# Sample size calculation for multivariable Cox regression for treatment comparison

I am trying to calculate the required sample size for a future study.

Specifically, the goal is to compare two treatments based on their survival. The Cox model will be used, and along with the treatment indicator (0/1) there will be also some other covariates, both binary and non-binary.

The big problem, as always, is that there is no data available. I found the function powerEpi in R, but this is only for two covariates in the model. Some other functions in the same package (powerSurvEpi) need actual/pilot data for the calculation.

Can somebody propose a function/software/formula for this case ?

Thank you!

Controlling for covariates other than treatment in power calculations depends on assumptions about how values of all the covariates will be associated both with the treatment groups and among each other. That's probably why tools in the R powerSurvEpi package stop at allowing for a single covariate along with a binary treatment choice. Then you only have to make one assumption: the association of the single covariate with treatment. Adding even a second covariate would require additional assumptions about the associations of the second covariate with: treatment, the first covariate, and the combination of treatment with the first covariate. If you are trying to convince a reviewer or funding agency about the quality of your study, adding additional assumptions (even if well founded) raises the risk that your audience will think that you cherry-picked a particular set of assumptions that makes your study look better than it really will be.