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2. Joint Statistical Meeting
Evaluation of Type 1 Error in a 2-in-1 Adaptive Phase 2/3 Design with Dual-Primary Endpoints in Oncology Studies
Li Fan and Jing Zhao
Merck & Co., Inc
Joint Statistical Meeting
Denver, CO
Jul 30, 2019

3. Outlines
Introduction/Motivation
Methods
Results
Conclusion

4. Introduction 2-in-1 Phase 2/3 Adaptive Design* Advantages:
FAST
Introduction
2-in-1 Phase 2/3 Adaptive Design*
Advantages:
Limited investment initially
Can quickly move to Ph 3 if Go Criteria are met
Ph 2 patients are included in Ph 3 analysis for registrational intent with reasonable multiplicity adjustment
No penalty needs to be paid for multiplicity control as long as the correlations for the 3 test statistics satisfy ρXY≥ρXZ
Y>w?
Keep as a Phase 2 No
X>C?
Phase 2 trial
Z>w?
Expand to Phase 3
Yes
* Chen C, Anderson K, Mehrotra DV, Rubin EH and Tse A. A 2-in-1 Adaptive Phase 2/3 Design for Expedited Oncology Drug Development. Contemporary Clinical Trials 2018; 64:

5. Introduction 2-in-1 Phase 2/3 Adaptive design? Why do we need it?
-- In the situation of the lack of Ph 2 support in oncology development, 2-in-1 design can mitigate the risk for Ph3.
Go/No-Go decision built in 2-in-1 design
--Decision criteria needs to be set up for continuation as Ph 2 or expansion to Ph 3

6. Introduction How to demonstrate Type 1 error well-controlled?
Let X, Y, Z are the standardized test statistics corresponding to the primary endpoint for adaptive decision, smaller trial and larger trial, respectively.
Let c be the cut-point for the decision making
𝑇𝑦𝑝𝑒 𝐼 𝑒𝑟𝑟𝑜𝑟= Pr 𝑋<𝑐,𝑌>𝑤 + 𝑷𝒓 𝑿≥𝒄,𝒁>𝒘
≤ Pr 𝑋<𝑐, 𝑌>𝑤 + 𝑷𝒓 𝑿≥𝒄,𝒀>𝒘 , 𝒊𝒇 𝝆 𝑿𝒀 ≥ 𝝆 𝑿𝒁 = Pr 𝑌>𝑤
Overall Type I error is controlled at the target alpha level
e.g. w=1.96 to ensure the Type 1 error to be 2.5%

7. Introduction Validation of correlation assumption ρXY ≥ ρXZ
(Cited from Table 1 of Chen 2018*)
In the most cases, the assumption holds; but if the assumption does not hold, need to calculate Type 1 error
Scenarios for endpoints
Implication to the assumption
X, Y, Z are same
Holds
X and Y are same, Z different
X and Z are same, Y different
May not hold
Y and Z are same, X different
Holds when 𝜌 𝑋𝑌 ≥ 0 and 𝜌 𝑋𝑍 ≥0
X, Y, Z are different
May hold

8. Motivation
It is illustrated a general idea for the case when there is single primary endpoint/hypothesis in Phase 3 portion of 2-in-1 Phase 2/3 adaptive design [Chen 2018].
How to demonstrate Type 1 error well-controlled with extensions from the original proposal?
Two extensions from Chen’s paper:
Dual-primary endpoints in the Phase 3 portion
Group sequential test in the Phase 3 portion

9. Method
Extension 1: dual-primary hypotheses/endpoints in the Phase 3 portion
Assume: X, Y and Z are test statistics for same endpoints, while S is different.
Test statistic
Analysis X
expansion from Phase 2 to Phase 3 Y
primary analysis of the Phase 2 portion Z
dual-primary analyses of the Phase 3 portion S

10. Pr (X<𝑐, reject H0 for Y in Ph2)
Method
Assign α=2.5%(one-sided) to either Phase 2 or 3.
Allocate α1 = x% for one of the dual-primary testing and α2 = (2.5-x)% for the other testing as the initial setting in Phase 3 portion.
Under the different scenarios of the correlations, calculate 𝐓𝐲𝐩𝐞 𝐈 𝐞𝐫𝐫𝐨𝐫, under H0 (assume True HR =1 for Y and =(1, 1) for Z and S), derived by
Pr (X<𝑐, reject H0 for Y in Ph2) +
Pr (X ≥𝑐, reject H0 for Z or S in Ph3)

11. Method Evaluate the impact of the correlation (α1=α2=1.25%)
Evaluate the impact of alpha splitting in Phase 3
ρXY
ρXZ/ρXS/ρZS
SC1
SC2
SC3
0.5
0.4/0.2/0.3
0.4/0.1/0.2
0.4/0.05/0.1
0.7
0.5/0.3/0.4
0.5/0.2/0.3
0.5/0.1/0.2
SC=Scenario
Scenario α1 α2
SC1
1.25%
SC2
0.50%
2.00%
SC3
1.00%
1.50%

12. Results
Overall Type 1 error is well-controlled at 2.5% under different scenarios of the correlations.

13. Results
Overall Type 1 error is well-controlled at 2.5% under different alpha splitting for the dual-primary in the Ph3.

14. Method Extension 2: Group Sequential Test in Phase 3
Assume: X, Y and Z are test statistics for same endpoints.
Test statistic
Analysis X
expansion from Phase 2 to Phase 3 Y
primary analysis of the Phase 2 portion Z1
interim analysis of the Phase 3 portion Z2
final analysis of the Phase 3 portion

15. Method Assign α=2.5%(one-sided) to either Phase 2 or 3.
Allocate α1 and α2 for the interim and final test under different scenario with combination of information fraction and α spending functions.
Under the different scenarios, calculate 𝐓𝐲𝐩𝐞 𝐈 𝐞𝐫𝐫𝐨𝐫, under H0 (assume True HR =1 for Y and =(1, 1) for Z1 and Z2), derived by
Pr (X<𝑐, reject H0 for Y in Ph2)
Pr (X ≥𝑐, reject H0 for Z1
at interim of Ph3) +
Pr (X ≥𝑐, Not reject H0 for Z1 at interim of Ph3,
But reject H0 for Z2 at final of Ph3) +

16. Hwang-Shih-DeCani (γ)
Method
Evaluate impact of the information fraction with using O’Brien-Fleming α spending function
Evaluate impact of α spending function with using the information fraction of 0.8
Information fraction
0.5
0.6
0.7
0.8
α spending function
O’Brien-Fleming
Hwang-Shih-DeCani (γ)
γ=-4
γ=-2
γ=1

17. Results
Overall Type 1 error is well-controlled at 2.5% under different information fraction in Phase 3 portion.

18. Results
Overall Type 1 error is well-controlled at 2.5% under different alpha spending function in the Ph3.

19. The overall Type 1 error is
Conclusion
Varying alpha splitting and correlation between dual primary endpoint;
Varying information fraction and alpha spending function in the group sequential testing;
Varying correlation between dual-primary endpoints within group sequential testing;
The overall Type 1 error is
well-controlled

20. Thanks and Questions
This Photo by Unknown Author is licensed under CC BY-SA

21. BACK UP

22. Method
Extension 1&2: Group Sequential Test for dual- primary hypotheses/endpoints in the Phase 3 portion
Assume: X, Y, and Z are test statistics for same endpoints, while S is different.
Test statistic
Analysis X
expansion from Phase 2 to Phase 3 Y
primary analysis of the Phase 2 portion
Z1 and S1
interim analyses for dual-primary in the Phase 3 portion
Z2 and S2
final analyses for dual-primary in the Phase 3 portion

23. Method Assign α=2.5%(one-sided) to either Phase 2 or 3.
Allocate α1 = 0.5% for one of the dual-primary testing and α2 = 2.0% for the other testing as the initial setting in Phase 3 portion.
Under the different scenarios, calculate 𝐓𝐲𝐩𝐞 𝐈 𝐞𝐫𝐫𝐨𝐫, under H0 (assume True HR =1 for Y and =(1, 1) for Z and S), derived by
Find a simple way to present
Pr (X<𝑐, reject H0 for Y in Ph2) +
Pr (X ≥𝑐, reject H0 for Z1 or for S1 at interim of Ph3)
Pr (X ≥𝑐, Not reject H0 for Z1 and S1 at interim of Ph3,
But reject H0 for Z2 or for S2 at final of Ph3) +

24. Method Evaluate the correlations Z and S ρZ1S1=ρZ2S2 ρZ1S2=ρZ2S1 SC1
0.2
0.1
SC2
0.05
SC3
0.07
0.03
X Z1 Z S1 S2 X Z1 Z2 S1 S2

25. Results
Overall Type 1 error is well-controlled under 2.5% under different correlation between Z and S in Phase 3 portion.