Causal Inference with Mismeasured Confounders or Mediators

Abstract

This thesis includes three projects to correct measurement error in covariates or mediators when estimating causal estimands under survival model, marginal structure model and covariate balancing models. In Chapter 2, we decompose the causal effect on difference scale with more than one mediator under additive hazard model, and correct the bias caused by error-prone covariates and mediators. The simulation study shows the good performance of the proposed method under various measurement error settings. The method is further applied to a real data study of HIV-infected adults (Hammer et al., 1996), where a causal interpretation of the mediated effects is given. The asymptotic distributions of estimators are provided in the appendix. In Chapter 3, we develop two estimation methods to correct the bias of average treatment effect via marginal structural model when covariate variables are subject to measurement error. We consider the scenario that the confounders and exposures are time-varying and the confounders are error-prone. The first approach depends on a logistic-based correction method, which corrects the error-prone confounders in the logistic regression model of the treatment variable (Stefanski & Carroll, 1987). The second one relies on the simulation-extrapolation-based correction method (Shu & Yi, 2019d), which corrects the error-prone average treatment effect directly and could be used when a closed form of weight can not be found. Simulation studies are provided and the proposed approaches are illustrated by a real data analysis of the Women’s Interagency HIV Study in the United States from 1993 to 2015. In Chapter 4, when pretreatment covariates are subject to measurement error, we apply the augmented simulation extrapolation estimation developed by Shu and Yi (2019d) to correct the estimates of average treatment effect on the treated via entropy balancing and covariate balancing propensity score methods. The correction method is illustrated by a real data set.