# [R] Log rank test power

Terry Therneau therneau at mayo.edu
Fri Feb 1 15:27:20 CET 2008

```> Does anyone have any ideas how I could do a power calculation for a log
> rank test.  I would like to know what the suggested sample sizes would
> be to pick a difference when the control to active are in a ratio of 80%
> to 20%.

Power for a log-rank test is the same as power for a Cox model.  For a 2-arm
study
d = (qnorm(.975) + qnorm(.85))^2 / (.2 *.8 * coef^2)

d = # deaths required
.975 = two sided alpha=.05
.85   = power of .85
.2, .8 = proportion in each group
coef = Cox model coef you want power against.  So for a 50% difference in
hazard rates (or median survival times) coef = log(1.5).

For a 50% change I get d=341.  Now for the hard part of sample size in a
survival study: how many people to you need to enroll and how long will you need
to follow them, to observe 341 total deaths?  This second step is usually a mix
of prior knowlege, enrollment expectations, and wild speculation.  In the words
of a prior director of research at U of Rochester:
"At the commencement of a study the incidence of the disease in question will
drop by one half, and will not return to its former levels until the study ends
or the principle investigator retires, whichever comes first."  L.L.

Terry Therneau

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