The role of the c-statistic in variable selection for propensity score models.

The applied literature on propensity scores has often cited the c-statistic as a measure of the ability of the propensity score to control confounding. However, a high c-statistic in the propensity model is neither necessary nor sufficient for control of confounding. Moreover, use of the c-statistic as a guide in constructing propensity scores may result in less overlap in propensity scores between treated and untreated subjects; this may require the analyst to restrict populations for inference. Such restrictions may reduce precision of estimates and change the population to which the estimate applies. Variable selection based on prior subject matter knowledge, empirical observation, and sensitivity analysis is preferable and avoids many of these problems.