Cluster Membership provides Guaranteed Balancing Scores.
*Robert L. Obenchain, Risk Benefit Statistics LLC
Keywords: propensity score, balancing score
In 1983, Rosenbaum & Rubin introduced the conditional independence theorem of propensity scoring and demonstrated that the unknown, true propensity score is the "most coarse" balancing score while the observed X-vector of covariate values is the "most detailed" balancing score. Here, we argue that membership in a X-space cluster of patients that is relatively small and compact provides a balancing score somewhere between the above extremes of coarse or detailed. In other words, it really is not necessary to estimate propensity scores and perform somewhat tedious checks for balance. Rather, local nonparametric estimates of propensity to be treated are provided by the observed treatment fractions within each cluster. Unlike LATE estimation where covariates are assumed to be instruments, we concentrate here on estimation of Local Treatment Differences (LTDs) within informative clusters.