How to compare groups when one treatment group has no events and the treatment variable is time varying - survival analysis

Question

I am comparing two treatment groups and I have 3 different types of outcomes. The dependent variable, treatment, is time dependent and so I conducted time dependent cox regression for each of the three outcomes.

However, for one of the outcomes, one treatment group had no events. Of course, the cox regression output for the estimated effect of that group will be −∞, and hence the hazard ratio in this scenario can't be interpreted.

I saw in another thread that the log rank test can be used in a scenario where one of the treatment groups has no events. However, my understanding is that while this may be a valid option for variables that are not time dependent (constant treatment value throughout study period), the standard log rank test can't be done in this scenario. Am I wrong? I tried doing this in R and the output had different estimates for each event strata.

Is there another way to compare the two groups?

I can clarify further in case the question isn't clear.

P.S. I have used the terms time dependent/varying interchangeably in this post.

Answer 1

Without events in a group you can't get finite regression-coefficient (or corresponding hazard-ratio) point estimates relative to that group in a Cox model even if covariate values are fixed in time. Nevertheless, you can get limits on confidence intervals (CI), in a way that works with time-varying covariates too. That's a useful way to present such results.

The CI can be found by calculating the profile (partial) likelihood of the data as you force the model to go through a range of finite values for the "infinite" regression coefficient. Then find the finite coefficient value that corresponds to a 95% confidence interval, given that the other end of the interval is infinite. The process is illustrated in R on this page. I understand that SAS can do this with built-in functionality.