A Sparse Random Projection-based Test for Overall Qualitative Treatment Effects.

TitleA Sparse Random Projection-based Test for Overall Qualitative Treatment Effects.
Publication TypeJournal Article
Year of Publication2020
AuthorsShi, Chengchun, Wenbin Lu, and Rui Song
JournalJ Am Stat Assoc
Date Published2020

In contrast to the classical "one size fits all" approach, precision medicine proposes the customization of individualized treatment regimes to account for patients' heterogeneity in response to treatments. Most of existing works in the literature focused on estimating optimal individualized treatment regimes. However, there has been less attention devoted to hypothesis testing regarding the existence of overall qualitative treatment effects, especially when there is a large number of prognostic covariates. When covariates don't have qualitative treatment effects, the optimal treatment regime will assign the same treatment to all patients regardless of their covariate values. In this paper, we consider testing the overall qualitative treatment effects of patients' prognostic covariates in a high dimensional setting. We propose a sample splitting method to construct the test statistic, based on a nonparametric estimator of the contrast function. When the dimension of covariates is large, we construct the test based on sparse random projections of covariates into a low-dimensional space. We prove the consistency of our test statistic. In the regular cases, we show the asymptotic power function of our test statistic is asymptotically the same as the "oracle" test statistic which is constructed based on the "optimal" projection matrix. Simulation studies and real data applications validate our theoretical findings.

Alternate JournalJ Am Stat Assoc
Original PublicationA sparse random projection-based test for overall qualitative treatment effects.
PubMed ID33311818
PubMed Central IDPMC7730172
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States