Advances in Statistical Causal Inference and Applications

How to deal with missing data in observational studies is a common concern for causal inference. When the covariates are missing at random (MAR), multiple approaches have been provided to help solve the issue. However, if the exposure is 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 this article, 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 triple robust (TR) estimator via WEE to further protect against the misspecification of the model. The asymptotic properties of WEE estimators are proved using properties of estimating equations. Based on the simulation studies, WEE methods outperform others including imputation-based approaches in terms of bias and standard error. Finally, an application study is conducted to identify the causal effect of the presence of cardiovascular disease on mortality for COVID-19 patients 

Hometime, the number of days a patient is home within a specified time period following a clinical event, is an important patient-centered outcome. Modeling hometime is challenging due to its zero-inflated, right-skewed, and right-censored distribution. There is a lack of consensus in clinical literature on how to best make inference on the average treatment effect on hometime. This work aims to provide practical recommendations on methods selection for this inference. As hometime's U-shaped distribution does not fit a known distribution, we simulate data by generating patients' daily status (home vs. not home) over two periods (90 days and 365 days) to obtain realistic data. Due to the unique data-generating process, any non-zero treatment effect is unknown. Using the simulated data, we compare popular methods of estimating a treatment effect on hometime under different settings, including various types of censoring. In order to compare a range of methods that estimate the treatment effect on different scales, we focus on performance with respect to type I error under the null and power under the alternative. Our findings are applied to a large cardiovascular disease registry. 

Mendelian randomization (MR) is a powerful tool for uncovering the causal effects in the presence of unobserved confounding. It utilizes single nucleotide polymorphisms (SNPs) as instrumental variables (IVs) to estimate the causal effect. However, SNPs often have small effects on complex traits, leading to bias and low statistical efficiency in MR analysis. The strong linkage disequilibrium among SNPs is compounding this issue, which poses additional statistical hurdles. To address these challenges, this paper proposes DEEM (Debiased Estimating Equation Method), a summary statistics-based MR approach that can incorporate numerous correlated SNPs with weak effects. DEEM effectively eliminates the weak IV bias, adequately accounts for the correlations among SNPs, and enhances efficiency by leveraging information from correlated weak IVs. DEEM is a versatile method that allows adjustment for pleiotropic effects and applies to both two-sample and one-sample MR analyses. We establish the consistency and asymptotic normality of the resulting estimator. Extensive simulations and two real data examples demonstrate that DEEM can improve the efficiency and robustness of MR analysis.