Two‐step estimation in ratio‐of‐mediator‐probability weighted causal mediation analysis

Abstract

This study investigates appropriate estimation of estimator variability in the context of causal mediation analysis that employs propensity score-based weighting. Such an analysis decomposes the total effect of a treatment on the outcome into an indirect effect transmitted through a focal mediator and a direct effect bypassing the mediator. Ratio-of-mediator-probability weighting estimates these causal effects by adjusting for the confounding impact of a large number of pretreatment covariates through propensity score-based weighting. In step 1, a propensity score model is estimated. In step 2, the causal effects of interest are estimated using weights derived from the prior step's regression coefficient estimates. Statistical inferences obtained from this 2-step estimation procedure are potentially problematic if the estimated standard errors of the causal effect estimates do not reflect the sampling uncertainty in the estimation of the weights. This study extends to ratio-of-mediator-probability weighting analysis a solution to the 2-step estimation problem by stacking the score functions from both steps. We derive the asymptotic variance-covariance matrix for the indirect effect and direct effect 2-step estimators, provide simulation results, and illustrate with an application study. Our simulation results indicate that the sampling uncertainty in the estimated weights should not be ignored. The standard error estimation using the stacking procedure offers a viable alternative to bootstrap standard error estimation. We discuss broad implications of this approach for causal analysis involving propensity score-based weighting.

A Two-Stage Joint Modeling Method for Causal Mediation Analysis in the Presence of Treatment Noncompliance

“…The E-step computes the expected values of sufficient statistics, given data and current estimates, and the M-step maximizes the likelihood shown in equation 4, given the updated sufficient statistics obtained from the E-step. These steps iterate until the estimates of the parameters become stabilized (See [11,16,24,25] for further details on this procedure).…”

Are there long-term benefits from early childhood education in low- and middle-income countries?

“…Other future studies with cross-sectional or panel data should consider causal mediation analytical techniques (see Bein et al, 2018;Pearl, 2012). As indicated in our conceptual framework, ECE affects long-term outcomes both directly and indirectly (via schooling).…”

Multisite Causal Mediation Analysis in the Presence of Complex Sample and Survey Designs and Non-Random Non-Response

“…To produce valid statistical inferences that incorporate the sampling uncertainty of the weights in the estimation of the causal parameters, we adopt a solution that extends an M-estimation procedure for single-site and multisite RMPW analysis (Bein et al, 2018;Qin and Hong, 2017). This approach estimates the weights and the site-specific causal effects jointly under a generalized method-of-moments (MOM) framework.…”

“…Earlier research has extended a two-step estimation procedure (Newey, 1984) to single-site (Bein et al, 2018) and multisite (Qin and Hong, 2017) RMPW analysis in which the RMPW weights are estimated. The rationale is to stack the estimating equations from both steps and to solve them simultaneously in the spirit of one-step generalized MOM estimation (Hansen, 1982).…”

“…We innovatively adapt these weighting adjustments to the context of mediation analysis by combining them with the ratio of mediator probability weighting (RMPW) strategy, which is for unpacking the causal mechanism and reducing mediator selection bias. RMPW was initially proposed by Hong (2010Hong ( , 2015 and others (Bein et al, 2018;Hong et al, 2011Hong et al, , 2015Hong and Nomi, 2012;Huber, 2014;Lange et al, 2012;Tchetgen Tchetgen and Shpitser, 2012) and was recently extended to multisite studies by Qin and Hong (2017). This strategy, without invoking functional form assumptions for the outcome model, is particularly flexible for accommodating treatment-by-mediator interactions and is suitable for discrete and continuous mediators and outcomes.…”