# [R] sample size for survival curves

Kevin E. Thorpe kevin.thorpe at utoronto.ca
Fri May 7 02:20:53 CEST 2010

```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
>
> 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

--
Kevin E. Thorpe
Biostatistician/Trialist, Knowledge Translation Program
Assistant Professor, Dalla Lana School of Public Health
University of Toronto
email: kevin.thorpe at utoronto.ca  Tel: 416.864.5776  Fax: 416.864.3016

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