Browsing by Author "Shi, Yuliang"

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Robust Methods and Model Selection for Causal Inference under Missingness of the Study Exposure
(University of Waterloo, 2025-04-28) Shi, Yuliang
The goal of this thesis is to develop new robust methods for the estimation of the causal effect and propose a model selection algorithm when the exposure variable is not fully observed. We mainly discuss the methods using propensity score (PS) and imputation approaches to address both missingness and confounding issues in the observational dataset. How to deal with missing data in observational studies is a common concern for causal inference. However, if the exposure is missing at random (MAR), few approaches are available, and careful adjustments on both missingness and confounding issues are required to ensure a consistent estimate of the true causal effect on the response. In Chapter 2, a new inverse probability weighting (IPW) estimator based on weighted estimating equations (WEE) is proposed to incorporate weights from both the missingness and PS models, which can reduce the joint effect of extreme weights in finite samples. Additionally, we develop a triply robust (TR) estimator via WEE to protect against the misspecification of the missingness model. The asymptotic properties of WEE estimators are shown using properties of estimating equations. Based on simulation studies, WEE methods outperform others, including imputation-based approaches, in terms of bias and variability. Additionally, properly selecting the PS model is a popular topic and has been widely investigated in observational studies. However, there are very few studies investigating the model selection issue for estimating the causal effect when the exposure is MAR. In Chapter 3, we discuss how to select both imputation and PS models, which can result in the smallest root mean squared error (RMSE) of the estimated causal effect. Then, we provide a new criterion, called the “rank score”, for evaluating the overall performance of both models. The simulation studies show that the full imputation plus the outcome-related PS models leads to the smallest RMSE, and the newly proposed criterion is also able to pick the best models. Compared to the MAR assumption, the missing not at random (MNAR) assumption allows for the association between the missingness and the exposure variable, which is a weaker assumption and more reasonable in some application studies. Even though many researchers have discussed how to deal with the missing outcome or confounders in observational studies, very little discussion focuses on the missing exposure under the MNAR assumption. In Chapter 4, we propose the IPW estimators using joint modelling, called “IPW-Joint'', to estimate the causal effect when the exposure is MNAR, which combines estimated weights from the missingness and PS models. Furthermore, to address the problem of model selection in the high-dimensional setting, we apply outcome-adaptive LASSO with weighted absolute mean difference (OAL-WAMD) as a new algorithm to select the outcome-related covariates when the exposure is MNAR. The simulation studies show that IPW-Joint contains more robust properties and smaller variance than the traditional IPW approach. In addition, OAL-WAMD outperforms the traditional LASSO in terms of higher true positive rates (TPR) and smaller variance in both low and high-dimensional settings. In Chapter 5, we summarize the major findings and discuss the potential extensions. The proposed methodology can be applied to several areas, including new drug development, complex missing data problems and finding real-world evidence in observational data.