Abstract

In clinical trials, it is not always the case that the treatment effect is homogeneous for the overall population. In particular, there might be a subgroup with certain personal attributes who benefits from the treatment more than the rest of the population. Furthermore, such attributes can be of high dimension if, for example, biomarkers or genome data are collected for each patient. With this practical application in mind, this study concerns testing the existence of a subgroup with an enhanced treatment effect under the setting where the subgroup membership is potentially characterized by high-dimensional covariates. The existing literature on testing the existence of the subgroup has the following two drawbacks. First, because parameter characterizing the membership of subgroup is unidentified under the null hypothesis of no subgroup, the asymptotic null distributions of test statistics proposed in the literature often have the intractable forms. Notably, they are not easy to simulate, and hence, the data analyst have to resort to computationally demanding method, such as bootstrap, to calculate the critical value. Second, most of the methods in the literature assume that the dimension of personal attributes characterizing the membership of subgroup is of low dimension. Because the complicated asymptotic null distributions of the test statistics usually depends on the dimension of the personal attributes, extension of their methods to high-dimensional case is nontrivial. To fix this problem, this research proposes a novel likelihood ratio-based test with a logistic-normal mixture model for testing the existence of the subgroup. The proposed test is built on a modified likelihood function that shrinks possibly high-dimensional unidentified parameter towards zero when there exists no subgroup. This shrinkage simplifies the asymptotic null distribution. Namely, we show that, under the null hypothesis, the test statistics weakly converges to half chi-square distribution, which is easy to simulate. Furthermore, this convergence result holds even under high-dimensional regime where the dimension of the personal attributes characterizing the classification of the subgroup exceeds the sample size.