[R] sample size for survival curves

[Frank E Harrell Jr]

On 05/06/2010 07:20 PM, Kevin E. Thorpe wrote:
> array chip wrote:
>> 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

Note that this formula makes an unnecessary approximation that the 
number of events is the same in both groups.

See the Hmisc package cpower, spower, ciapower functions for more info.

Frank

>>
>> Because number of events required only depends on hazard ratio.
>>
>> Thanks for any suggestions.
>>
>> John
>
> As I recall, the survival probability used in Freedman is not at some
> arbitrary time of your choosing, but rather at the average length of
> follow-up time anticipated in the study.
>
> Kevin
>


-- 
Frank E Harrell Jr   Professor and Chairman        School of Medicine
                      Department of Biostatistics   Vanderbilt University