Causal inference with observational data under cluster-specific non-ignorable assignment mechanism

An estimator of the population average causal treatment effect is proposed for multi-level clustered data from observational studies when the treatment assignment mechanism is cluster-specific non-ignorable. This is motivated from a health policy study to evaluate the cost associated with rehospitalization due to premature discharge. The proposed estimator utilizes cluster-level calibration condition and is shown to be consistent and asymptotically normal. The proposed method is evaluated along with existing methods through simulations and is applied to the health care cost study using California inpatient dataset.