# [R] sample size for survival curves

array chip arrayprofile at yahoo.com
Fri May 7 07:35:46 CEST 2010

```Thanks Kevin. I thought the time t is at the end of follow-up (length of follow-up)?

John

--- On Thu, 5/6/10, Kevin E. Thorpe <kevin.thorpe at utoronto.ca> wrote:

> From: Kevin E. Thorpe <kevin.thorpe at utoronto.ca>
> Subject: Re: [R] sample size for survival curves
> To: "array chip" <arrayprofile at yahoo.com>
> Cc: r-help at r-project.org
> Date: Thursday, May 6, 2010, 8:20 PM
> 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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