TY - JOUR
T1 - Optimal Tests of Treatment Effects for the Overall Population and Two Subpopulations in Randomized Trials, Using Sparse Linear Programming
AU - Rosenblum, Michael
AU - Liu, Han
AU - Yen, En Hsu
N1 - Funding Information:
Michael Rosenblum, Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205 (E-mail: mrosenbl@jhsph.edu). Han Liu is Professor, Department of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 08544 (E-mail: hanliu@princeton.edu). En-Hsu Yen, Department of Computer Science, University of Texas at Austin, TX 78712 (E-mail: a061105@gmail.com). This research was supported by U.S. F.D.A. Partnership in Applied Comparative Effectiveness Science (HHSF2232010000072C); NSF Grants III-1116730, III-1332109; and, NIH Grants R01MH102339, R01GM083084, R01HG06841. This publication’s contents are solely the responsibility of the authors and do not necessarily represent the official views of the above agencies. The authors thank Thomas A. Louis and the referees for their helpful feedback.
Publisher Copyright:
© 2014 American Statistical Association.
PY - 2014/9
Y1 - 2014/9
N2 - 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.
AB - 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.
KW - Optimal multiple testing procedure
KW - Treatment effect heterogeneity
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U2 - 10.1080/01621459.2013.879063
DO - 10.1080/01621459.2013.879063
M3 - Article
C2 - 25568502
AN - SCOPUS:84907495289
SN - 0162-1459
VL - 109
SP - 1216
EP - 1228
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 507
ER -