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

Abstract

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 cutoff 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.

Multi-stage adaptive enrichment trial design with subgroup estimation

“…This function is proportional to the power of treatment comparison or, equivalently, the non-centrality parameter in the test for the treatment effect. Joshi et al (2019) showed that for weights larger than 1, the best subgroup always coincides with the whole population under the assumption that the treatment response in the experimental treatment group is no worse than the response in the control arm. Joshi et al (2019) considered the utility U 2 = U(S, γ = 0.75) = π(S) 0.75 [μ T (S) − μ C (S)] that favors larger subgroups compared to U 1 .…”

“…The first way is to define the best subgroup as subjects within the biomarker subset where the treatment effect is equal to or higher than a minimally clinically relevant treatment effect (Friedlin and Simon 2005;Renfro et al 2014). The other way to define the best subgroup is through a utility function (Lai et al 2014;Graf et al 2015;Zhang et al 2017;Graf et al 2019;Joshi et al 2019). The utility function specifies the trade-off between the size of the subgroup and the treatment effect in the subgroup.…”

“…Under the assumption of equal variances of the treatment effect in all subgroups, maximizing this utility is the same as maximizing the square root of the prevalence of the subgroup multiplied by the treatment effect in the subgroup and is the same as maximizing the power of the treatment comparison. The subgroup defined this way yields good power of treatment comparison in a post-hoc analysis of an unenriched population when the subgroup is estimated and tested (Joshi et al 2019). The advantage of the utility function approach is that there is no need to pre-specify the minimum treatment effect.…”

Finding the best subgroup with differential treatment effect with multiple outcomes

“…Joshi et al adopt this definition and consider subgroup prevalence raised to the power of 0.75 for the design purposes and 0.5 for estimation. 8,9 Some definitions include the sample size. Chen et al 10 define the best subgroup as the one comprising all individuals with greater CATE and stronger statistical significance of testing the CATE than its complement.…”

Inference on subgroups identified based on a heterogeneous treatment effect in a post hoc analysis of a clinical trial

“…2,4,5 The selection criteria vary across the methods, depending on the predetermined targets-maximizing CATE, a utility function that takes into account the ''treatment burden,'' predictive power of future trials, or the value function of the optimal treatment assignment rule. 1,2,[4][5][6][7][8][9][10][11][12][13][14] In this article, we assume that a subgroup identification method has been previously selected for analysis and focus on the confirmatory phase. The goal of the subgroup confirmation phase is to obtain unbiased estimates and reliable inference of CATEs in the identified subgroups, also known as ''honest'' estimates.…”