Assessing Covariate Balance with Small Sample Sizes.

Propensity score adjustment addresses confounding by balancing covariates in subject treatment groups through matching, stratification, inverse probability weighting, etc. Diagnostics ensure that the adjustment has been effective. A common technique is to check whether the standardized mean difference for each relevant covariate is less than a threshold like 0.1. For small sample sizes, the probability of falsely rejecting the validity of a study because of chance imbalance when no underlying balance exists approaches 1. We propose an alternative diagnostic that checks whether the standardized mean difference statistically significantly exceeds the threshold. Through simulation and real-world data, we find that this diagnostic achieves a better trade-off of type 1 error rate and power than standard nominal threshold tests and not testing for sample sizes from 250 to 4000 and for 20 to 100,000 covariates. In network studies, meta-analysis of effect estimates must be accompanied by meta-analysis of the diagnostics or else systematic confounding may overwhelm the estimated effect. Our procedure for statistically testing balance at both the database level and the meta-analysis level achieves the best balance of type-1 error rate and power. Our procedure supports the review of large numbers of covariates, enabling more rigorous diagnostics.