Complier stochastic direct effects: identification and robust estimation

TL;DR

This paper introduces a new causal effect estimand called the complier stochastic direct effect (CSDE), and develops robust estimators for it using various statistical techniques, applicable across different study designs.

Contribution

The paper is the first to define and estimate the IV-direct effect of exposure on outcome not through mediators, with new estimators evaluated for robustness and efficiency.

Findings

IPTW estimator shows high bias in small samples.

EE and TMLE estimators are more robust and efficient.

Proposed estimators applicable to diverse study designs.

Abstract

Mediation analysis is critical to understanding the mechanisms underlying exposure-outcome relationships. In this paper, we identify the instrumental variable (IV)-direct effect of the exposure on the outcome not through the mediator, using randomization of the instrument. To our knowledge, such an estimand has not previously been considered or estimated. We propose and evaluate several estimators for this estimand: a ratio of inverse-probability of treatment-weighted estimators (IPTW), a ratio of estimating equation estimators (EE), a ratio of targeted minimum loss-based estimators (TMLE), and a TMLE that targets the CSDE directly. These estimators are applicable for a variety of study designs, including randomized encouragement trials, like the MTO housing voucher experiment we consider as an illustrative example, treatment discontinuities, and Mendelian randomization. We found the IPTW estimator to be the most sensitive to finite sample bias, resulting in bias of over 40% even when all models were correctly specified in a sample size of N=100. In contrast, the EE estimator and compatible TMLE estimator were far less sensitive to finite samples. The EE and TMLE estimators also have advantages over the IPTW estimator in terms of efficiency and reduced reliance on correct parametric model specification.