Wang, Chia-Hao
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Publication Causal Effect Estimation Under Linear and Log-Linear Structural Nested Mean Models in the Presence of Unmeasured Confounding(2010-08-13) Wang, Chia-HaoIn randomized clinical trials where the effects of post-randomization factors are of interest, the standard regression analyses are biased due to unmeasured confounding. The instrumental variables (IV; Angrist et al., 1996) and G-estimation procedures under structural nested mean models (SNMMs; Robins, 1994) allow one to make valid inference even if unmeasured confounding is present. Two IV approaches, the two-stage predictor substitution (2SPS) and two-stage residual inclusion (2SRI), are typically applied in analysis assuming the exclusion restriction. However, the exclusion restriction may be violated in clinical applications when the mechanism of treatment is assessed under mediation analyses. Accordingly, we focus on estimating the direct effect of the randomized treatment adjusting for a post-randomization mediator. We extend the two IV approaches to estimate the direct effect, and evaluate the corresponding theoretical properties under the linear SNMM. Under certain assumptions, we have shown that the two IV approaches are equivalent to the linear SNMM. We further extend and investigate the validity of these IV methods for estimation under a log-linear SNMM. The results show that the IV estimators are biased in the presence of unmeasured confounding. Therefore, we consider the G-estimation approach as an alternative solution to remove bias under the log-linear SNMM. The method was previously developed under either the exclusion restriction assumption or the sequential ignorability assumption. We present a general framework where these two assumptions are relaxed. In contrast to the IV log-linear regression methods, we have shown that the proposed G-estimators are unbiased in the presence of unmeasured confounding.