Keywords: clustered data, administrative data, causal inference, average causal effect, dual-model
We study causal inference using potentially observable framework in clustered data settings where observational units are clustered in naturally occurring groups (e.g. patients within hospitals). To incorporate the correlated nature of the data, we employ mixed-effects models and sandwich estimator to make inferences on the average causal effect (ACE). Our methods apply the concept of potential outcomes in Rubin Causal Model (RCM) and extend Schafer's method of estimating the variance of ACE. Particularly, we develop two model-based approaches to estimate the ACE under dual-modeling strategy which adjusts for the confounding effect by inverse probability weighting (IPW). These two approaches use linear mixed-effects models for the estimation of potential outcomes, but differ in the treatment assignment model in its handling of the correlated observations. We present a summary of our comprehensive simulation study assessing the operational sampling characteristics of the two approaches. Finally, we report our findings on an application to study the ACE of inadequate prenatal care on birth weight among low income women in New York state.