Multiple-Model-based Robust Estimation of Causal Treatment Effect on a Binary Outcome with Integrated Information from Secondary Outcomes

An assessment of the causal treatment effect in the development and progression of certain diseases is important in clinical trials and biomedical studies. However, it is not possible to infer a causal relationship when the treatment assignment is imbalanced and confounded by other mechanisms. Specifically, when the treatment assignment is not randomized and the primary outcome is binary, a conventional logistic regression may not be valid to elucidate any causal inference. Moreover, exclusively capturing all confounders is extremely difficult and even impossible in large-scale observational studies. We propose a multiple-model-based robust (MultiMR) estimator for estimating the causal effect with a binary outcome, where multiple propensity score models and conditional mean imputation models are used to ensure estimation robustness. Furthermore, we propose an enhanced MultiMR (eMultiMR) estimator that reduces the estimation variability of MultiMR estimates by incorporating secondary outcomes that are highly correlated with the primary binary outcome. The resulting estimates are less sensitive to model mis-specification compared to those based on state-of-the-art doubly-robust methods. These estimates are verified through both theoretical and numerical assessments. The utility of (e)MultiMR estimation is illustrated using the Uniform Data Set (UDS) from the National Alzheimer's Coordinating Center with the objective of detecting the causal effect of the short-term use of antihypertensive medications on the development of dementia or mild cognitive impairment. The proposed method has been implemented in an R package and is available at https://github.com/chencxxy28/eMultiMR.