When should Standardized Mean Differences (SMD) be used? If there is a significant difference, is Cox regression or Propensity Score Matching more appropriate?

Hello, I have a methodological question. I am looking to assess whether variables such as antibiotic use or specific microbiota families are associated with decreased survival in patients undergoing immunotherapy. Should I first check for substantial differences in standardized mean differences between the groups who used antibiotics and those who did not? Would it suffice to simply perform a Cox regression analysis adjusting for clinically significant variables, or would it be incorrect if there were substantial standardized mean differences (greater than 0.3)? Should I consider conducting a propensity score analysis before proceeding with Cox regression? Thank you!

How was the observational study designed? Did you survey 10 experts to find out the treatment selection cues, then make sure you measure all those potential confounders? Design is everything.

I for one don’t believe in looking at SMDs as this approach assumes distributions are symmetric and that differences of interest are only in the means. I would instead specify a model that is as flexible as the sample size allows (using splines etc.) and fit that model. Try to use analysis strategies that are one-step and do not require decisions along the way.

I don’t see many examples where propensity score analysis is a good idea. But if you do, pre-specify a few important covariates and add to the model a spline function of the logic of the propensity score.