🤖 AI Summary
This study addresses the failure of inference for data-driven subgroup identification in within-sample evaluation due to selection bias—particularly when subgroup boundaries are non-smooth and depend on infinite-dimensional functionals. The authors propose a conditional adaptive perturbation method grounded in a triple robustness theoretical framework, which accommodates any machine learning algorithm, including black-box models, without requiring parametric assumptions or smoothness conditions on subgroup boundaries. The approach jointly optimizes subgroup identification and nuisance parameter estimation rates, enabling fully efficient, unbiased within-sample inference without data splitting. In a reanalysis of the ACTG 175 clinical trial, the method substantially improves estimation stability and statistical efficiency while avoiding the information loss inherent in conventional sample-splitting strategies.
📝 Abstract
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.