Suppose I aim to examine if treatment A is better than treatment B. My dataset consists of 10,000 individuals with a total of 100,000 observations. Thus each individual is observed 10 times and his covariates (blood pressure, blood lipids etc) are updated each visit. To provide more robust estimates, I use all observations in the Cox regression, by counting process syntax. I would like to adjust for propensity score as well but the problem is:
(1) Should the propensity score be calculated for each observation (i.e 10 times for each individual)?
(2) Should the propensity score be calculated once (per individual) and then held fixed?
My second question
I have read R D'Agostinos review (http://www.stat.ubc.ca/~john/papers/DAgostinoSIM1998.pdf) on use of propensity score but after reading a paper (which investigated differences in treatment A and treatment B on risk of death), where authors stated that their covariance adjustment was done only by stratification with a propensity score; is it not "better" to include the covariates in the Cox regression as well, despite being included in the prop score?
I did not attach a data set because this is a methodological discussion.