Selective Inference in Propensity Score Analysis

TL;DR

This paper develops a method for valid selective inference in propensity score analysis, providing confidence intervals for selected confounders without needing to model outcome regression functions.

Contribution

It introduces a semiparametric selective inference approach with Lasso-type variable selection in causal inference, ensuring valid inference post-model selection.

Findings

Provides asymptotic confidence intervals for selected confounders

Does not require modeling nonparametric outcome functions

Ensures valid inference after variable selection

Abstract

Selective inference (post-selection inference) is a methodology that has attracted much attention in recent years in the fields of statistics and machine learning. Naive inference based on data that are also used for model selection tends to show an overestimation, and so the selective inference conditions the event that the model was selected. In this paper, we develop selective inference in propensity score analysis with a semiparametric approach, which has become a standard tool in causal inference. Specifically, for the most basic causal inference model in which the causal effect can be written as a linear sum of confounding variables, we conduct Lasso-type variable selection by adding an $\ell_1$ penalty term to the loss function that gives a semiparametric estimator. Confidence intervals are then given for the coefficients of the selected confounding variables, conditional on the event of variable selection, with asymptotic guarantees. An important property of this method is that it does not require modeling of nonparametric regression functions for the outcome variables, as is usually the case with semiparametric propensity score analysis.