Identifiability, stratification and minimum variance estimation of causal effects.

Abstract

The weakest sufficient condition for the identifiability of causal effects is the weakly ignorable treatment assignment, which implies that potential responses are independent of treatment assignment in each fine subpopulation stratified by a covariate. In this paper, we expand the independence that holds in fine subpopulations to the case that the independence may also hold in several coarse subpopulations, each of which consists of several fine subpopulations and may have overlaps with other coarse subpopulations. We first show that the identifiability of causal effects occurs if and only if the coarse subpopulations partition the whole population. We then propose a principle, called minimum variance principle, which says that the estimator possessing the minimum variance is preferred, in dealing with the stratification and the estimation of the causal effects. The simulation results with the detail programming and a practical example demonstrate that it is a feasible and reasonable way to achieve our goals.