Keywords: Post-Hoc, Biomarker, Subgroup Estimation, Hochberg
We consider the problem of estimating a biomarker-based subgroup and testing for treatment effect in the overall population and in the subgroup after the trial. We define the best subgroup as the subgroup that maximizes a utility function that reflects the trade-off between the best subgroup size and the treatment effect, for comparing the experimental treatment with the control. In the case of continuous outcome and a single continuous biomarker, we conclude that a non-parametric method of estimating the subgroup is better than a method based on fitting a linear model with treatment by biomarker interaction to the data. Several procedures for testing for treatment effect in all and in the subgroup are discussed. Cross-validation with two cohorts is used to estimate the biomarker cut-off to determine the best subgroup and to test for treatment effect. An approach that combines the tests in all patients and in the subgroup using Hochberg’s method is recommended. This test performs well in the case when there is a subgroup with sizable treatment effect and in the case when the treatment is beneficial to everyone. For a two-biomarker subgroup estimation problem, for moderate effects sizes and sample sizes, simpler regression based methods worked better than more complex tree- based regression approaches.