Department of Biostatistics Seminar/Workshop Series

Propensity score calipers and the overlap condition

Ben B. Hansen, Ph.D

Associate Professor, Department of Statistics

University of Michigan

Propensity scores (Rosenbaum and Rubin, 1983) appear as central contributors to a number of widely used methods of confounder control. They also arise in connection with the antecedent question of whether non-equivalent treatment and control groups are suitable for comparison at all, with or without covariate adjustments.

"Common support", the assumption that propensity scores are bounded away from 1 (Heckman et al, 1998), is so named because for large samples it entails that the propensity support of the treatment group be contained within that of the control group. This entailment may appear to be simple to check, but it is not: it refers to true propensity scores, not estimates of them; and even if true propensity score supports coincide supports on the estimated propensity often will not. The few methodologists who have addressed the issue have tended to do so by changing the subject, specifying sample trimming rules suited to technical objectives other than the straightforward one of ensuring that like be compared to like (Crump et al, 2009; Rosenbaum 2012).

The approach I suggest is to match within propensity score calipers, thus trimming only the subjects for whom there are no counterpart within caliper distance, while using a novel procedure to determine the value of the caliper. I'll discuss two examples, one from education and the other from sociology and public health.