# st: sample size for equivalence tests

 From Philip Ryan To statalist@hsphsun2.harvard.edu Subject st: sample size for equivalence tests Date Sun, 09 Feb 2003 15:33:53 +1030

Paul

No easy suggestions. With proportions like that you are probably looking at quite substantial sample sizes.
I would hit the reference indices in Biometrics and Statistics in Medicine etc.

I notice that Chapman & Hall have recently published "Testing Statistical Hypotheses of Equivalence" by Welleck (2002) which has a section on exact equivalence tests for proportions, but I don't know if that has a discussion on sample size considerations.

nQuery Advisor 4.0 implements a simulation based procedure for equivalence confidence intervals using the Newcombe-Wilson method (Newcombe RG Interval estimation for the difference between independent proportions: comparison of eleven methods. Statistics in Medicine 1988 ;17:873-890.) I do not know the properties of this method for tiny proportions and I am not near my library at the moment to check out the Stats in Med article, but for what it's worth - maybe nothing - an example shows what you might be up against in terms of numbers:

If your old and new success rates are both 0.01 and you want sufficient (say, 80%) power for the lower limit of the observed 95% confidence interval of the difference in proportions to exceed -.005 (that is, you will tolerate - and still call equivalent - the new treatment's success rate being not worse than .005 below the old rate) you will need 5000 (five thousand) subjects in each group (total 10,000). If you are willing to tolerate a difference of the same order of magnitude as the proportions themselves, that is, -.01, you will need about 1300 subjects per group.

Finally, Al Feiveson wrote an article on power by simulation in an issue of the Stata Journal (Vol 2 No 2, 2002). This might be a useful starting point if you felt the need to do things from first principles.

Good luck.

Phil

At 08:24 PM 8/02/2003 +0000, you wrote:

```On 8-2-03 2:08 pm, "Philip Ryan" <philip.ryan@adelaide.edu.au> wrote:

> Remember this simple program uses normal approximations, so when dealing
> with proportions less than about 0.2 you are on shaky ground.
>

Thanks Philip,

Unfortunately I am dealing with proportions of the order of 0.01.

Any suggestions.

Paul
```
```
Philip Ryan
Associate Professor
Department of Public Health
Medical School
South Australia

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