Causal Effect Estimation with TMLE: Handling Missing Data and Near-Violations of Positivity

Abstract: We evaluate the performance of targeted maximum likelihood estimation (TMLE) for estimating the average treatment effect in missing data scenarios under varying levels of positivity violations. We employ model- and design-based simulations, with the latter using undersmoothed highly adaptive lasso on the 'WASH Benefits Bangladesh' dataset to mimic real-world complexities. Five missingness-directed acyclic graphs are considered, capturing common missing data mechanisms in epidemiological research, particularly in one-point exposure studies. These mechanisms include also not-at-random missingness in the exposure, outcome, and confounders. We compare eight missing data methods in conjunction with TMLE as the analysis method, distinguishing between non-multiple imputation (non-MI) and multiple imputation (MI) approaches. The MI approaches use both parametric and machine-learning models. Results show that non-MI methods, particularly complete cases with TMLE incorporating an outcome-missingness model, exhibit lower bias compared to all other evaluated missing data methods and greater robustness against positivity violations across. In Comparison MI with classification and regression trees (CART) achieve lower root mean squared error, while often maintaining nominal coverage rates. Our findings highlight the trade-offs between bias and coverage, and we recommend using complete cases with TMLE incorporating an outcome-missingness model for bias reduction and MI CART when accurate confidence intervals are the priority.