1. A Stagewise Prognostic Control Predictive Approach (SPCPA) for Subgroup Identification
with application in a phase II study
Wanying Li, Wangshu Zhang, Lovely Goyal, Yuanyuan Xiao
Biomarker Biostatistics, Gilead Sciences, Foster City, CA
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2. Fundamental statistical problems underlying “exploratory” subgroup identification
prognostic only
prognostic and predictive
Identify the predictive factors of differential treatment effect
Determine an algorithm to define the subgroup (including cutoff determination)
predictive only
neither prognostic nor predictive
Adapted from Fridlyand J 2013

3. Identify Predictive Factors
Stagewise Prognostic Control Predictive Approach (SPCPA) with the advantage of improving signal detection power by adjusting for the prognostic effects
Prognostic Factors
Placebo patients
Treated patients
Predictive Factors
Identify Prognostic Factors, Derive Prognostic Score and Estimate Individual Treatment Effect
This approach borrows concepts from counterfactual models, in which there are two possible outcomes for each person (one under each treatment assignment), only one of which can be observed, and it is the difference between the two outcomes that is important. SPCPA first calculates the Individual Treatment Effect (ITE) according to the counterfactual concept in causal inference; it then applies GUIDE/SIDES to identify the subgroup(s) oand predictive factors based on the ITE.
Identify Predictive Factors
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4. A Phase II study example
N = ~240, randomized 1:2 to placebo:active arms
Response rate (RR):
~50% in the active arm, vs ~20% in the placebo arm
Similar RR to other competitor drugs
Objective: to support ongoing phase III trials
Identify prognostic factors
Identify a subpopulation that can have further improvement in RR

5. Multiplicity adjusted p-value
A promising subgroup was identified based on a signature of two variables
Sample size
Prognostic effect adjusted response*
P value
Multiplicity adjusted p-value
Overall
Active
Placebo
Diff
Treatment effect
Treatment effect improvement
Overall population
233
154 79
0.386
0.027
0.359
1.14E-09
Variable 1 ≤ 3rd quartile
176
121 55
0.435
-0.024
0.459
1.45E-11
0.0034
0.108
Variable 1 ≤ 3rd quartile & Variable 2 category 1
141 96 45
0.481
-0.041
0.522
1.99E-12
0.0006
0.021
*After adjustment of placebo and prognostic effect, the expected response rate in the placebo arm should be 0.

6. Conclusions
We proposed a framework that integrates the process of identifying prognostic and predictive factors. This framework can handle most types of the response endpoints except for time-to-event endpoint.
This new approach potentially can increases detection power by adjusting for prognostic effects. Its output has type I error assessment and has explicit final algorithm with cutoffs, which can facilitate clinical and biological interpretations.
Simulation work on comparing SPCPA with other existing methods is still ongoing.

7. Acknowledgements References
Gilead Biomarker Biostat, Tuan Nguyen, Jacqueline Tarrant, Julie Ma, Neby Bekele
References
Fridlyand J, Yeh RF, Mackey H, Bengtsson T, Delmar P, Spaniolo G, Lieberman G An industry statistician's perspective on PHC drug development. Contemp Clin Trials. 36(2):624-35
Lipkovich I, Dmitrienko A, Denne J, Enas G Subgroup identification based on differential effect search (SIDES): a recursive partitioning method for establishing response to treatment in patient subpopulations. Statistics in Medicine; 30:2601–2621.
Lipkovich, I. and Dmitrienko, A., Tutorial in biostatistics: data‐driven subgroup identification and analysis in clinical trials. Statistics in Medicine, 36(1), pp