# Re: st: Power calculation and sample sizes

 From "Svend Juul" To Subject Re: st: Power calculation and sample sizes Date Fri, 17 Aug 2007 14:03:56 +0200

```Cecilia wrote:

I would like to determine the sample size for a RCT. Control and
intervention
groups will have the same size.
The intention of the intervention is to increase a certain preventive
measure
among patients.
We will measure prevalence of the preventive measure at baseline for
both groups
and expect to find that 20% of all the patients (control and
the measure before the experiment.
We would like to be able to detect a change from 20% to 40% in the
intervention
group, while we expect that the control group will change their adoption
rates
from 20% to 25%.

My first plan was to simulate some samples, starting with some
hypothetical
sample size, then run a logistic model multiple times, and calculate
power as a
proportion of times when the expected coeficients were significant. Then
repeat
the simulations for different sample sizes until I could had an idea of
sample
size versus power.

-------------------------------------------------------------------

-search sample size- points, among other things, to the official Stata
command
-sampsi-.

A change from 20% to 40% means an increase of 25% among the 80%
at baseline, and a change from 20% to 25 % means an increase of 6.25%.

The command now is:

. sampsi .25 .0625

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 =   0.9000
p1 =   0.2500
p2 =   0.0625
n2/n1 =   1.00

Estimated required sample sizes:

n1 =       88
n2 =       88

Now, the 88 + 88 are the numbers for 80% non-adopters at baseline, so
you
should add 25% to these figures, i.e. 110 + 110. - if you want
alpha=0.05
and power=0.90.

Hope this helps
Svend

__________________________________________

Svend Juul
Institut for Folkesundhed, Afdeling for Epidemiologi
(Institute of Public Health, Department of Epidemiology)
Vennelyst Boulevard 6
DK-8000  Aarhus C, Denmark
Phone: +45 8942 6090
Home:  +45 8693 7796
Email: sj@soci.au.dk
__________________________________________

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```