Semiparametric localized principal stratification analysis with continuous strata

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 (PCEs). Inspired by recent research, we resolve these challenges by first using a flexible copula-based principal score model to identify PCE under weak principal ignorability. We then target the local functional substitute of PCE, which is statistically regular and can accurately approximate PCE 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 PCE 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 PCE. 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.