# [R] Binomial Power/Sample Size

Marc Schwartz marc_schwartz at comcast.net
Thu Oct 18 18:18:10 CEST 2007

```On Thu, 2007-10-18 at 10:18 -0500, Bret Collier wrote:
> All,
>
> I have been digging around in the help files and found bsamsize in
> Hmisc, but I am wondering if i am using it right.
>
> So, here is the question:  given a binomial response (success/failure)
> for 2 groups (treatment/control) and I want to estimate the necessary
> sample size (n) to determine if the magnitude of the difference between
> treatments and controls is a 25% increase in success probability.
>
> Pilot data indicated that treatment success was ~0.32, control success
> ~0.09.  So, using bsamsize (code below), I am interested in determining
> what sample size (n) is needed such that I can detect a 25% change in
> success between treatments/controls.
>
> I tried this but I can't shake the feeling I am doing something wrong,
>
>  > power_b<-bsamsize(.25, .0, fraction =0.5, alpha=0.10, power=0.80)
>  > power_b<-as.data.frame(round(power_b, digits=1))
>  > power_b
>     round(power_b, digits = 1)
> n1                       20.6
> n2                       20.6
>
> Any suggestions on approaches, places I should have looked would be helpful,

Your code above suggests that you want to be able to detect a 25%
increase from 0%, which is not what you want.

presumably you want an 80% probability of detecting a 25% improvement
over the 9% success in the control group, which means you would be
looking for 11.25% in the treatment group.

Presuming that your subjects are randomized 1:1, you would use:

> bsamsize(0.09, 0.1125)
n1       n2
2820.493 2820.493

which means you need 2821 subjects in EACH arm of the study.

You can also use power.prop.test(), which is in the base 'stats'
package:

> power.prop.test(p1 = 0.09, p2 = 0.1125, power = 0.8)

Two-sample comparison of proportions power calculation

n = 2820.493
p1 = 0.09
p2 = 0.1125
sig.level = 0.05
power = 0.8
alternative = two.sided

NOTE: n is number in *each* group

Same answer and in both cases, we are presuming a two-sided hypothesis.

I might also note that given the pilot study data, a 25% increase in the
treatment group seems rather conservative. This suggests that if this is
actually part of a study design, you might want to revisit the relative
improvement you seek and/or consider implementing interim stopping
rules.

HTH,

Marc Schwartz

```