# st: power or sample size by survival vs. comparison of proportions

 From "Rosy Reynolds" To "statalist" Subject st: power or sample size by survival vs. comparison of proportions Date Fri, 20 Jun 2008 22:15:00 +0100

This question has been puzzling me for hours this evening, and I have a nagging feeling that I am missing something obvious.
Suppose there are two groups of equal size in a (proportional hazards) survival study. I follow them up for such a time that overall 50% of participants die, and I am looking for a hazard ratio of 1.5. By the end of follow-up, therefore, 60% would die in the higher risk group and 40% in the lower risk group.
If I was going to analyse simply by comparing the proportions who died in the two groups, I could estimate the number needed for 80% power, 5% significance, with
sampsi 0.6 0.4, power(0.8) alpha(0.05)
If I was going to analyse by using Cox regression, I could estimate the number with
stpower cox, hratio(1.5) power(0.8) alpha(0.05) failprob(0.5)

-sampsi- estimates that I need 214 participants (107 in each group), while -stpower- estimates a need for 382 participants to observe 191 deaths. (Stata output below.)
It seems very surprising that the Cox method should need so many more patients than the comparison of proportions method. Where have I gone wrong in my thinking? Or, if I haven't gone wrong, why is Cox regression so much less powerful than comparison of proportions?

Rosy Reynolds
Bristol

Commands and output
*****************
. sampsi 0.6 0.4, power(0.8) alpha(0.05)

Estimated sample size for two-sample comparison of proportions

Test Ho: p1 = p2, where p1 is the proportion in population 1
and p2 is the proportion in population 2
Assumptions:

alpha = 0.0500 (two-sided)
power = 0.8000
p1 = 0.6000
p2 = 0.4000
n2/n1 = 1.00

Estimated required sample sizes:

n1 = 107
n2 = 107

*****************
. stpower cox, hratio(1.5) power(0.8) alpha(0.05) failprob(0.5)

Estimated sample size for Cox PH regression
Wald test, log-hazard metric
Ho: [b1, b2, ..., bp] = [0, b2, ..., bp]

Input parameters:

alpha = 0.0500 (two sided)
b1 = 0.4055
sd = 0.5000
power = 0.8000
Pr(event) = 0.5000

Estimated number of events and sample size:

E = 191
N = 382

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