditional power among SSR rules with matching nmax and E(N)

• Benchmarking tool for adaptive designs

Jennison Turnbull (JT) Optimal SSR Rule

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* *

θ 1 2 2 θ 1 1max CP (z ,n )-γn f ( )dzz

Efficiency Comparison with JT Optimal Design

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• Method: For each 𝜃, compare unconditional power of AD against JT design with 𝛾 chosen so expected sample size matches AD

Efficiency Comparison with JT Optimal Design

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• Comparison at 𝜃 = 0.29

Pr(zone)=0.54

Pr(zone)=0.43

Does it meet the sponsor’s objectives?

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Conclusions

• JT Optimal Design gains 2-3% unconditional power

• Requirement of high CP at lowest meaningful 𝜃 is not met by JT Design

Constrained JT Rule

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• Impose an additional CP constraint on the JT SSR rule.

• Constrained SSR Rule: Final sample size 𝑛2∗ determined by:

Objective: Maximize 𝐶𝑃𝜃 𝑧1, 𝑛2∗ − 𝛾𝑛2

∗

Constraint 1: 𝑛2 ≤ 𝑛2∗ ≤ 𝑛𝑚𝑎𝑥

Constraint 2: 𝐶𝑃0.29 𝑧1, 𝑛2∗ ≥ 80%

• Optimality property: Highest unconditional power among promising zone designs satisfying same constraints and matching E(N)

Comparison of AD and Constrained JT

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• Method: For each 𝜃, compare unconditional power of AD against constrained JT Design with 𝛾 chosen so expected sample size matches AD

Comparison of AD and Constrained JT

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• Comparison at 𝜃 = 0.29

Comparison AD and Constrained JT

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Conclusions

• Equally efficient in terms of unconditional power

• Similar conditional power profiles

Conclusions

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• We considered a promising zone AD for an oncology trial

• Maximize CP

• Require sufficiently high CP to justify sample size increase

• Provide method for objective efficiency comparison

• 2-3% loss of unconditional power compared to optimal JT design which has wider SSR zone and recommends increasing N at lower 𝑧1 values

• No loss of efficiency compared to optimal constrained JT design which requires 𝐶𝑃0.29 𝑧1, 𝑛2

∗ > 80%

• Sponsor’s utility will determine whether a CP constraint makes sense, at the cost of some efficiency loss compared to JT

References

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• Liu, Lingyun, Sam Hsiao, and Cyrus R. Mehta. 2017. “Efficiency Considerations for Group Sequential Designs with Adaptive Unblinded Sample Size Re-Assessment.” Statistics in Biosciences, March.

• Mehta, Cyrus, and Lingyun Liu. 2016. “An Objective Re-Evaluation of Adaptive Sample Size Re-Estimation: Commentary on ‘Twenty-Five Years of Confirmatory Adaptive Designs.’” Statistics in Medicine 35: 350–58.

• Jennison, Christopher, and Bruce W. Turnbull. 2015. “Adaptive Sample Size Modification in Clinical Trials: Start Small Then Ask for More?” Statistics in Medicine 34 (29): 3793–3810.