1. A Confirmatory Basket Trial Design Based on Conditional Power
Huiling Li a
Joint work with Xiaolong Luob, Jianming Wangb, and Yeongjin Gwonc
a Iovance Biotherapeutics.
b Celgene Corporation, c University of Connectict

2. Outline
An overview of Cong Chen, et al. (2016) Basket Trial Design and Areas for Improvement
Proposed Approach based on Conditional Power
Simulation Study
Concluding Remarks

3. Basket Trials in Oncology
A trial that pools cohorts with differing histologic tumor types and a common molecular subtype in a single trial (Beckman et al., 2016)
Benefit: more efficient and flexible
Less patients, shorter development timelines, accelerated development, and etc.

4. Statistical Design and Considerations of a Phase 3 Basket Trial (Cong Chen, et al., 2016)
Prune the inactive indications at an interim analysis: based on a p-value threshold
Based on interim data only without accounting for future data
Sample size calculation after interim analysis
Three sample size adjustment strategies, but no further adaption regardless of interim results
Can be underpowered or overpowered
Pool the active indications in the final analysis

5. Proposed Basket Trial Design
Prune the inactive indications based on CP rather than a p- value threshold
Account for future data after interim
Build in sample size re-estimation after interim based on promising zone method (Mehta and Pocock, 2011)
Ensure appropriate power for the selected indications
No further adjustment for type I error rate

6. Notations Notation Description 𝑘 The number of indications 𝑚
The number of selected indications
𝛼, 𝛽
Type I error and type II error 𝑡
Information fraction at interim 𝜃
Hazard ratio (HR) 𝛾
Conditional power threshold
𝛼 𝑡
P-value threshold
𝛼 ∗
Adjusted type I error at the final analysis
𝑌 𝑖1 , 𝑌 𝑖2
Test statistic for indication 𝑖 at interim and final, respectively
𝑉 𝑚
Pooled test statistic for selected indications at final
𝐼 1 , 𝐼 2
Interim and final information level

7. Sketch of the Proposed Approach
Given the 𝐶𝑃 threshold (𝛾), calculate the corresponding test statistic threshold ( 𝑌 𝑖1 ) and p-value threshold at interim ( 𝛼 𝑡 )
Calculate 𝛼 ∗ to control overall type I error rate accounting for all possible choices of selected indications
Calculate combined 𝐶𝑃 𝑚 for selected indications (𝑚)
Sample Size Re-estimation (SSR) based on promising zone method

8. 1. 𝐶𝑃 (𝛾) and p-value threshold ( 𝛼 𝑡 ) for each Indication
Conditional power for each indication
Conditional probability of rejecting 𝐻 0 given the interim data
𝐶𝑃 𝑖 =𝑃 𝑌 𝑖2 > 𝑍 1−𝛼 𝑌 𝑖1 =𝛾
Under 𝐻 0 : 𝛿 𝑖 =0 for all 𝑖, where 𝛿 𝑖 =−log( 𝜃 𝑖 ) the conditional power from Jennison and Turnbull (2000) is defined as
𝐶𝑃 𝑖 =Φ −𝑌 𝑖1 𝐼 𝑖1 − 𝑍 1−𝛼 𝐼 𝑖 𝐼 𝑖2 − 𝐼 𝑖1 =𝛾 (𝟏)
Calculate corresponding interim test statistic and p- value threshold
𝑌 𝑖1 can be obtained by inverting the equation (𝟏)
𝛼 𝑡 is calculated using 𝑌 𝑖1

9. 2. Adjusted Type I error 𝛼 ∗ at the final analysis (Cong Chen, et al
The probability of 𝑉 𝑚 being significant at 𝛼 ∗
𝑄 0 𝛼 ∗ | 𝛼 𝑡 ,𝑚 = 𝑃 𝐻 0 𝑖=1 𝑚 𝑌 𝑖1 > 𝑍 1− 𝛼 𝑡 , 𝑉 𝑚 > 𝑍 1− 𝛼 ∗ 𝑖=𝑚+1 𝐾 (1− 𝛼 𝑡 ) (𝟐)
The nominal 𝛼 ∗ is obtained from the following equation:
𝑚=1 𝑘 𝑐(𝑘,𝑚) 𝑄 0 𝛼 ∗ | 𝛼 𝑡 ,𝑚 =𝛼 𝟑
where 𝑐(𝑘,𝑚) is the number of choices to select 𝑚 indications from 𝐾
We need the correlation 𝑐𝑜𝑟𝑟 𝑌 𝑖1 , 𝑉 𝑚 =𝑐𝑜𝑟𝑟 𝑌 𝑖1 , 𝑌 𝑖2 ×𝑐𝑜𝑟𝑟( 𝑌 𝑖2 , 𝑉 𝑚 ) for solving the equation 𝟑

10. 3. Combined 𝐶𝑃 𝑚 for Selected Indications (𝑚)
Assume that 𝑚 indications are selected from interim analysis
The pooled statistics is given by
𝑉 𝑚 = 𝑖=1 𝑚 𝑛 𝑖1 𝑗=1 𝑚 𝑛 𝑗1 𝑌 𝑖1
The conditional power for the selected indications is given by
𝐶𝑃 𝑚 =𝑃 𝑉 𝑚 ∗ > 𝑍 1− 𝛼 ∗ 𝑉 𝑚
=Φ −𝑉 𝑚 𝐼 𝑚1 − 𝑍 1− 𝛼 ∗ 𝐼 𝑚2 −log⁡( 𝜃 𝑚 )( 𝐼 𝑚2 − 𝐼 𝑚1 ) 𝐼 𝑚2 − 𝐼 𝑚1
where 𝐼 𝑚1 and 𝐼 𝑚2 are the combined information level for the selected 𝑚 indications at interim and final analysis, respectively, while 𝜃 𝑚 is hazard ratio for the 𝑚 indications.

11. 4. SSR based on Promising Zone Method (Mehta and Pocock, 2010)
Sample size adjustment algorithm
1. Unfavorable Zone
If 𝐶𝑃 𝑚 𝑉 𝑚 , 𝑛 𝑚2 < 𝐶𝑃 𝑚𝑖𝑛 , no sample size re-estimation
2. Favorable Zone
If 𝐶𝑃 𝑚 𝑉 𝑚 , 𝑛 𝑚2 > 𝐶𝑃 𝑚𝑎𝑥 , no sample size re-estimation
3. Promising Zone
If 𝐶𝑃 𝑚𝑖𝑛 < 𝐶𝑃 𝑚 𝑉 𝑚 , 𝑛 𝑚2 < 𝐶𝑃 𝑚𝑎𝑥 then increase to
𝑛 𝑚2 ∗ = min 𝑛 𝑚2 ′ , 𝑛 𝑚2 𝑚𝑎𝑥
where 𝑛 𝑚2 ′ is the sample size such that 𝐶𝑃 𝑚 𝑉 𝑚 , 𝑛 𝑚2 = 𝐶𝑃 𝑚𝑎𝑥 , while 𝑛 𝑚2 𝑚𝑎𝑥 is predetermined maximum cap.

12. Simulation Study
To assess the operating characteristics of the proposed method
A simulation setting to compare with Cong Chen (2016), D1 strategy
Parameters
Values 𝑘 6 𝑚
3, 4, 5, 6 𝛼
2.5% 𝛾
5% ( 𝛼 𝑡 =0.4) 𝑡
0.5
𝛼 ∗
0.32% 𝜃
0.6
Planned events
300
SSR Cap
1.5
Target power for SSR
90%

13. Simulation Results to Compare Study Power
Number of active tumor indications
Power (%) for a positive study
D1 strategy (in Cong Chen, 2016)
Our approach 6 96 97 5 91 94 4 81 3 64 82

14. Concluding Remarks
Developed a CP based method for basket trial design in confirmatory studies
Prune the inactive indications based on CP rather than a p- value threshold
The SSR using promising method: ensure appropriate power for the selected indication with no further adjustment for type I error rate

15. Selected References
Chen C., Li X., Yuan S., Antonijevic Z., Kalamegham R., and Beckman R. A. (2016) Statistical Design and Considerations of a Phase 3 Basket Trial for Simultaneous Investigation of Multiple Tumor Types in One Study. Statistics in Biopharmaceutical Research 8:3,
Mehta C. R and Pocock S. J. (2011). Adaptive increase in sample size when interim results are promising: A practical guide with examples. Statistics in Medicine 30,
Gao P., Ware J. H., and Mehta C. (2008). Sample size re-estimation for adaptive sequential design in clinical trials. Journal of Biopharmaceutical Statistics 18,
Conditional Power of Logrank Test Chapter 701, PASS Sample Size Software, NCSS.
Jennison C. and Turnbull B. W. (2000). Group sequential methods with applications to clinical trials. Chapman & Hall/CRC. Boca Raton, FL.
Beckman R. A., Antonijevic Z., Kalamegham R., and Chen C. (2016) Adaptive design for a confirmatory basket trial in multiple tumor types based on a putative predictive biomarker. Clinical pharmacology & Therapeutics 100:6,