Estimating the subgroup and testing for treatment effect in a post-hoc analysis of a clinical trial with a biomarker.

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 the power for comparing the experimental treatment with the control. In the case of continuous outcome and a single biomarker, both a non-parametric method of estimating the subgroup and a method based on fitting a linear model with treatment by biomarker interaction to the data perform well. 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.