Causal inference with missingness in confounder

Causal inference is a process of uncovering causal relationship between effect variable and disease outcome in epidemiologic research. When estimating causal effect in observational studies, confounders that influence both the effect variable and the outcome need to be adjusted for in the estimation process. In addition, missing data often arise in data collection procedure; working with complete cases often results in biased parameter estimates. We consider the causal effect estimation in the presence of missingness in the confounders under the missing at random assumption. We investigate how the double robust estimators perform when applying complete-case analysis or multiple imputations. Given the uncertainty of appropriate imputation model and computational challenge for many imputations, we propose an expectation-maximization (EM) algorithm to estimate the expected values of the missing confounder and utilize a weighting approach in the estimation of the average treatment effect. Simulation studies are conducted to see whether there is any gain in estimation efficiency using the proposed method, instead of the complete case analysis and multiple imputations. The results identified EM as the most efficient and accurate method for dealing with missingness in confounder. Our study result is applied in a B-aware trial, which is a multi-centre clinical trial, to estimate the effect of total intravenous anaesthetic on post-operative anxiety.