In-Sample Evaluation of Subgroups Identified by Generic Machine Learning

When a subgroup is identified from the data, it must be evaluated in a replicable way. The usual in-sample approach, which evaluates the post-hoc identified subgroup as predefined, might suffer from selection bias. This issue of in-sample evaluation of data-dependent objects is well recognized but particularly challenging here. Unlike discrete or finite-dimensional data-dependent objects addressed before, the selection bias here is induced by post-hoc identified subgroups, data-dependent sets potentially defined by infinite-dimensional functionals with nonsmooth boundaries known as nonregularity. The out-of-sample approach, which splits data for subgroup identification and evaluation, can help address selection bias but might suffer from efficiency loss and instability. In this paper, we propose a conditional adaptive perturbation approach to remove selection bias in in-sample subgroup evaluation and deliver valid inference on subgroups identified from the whole dataset by generic machine learning, regardless of whether regularity is satisfied. The proposed method is easy-to-compute, allows model-free and even black-box subgroup identification, and achieves full efficiency across broad scenarios of subgroup analysis through a novel theoretical framework of triple robustness linking rates of subgroup identification and nuisance estimation. The merits of the proposed method are demonstrated by a re-analysis of the ACTG 175 trial.