I am studying how to handle survival data when the follow-up is long. When I have a long follow-up, the assumption of proportionality of HR in the Cox model tends to fail, because the covariates change over time. To deal with time dependent covariates in a Cox model, one can try to split the follow-up time in several intervals. Then, a Cox model for each interval is computed.

Suppose now that I have one interval without events, perhaps because the interval is too short and the outcome is rare. In such a case, this strategy cannot be applied, I guess. Am I correct?

Also, using this strategy I get many hazard ratio (one HR for each interval), and so I have to compute a total HR. I believe this total HR should be computed as a weighted average of the time interval HRs. How are the weights assigned for each interval? I could not find any indication for this.

Thank you for your help!

I am studying how to handle survival data when the follow-up is long. When I have a long follow-up, the assumption of proportionality of HR in the Cox model tends to fail, because the covariates change over time. To deal with time dependent covariates in a Cox model, one can try to split the follow-up time in several intervals. Then, a Cox model for each interval is computed.

Suppose now that I have one interval without events, perhaps because the interval is too short and the outcome is rare. In such a case, this strategy cannot be applied, I guess. Am I correct?

Also, using this strategy I get many hazard ratio (one HR for each interval), and so I have to compute a total HR. I believe this total HR should be computed as a weighted average of the time interval HRs. How are the weights assigned for each interval? I could not find any indication for this.