# [R] Power analysis for Cox regression with a time-varying covariate

Terry Therneau therneau at mayo.edu
Wed Jul 18 15:24:03 CEST 2012

```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.

```