Abstract: In this project we propose a statistical model for the purpose of identifying a subgroup that has an enhanced treatment effect as well as the variables that are predictive of the subgroup membership. The need for such subgroup identification arises in clinical trials and in market segmentation analysis. By using a structured logistic-normal mixture model, our proposed framework enables us to perform a confirmatory statistical test for the existence of subgroups, and at the same time, to construct predictive scores for the subgroup membership. The inferential procedure proposed in the paper is built on the recent literature on hypothesis testing for Gaussian mixtures, but the structured logistic-normal mixture model enjoys some distinctive properties that are unavailable to the simpler Gaussian mixture models. With the bootstrap approximations, the proposed tests are shown to be powerful, and equally importantly, insensitive to the choice of tuning parameters. As an illustration, we analyze a data set from the AIDS Clinical Trials Group $320$ study and show how the proposed methodology can help detect a potential subgroup of AIDS patients who may react much more favorably to the addition of a protease inhibitor to a conventional regimen than other patients.
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