Primary Submission Category: Causal Discovery
Valid post-selection inference for penalized G-estimation
Authors: Ajmery Jaman, Ashkan Ertefaie, Michèle Bally, Renée Lévesque, Robert Platt, Mireille Schnitzer, Ajmery Jaman,
Presenting Author: *
Understanding treatment effect heterogeneity is important for decision-making in medical and clinical practices, or handling various engineering and marketing challenges. When dealing with high-dimensional covariates or when the effect modifiers are not predefined and need to be discovered, data-adaptive selection approaches become essential. However, data-driven model selection complicates the quantification of statistical uncertainty in post-selection inference and makes it difficult to approximate the sampling distribution of the target estimator. Such model selection tends to favor models with strong effect modifiers with an associated cost of inflated type I errors. Although several frameworks and methods for valid statistical inference have been proposed for ordinary least squares regression following data-driven model selection, fewer options exist for valid inference for effect modifier discovery in causal modeling contexts. To fill this gap, we extend two different methods to develop valid inference for penalized G-estimation that investigates effect modification of proximal treatment effects within the structural nested mean model framework. In our simulation study, the proposed methods effectively controlled the false coverage rates for the target parameters, while the naive inference based on the sandwich variance estimator resulted in false coverage rates higher than the nominal level. We also illustrate these methods with a real-data application.