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
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