Statistical Performance Guarantee for Subgroup Identification with Generic Machine Learning

Across a wide array of disciplines, many researchers use machine learning (ML) algorithms to identify a subgroup of individuals who are likely to benefit from a treatment the most (``exceptional responders'') or those who are harmed by it. A common approach to this subgroup identification problem consists of two steps. First, researchers estimate the conditional average treatment effect (CATE) using an ML algorithm. Next, they use the estimated CATE to select those individuals who are predicted to be most affected by the treatment, either positively or negatively. Unfortunately, CATE estimates are often biased and noisy. In addition, utilizing the same data to both identify a subgroup and estimate its group average treatment effect results in a multiple testing problem. To address these challenges, we develop uniform confidence bands for estimation of the group average treatment effect sorted by generic ML algorithm (GATES). Using these uniform confidence bands, researchers can identify, with a statistical guarantee, a subgroup whose GATES exceeds a certain effect size, regardless of how this effect size is chosen. The validity of the proposed methodology depends solely on randomization of treatment and random sampling of units. Importantly, our method does not require modeling assumptions and avoids a computationally intensive resampling procedure. A simulation study shows that the proposed uniform confidence bands are reasonably informative and have an appropriate empirical coverage even when the sample size is as small as 100. We analyze a clinical trial of late-stage prostate cancer and find a relatively large proportion of exceptional responders.