# Re: Power analysis for Cox regression with a time-varying covariate

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## Re: Power analysis for Cox regression with a time-varying covariate

 Marc gave the referencer for Schoenfeld's article.  It's actually quite simple. Sample size for a Cox model has two parts:   1. Easy part: how many deaths to I need        d = (za + zb)^2 / [var(x) * coef^2]        za = cutoff for your alpah, usually 1.96 (.05 two-sided)        zb = cutoff for power, often 0.84 = qnorm(.8) = 80% power        var(x) = variance of the covariate you are testing.  For a yes/no variable like treatment this would be p(1-p) where p = fraction on the first arm        coef = the target coefficient in your Cox model.  For an "increase in survival of 50%" we need exp(coef)=1.5 or coef=.405 All leading to the value I've memorized by now of (1.96 + 0.84)^2 /(.25* .405^2) = 191 deaths for a balanced two arm study to detect a 50% increase in survival.   2. Hard part: How many patients will I need to recruit, over what interval of time, and with how much total follow-up to achieve this number of events?     I never use the canned procedures for sample size because this second part is so study specific.  And frankly, it's always a guesstimate.  Death rates for a condidtion will usually drop by 1/3 as soon as you start enrolling subjects. Terry T. ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.