# 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!

If this is a prospective randomized controlled trial, then there is little need to incorporate other covariates into your estimates for power analysis. Randomization ideally will balance out the effects of the covariates, although further adjustment for covariates might be useful in later analysis. If adjustment for outcome-related covariates does end up being useful, then ignoring them in the power calculation will overestimate the necessary sample size, a conservative approach that will enhance the chances of study success. An exponential survival model (hazard constant in time) is generally accepted absent more detailed information and is the typical default in power-calculation functions for survival. Specify the hazard ratio for treatment you would like to be able to detect, and the planned accrual and follow-up patterns; standard power-calculation functions will then provide a useful estimate of sample size.

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.

So a simple power calculation for two treatment groups may be the best way to proceed.

• Thank you very much @EdM ! That is a really good answer :) – GiannisZ Jun 7 '19 at 20:20