Difference of baseline data between groups NOT significant on pre-matching In a retrospective observational study, I'd like to compare the efficacy of drug A vs drug B, and was considering propensity score matching on age, gender, history of diabetes mellitus, and history of hypertension, of which I considered as covariates.
Before PSM, I found there was already no significant difference between the two groups regarding age (via independent two-sample t-test, variances were homogeneous), as well as gender, DM, and HT (via Chi-square test).
My questions are, as this situation came unexpectedly, is that I still need to do PSM, or I can directly compare the efficacy of the two drugs? It seems that these variates didn't contribute on the chance by which a patient received drug A or B, can these variates still be called "covariates"?

The purpose of matching is to make your groups comparable with respect to the covariates. If the groups are already comparable, then you don't need to do that. A possible problem is that a non-significant test does not say there are no differences. It only says that you could not find differences with your data. There are two possible reasons why one cannot find something: a) there was nothing there (the null hypothesis is true), or b) you did not look hard enough (not enough power). We just don't know.
So you should also look at the actual differences. Be careful, we humans are very good at seeing patterns in random noise. The non-significant test result indicates that it is possible that what you see is just random noise. But don't underinterpret the differences either, for the reasons discussed above. Than you make a judgement call whether or not you need matching.
A judgement call sounds very subjective an unscientific, but remember that what makes a study scientific is that the steps taken that lead to your conclusion are transparent and clearly documented and communicated. Scientific does not mean that a robot could do it.
