Optimal MILP Approach to Group Sequential Hypothesis Test

2026-05-05

AI Summary

This study addresses a central challenge in group sequential hypothesis testing: how to reject the null hypothesis as early as possible while strictly controlling both Type I and Type II error rates. The work formalizes the optimal stopping time problem as a tractable optimization framework and introduces a novel approach based on Sample Average Approximation combined with Mixed-Integer Linear Programming (S-MILP) to directly optimize the rejection rule. This method reveals that the optimal alpha-spending strategy favors aggressive early allocation of the error budget, challenging conventional conservative paradigms. Empirical evaluations demonstrate that S-MILP consistently outperforms classical methods—including Lan–DeMets, Pocock, and O’Brien–Fleming—by achieving statistical significance earlier, both in simulation studies and in a real-world clinical trial on acute kidney injury interventions.

Abstract

Sequential hypothesis tests are widely adopted as a principled way to perform multiple tests on data that arrives over time. In particular, researchers frequently utilize group sequential hypothesis tests (GST) to test the same hypotheses at K times or "groups" while data arrives sequentially. In this setting, many methods have been proposed to allow researchers to uniformly control type-1 error across K checks (often known as various alpha-spending budgets). Although these methods are all successfully valid in controlling uniform type-1 error, it is not clear which of these methods are optimal when trying to reject the null as soon as possible. In this paper, we directly optimize the rejection criterion in the GST setting under the same constraints of controlling type-1 and type-2 errors. We use a sample average approximation combined with mixed integer linear programming (S-MILP) approach for this problem and show how our S-MILP approach dominates classical GST procedures such as Lan-DeMets, Pocock, and O'Brien-Fleming methods. We also find that the optimal solution typically aggressively spends the alpha-budget early, shedding insight to the long-standing debate of which alpha-spending budgets are more efficient. We finally apply our optimal S-MILP approach to a recent study on acute kidney injury interventions and find our optimal S-MILP approach can reach the same statistically significant conclusion faster than the original study and other GST methods.

Problem

• group sequential test
• optimal rejection criterion
• type-I error control
• alpha-spending
• hypothesis testing

Innovation

• group sequential testing
• mixed integer linear programming
• alpha-spending
• sample average approximation
• optimal hypothesis testing