New multivariate tests for assessing covariate balance in matched observational studies

We propose new tests for assessing whether covariates in a treatment group and matched control group are balanced in observational studies. The tests exhibit high power under a wide range of multivariate alternatives, some of which existing tests have little power for. The asymptotic permutation null distributions of the proposed tests are studied and the p-values calculated through the asymptotic results work well in finite samples, facilitating the application of the test to large data sets. The tests are illustrated in a study of the effect of smoking on blood lead levels. The proposed tests are implemented in an R package BalanceCheck.