I have question regarding survival analysis. I am looking at observational studies comparing patient survival who received treatments A or B at different centres (>10), for the same condition and have been followed-up for different time periods (between 1 and 10 years). I have the duration of follow-up for all participants (or time to death), as well as data for some covariates.

I am wondering what the best way to compare the effect of treatments A and B on survival. My current plan was to attempt an analysis pooling the log hazard ratios/standard errors of the Cox model for each centre, as often done with other meta-analyses.

  1. Is it an issue that there are quite a lot of varying ratios of participants receiving treatment A or B depending on the centre (these are observational studies), varying sample sizes and that the follow up periods vary by centre, particularly when combining all centres? Or is there a better analysis strategy?

  2. The Cox regression model assumes proportional hazards, but most likely adverse effects of the treatment would occur in the first year. Is there a way to account for this in the model, or elsewhere? I understand the Cox regression would consider survival across the entire follow-up period, but would it be worth, for this reason, to compare survival at 1 year as well?

  3. I suppose this approach would be superior to simply indiscriminately pooling all participants and running a singular Cox regression on it, due to centre-specific biases (given the treatment is surgical) and population/selection biases. Is there a way I could estimate this bias to see whether it actually exists (in case that the demographics are all comparatively similar between centres/groups)?

Thank you!

  • $\begingroup$ Are you interested in measuring the effect of center on the effect of treatment? $\endgroup$
    – Todd D
    Commented Jun 27, 2022 at 17:10
  • $\begingroup$ @ToddD The main questions is just the effect of treatment A vs. B on survival, based on participants from different centres. But I was curious if being at a different centre affected this particular effect (given the treatment is a surgical intervention). $\endgroup$
    – hyst111
    Commented Jun 27, 2022 at 17:46

1 Answer 1


If you have corresponding covariate values from all of the institutions, then one approach would be to build a Cox model with all the cases while including the institutions as a type of random effect. That could be done with a gamma frailty term in the original coxph() modeling in R, or a Gaussian random effect in the coxme package. That allows for a distribution of center-specific hazards beyond those associated with the covariates, providing at least a start at addressing the issues in questions 1 and 3.

With respect to question 2, if you expect that most events of interest happen in the first year and you have reasonably complete follow-up through at least 1 year, then you could do a binomial regression with respect to outcomes at 1 year. Note that your expectation does not necessarily invalidate the proportional hazards (PH) assumption; your assumption has to do with the baseline hazard, and it's possible that PH still holds at later times around a lower overall hazard.

For further investigation of center-specific bias in terms of treatment selection, you could consider evaluating the propensity of receiving treatment A versus B as a function of covariates, including the institution as a predictor. That's often done with a logistic regression, but the more flexible propensity modeling provided by the twang package can be helpful. You also could then incorporate the propensity of having received treatment A versus B into your survival model to try to correct further. See the many posts on this site about propensity-scores.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.