# [R] sample size for survival curves

array chip arrayprofile at yahoo.com
Fri May 7 01:45:47 CEST 2010

```Dear R users, I am not asking questions specifically on R, but I know there are many statistical experts here in the R community, so here it goes my questions:

Freedman (1982) propose an approximation of sample size/power calculation based on log-rank test using the formula below (This is what nQuery does):
(Z(1-α/side)+Z(power))^2*(hazard.ratio+1)^2
N  =  ---------------------------------------------
(2-p1-p2)*(hazard.ratio-1)^2

Where Z is the standard normal cumulative distribution. p1 and p2 are the survival probability of the 2 groups at a given time, say t.

As you can see, the sample size depends on the survival probabilities, p1 and p2. This is where my question lies. Let’s say we have 2 survival curves. I can choose p1 and p2 at time 1 year, and calculate a sample size. I can also choose p1 and p2 at time 5 years (still the same hazard ratio since the same 2 survival curves), and calculate a different sample size. How to interpret the 2 estimates of sample size?

This problem doesn’t occur when we calculate the number of events required using this formula:
4*( Z(α/side)+Z(power))^2
--------------------------
(log(hazard.ratio))^2

Because number of events required only depends on hazard ratio.

Thanks for any suggestions.

John

```