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Optimal Tests of Treatment Effects for the Overall Population and Two Subpopulations in Randomized Trials, Using Sparse Linear Programming

Author(s): Rosenblum, Michael; Liu, Han; Yen, En-Hsu

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Abstract: We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such subpopulations could be defined by a biomarker or risk factor measured at baseline. The goal is to simultaneously learn which subpopulations benefit from an experimental treatment, while providing strong control of the familywise Type I error rate. We formalize this as a multiple testing problem and show it is computationally infeasible to solve using existing techniques. Our solution involves a novel approach, in which we first transform the original multiple testing problem into a large, sparse linear program. We then solve this problem using advanced optimization techniques. This general method can solve a variety of multiple testing problems and decision theory problems related to optimal trial design, for which no solution was previously available. In particular, we construct new multiple testing procedures that satisfy minimax and Bayes optimality criteria. For a given optimality criterion, our new approach yields the optimal tradeoff between power to detect an effect in the overall population versus power to detect effects in subpopulations. We demonstrate our approach in examples motivated by two randomized trials of new treatments for HIV. Supplementary materials for this article are available online.
Publication Date: 2014
Electronic Publication Date: 2-Oct-2014
Citation: Rosenblum, Michael, Han Liu, and En-Hsu Yen. "Optimal tests of treatment effects for the overall population and two subpopulations in randomized trials, using sparse linear programming." Journal of the American Statistical Association, 109, no. 507 (2014): 1216-1228. doi:10.1080/01621459.2013.879063
DOI: doi:10.1080/01621459.2013.879063
ISSN: 0162-1459
EISSN: 1537-274X
Pages: 1216 - 1228
Type of Material: Journal Article
Journal/Proceeding Title: Journal of the American Statistical Association
Version: Author's manuscript

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