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Causal inference in outcome‐dependent two‐phase sampling designs

Summary.  We consider estimation of the causal effect of a treatment on an outcome from observational data collected in two phases. In the first phase, a simple random sample of individuals is drawn from a population. On these individuals, information is obtained on treatment, outcome and a few low dimensional covariates. These individuals are then stratified according to these factors. In the second phase, a random subsample of individuals is drawn from each stratum, with known stratum‐specific selection probabilities. On these individuals, a rich set of covariates is collected. In this setting, we introduce five estimators: simple inverse weighted; simple doubly robust; enriched inverse weighted; enriched doubly robust; locally efficient. We evaluate the finite sample performance of these estimators in a simulation study. We also use our methodology to estimate the causal effect of trauma care on in‐hospital mortality by using data from the National Study of Cost and Outcomes of Trauma.