Controlling Selection Bias In Causal Inference

Abstract

Selection bias, caused by preferential exclusion of samples from the data, is a major obstacle to valid causal and statistical inferences; it cannot be removed by randomized experiments and can hardly be detected in either experimental or observational studies. This paper highlights several graphical and algebraic methods capable of mitigating and sometimes eliminating this bias. These nonparametric methods generalize previously reported results, and identify the type of knowledge that is needed for reasoning in the presence of selection bias. Specifically, we derive a general condition together with a procedure for deciding recoverability of the odds ratio (OR) from s-biased data. We show that recoverability is feasible if and only if our condition holds. We further offer a new method of controlling selection bias using instrumental variables that permits the recovery of other effect measures besides OR.