Semiparametric Localized Principal Stratification Analysis with Continuous Strata

TL;DR

This paper develops a novel semiparametric method for analyzing causal effects with continuous intermediate variables, addressing nonidentifiability and nonregularity issues through a copula-based model and local functional approximation.

Contribution

It introduces a flexible copula-based principal score model and a local functional approach for regular estimation of principal causal effects with continuous strata.

Findings

Estimator is computationally efficient and double robust.

Achieves minimax optimality with vanishing bandwidth.

Demonstrates strong performance in simulations and real data.

Abstract

Principal stratification is essential for revealing causal mechanisms involving post-treatment intermediate variables, in real-world applications like surrogate marker evaluation. Principal stratification analysis with continuous intermediate variables is increasingly common but challenging due to the infinite principal strata and the nonidentifiability and nonregularity of principal causal effects. Inspired by recent research, we resolve these challenges by first using a flexible copula-based principal score model to identify principal causal effect under weak principal ignorability. We then target the local functional substitute of principal causal effect, which is statistically regular and can accurately approximate principal causal effect with vanishing bandwidth. We simplify the full efficient influence function of the local functional substitute by considering its oracle-scenario alternative. This leads to a computationally efficient and straightforward estimator for the local functional substitute and principal causal effect with vanishing bandwidth. We prove the double robustness of our proposed estimator, and derive its asymptotic normality for inferential purposes. With a vanishing bandwidth, our method attains minimax optimality for the nonparametric estimation of the principal causal effect. With a fixed bandwidth, it achieves semiparametric efficiency in estimating its local functional substitute. We demonstrate the strong performance of our proposed estimator through simulations and apply it to surrogate analysis of short-term CD4 count in ACTG 175.