Propensity Score Interval Matching Using Bootstrap Nonparametric Confidence Intervals

Propensity score matching (PSM) is an essential procedure in propensity score analysis. The matching technique in current PSM methods is to match each case in the treatment group with one or more in the control group based on the closeness of the propensity score that is the point estimate of the probability of the case being assigned to the treatment group. The problem with this technique is that it is difficult to establish a sensible criterion to evaluate the closeness of the matched cases without knowing the standard errors or estimation errors of the propensity score. Cochran and Rubin (1973) suggested using a caliper band in caliper matching to avoid “bad” matches that are not close enough. However, the caliper band in caliper matching is fixed or case-invariant. In other words, it takes the same value that is in proportion of the pooled standard deviation of the propensity score for all the cases and, therefore, caliper matching still cannot address this issue. Moreover, the estimation errors of the propensity score are case-specific. The present study extends caliper matching to a new PSM, interval matching, to utilize the estimation error of the propensity score for each case with case-specific bootstrap nonparametric confidence intervals. In interval matching, if the confidence interval of a case in the treatment group overlaps with that of one or more cases in the control group, they will be taken as “good” matches. The implementation of interval matching is illustrated with an empirical example in public health research.