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

TL;DR

This paper introduces a novel optimization-based method for analyzing randomized trials with two subpopulations, enabling optimal detection of treatment effects while controlling error rates, demonstrated through HIV treatment examples.

Contribution

The paper presents a new approach transforming multiple testing problems into sparse linear programs, allowing for optimal trial analysis and decision-making in complex subpopulation scenarios.

Findings

New optimal testing procedures satisfying minimax and Bayes criteria.

Method achieves the best tradeoff between overall and subpopulation detection power.

Demonstrated effectiveness in HIV treatment trial examples.

Abstract

We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations 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.