I am working on a project where I am comparing the effects of a particular treatment on patients with other patients who didn't receive the treatment. As I am trying to replicate a randomized experiment using data from a observational experiment, I am using matching (I'm trying propensity score, euclidean and mahalanobis distance matching separately to see what produces the best matches) to find a subset of the control group that is best-matched to my treatment group. This essentially means finding control patients that are most similar to the treated patients, according to the available data (demographics and testing data).
For evaluating how well the groups are matched, it is common to look at the ratio of the variances for each co-variate between the treated and the matched control group, the ideal range of ratios being close to 1. It is also common to look at the standardized difference of means for each co-variate between the treated and matched control group, the ideal values considered to be less than 0.25 and as close to 0 as possible.
The problem I am coming across is that some of these covariates end up having a variance of 0 either in the treated set or the matched-control set. Which means all the patients in either the treated or control group are identical in terms of that co-variate. This means the standardized difference of means becomes infinity for a covariate when the standard deviation for that co-variate is 0 in the treated group. It also means that the ratio of variances can lead to a value of 0 or infinity.
What is the proper way to deal with such cases?