Causal Inference with observational data in CSNI(cluster-specific non-ignorable) condition

Abstract

Due to absence of randomization procedure, causal inference is a lot more delicate procedure with observational data as compared with experimental data. The propensity score weighting method is being increasingly used in such disciplines so as to achieve balance of observed confounders in order to remove their confounding effects. However, this method hasnt been developed so far so as to cope with unmeasured confounders efficiently. Meanwhile, observational data often have analytically relevant multilevel or clustered structure, which can be the source of cluster-specific unmeasured confounders. In this paper, we propose an unbiased estimator for the population average causal effect of a binary treatment from observational data when the treatment assignment mechanism is assumed to be CSNI (cluster-specific non-ignorable). We also propose a consistent estimator of its variance, using standard linearization method. This new estimator turns out to satisfy consistency and asymptotic normality also, which will be proven successively.