I am trying to investigate if there is a relation between Occupational Therapy (OT) dosage for stroke patients and patient recovery. I have separated the patients into 2 groups by the amount of therapy they received, Low Dose vs High Dose, and am testing for inter-group differences. Because patients were not randomly assigned to the 2 groups and I am using data from a different study, we have to account for confounding factors separating the groups. We do so by using Genetic Matching and ensuring the Low Dose and High Dose groups are balanced in their observed covariates (features about patients). We tried to include as many covariates as we could as Matching covariates, but had to leave out some binary features because the subjects overwhelmingly fell in just one category.
For example: Only 5% of the patients had their preferred language as Spanish as opposed to English. If we included preferred language as a matching feature, it would be hard to find a similar (19:1) balance in both the Low Dose and the High Dose group, given that our Matching methods were also trying to simultaneously find balance across 20 other covariates.
This brings me to a fundamental question: For Binary features where the overwhelming majority of subjects fall in one category, how big should this discrepancy be before we start leaving features out as they lead to imbalanced groups after matching. I cannot arbitrarily come up with a number like 10%. I feel like there has to be some justification for selecting a threshold, but can't find literature on this anywhere.