I am performing a propensity score analysis with weights on different medications. I'm obtaining a very low misclassification rate based on the fact that these medicines were introduced at different times and, the data seem to say, were most often prescribed right after their introduction to the market. By including when the patient first got their prescription I'm able to predict with a fairly high degree on certainty what drug she got.
The problem is that other variables pivotal to the clinical outcomes, such as measures of cardiovascular or overall health, are not as predictive and so remain unbalanced after propensity score weighting.
Since it seems to me that the outcomes (stroke and adverse bleeding) are not dependent upon when the drug was prescribed am I right in thinking that I can exclude the date of the first script as a predictor, settle for a much higher misclassification rate and conduct a more rigorous propensity score analysis with only those confounders included that I think will have an effect on the clinical outcomes?