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

["Rosy Reynolds" <rr@dandr.demon.co.uk>]

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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