st: sample size for equivalence tests

[Philip Ryan <philip.ryan@adelaide.edu.au>]

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
University of Adelaide
Adelaide 5005
South Australia

tel: +61 8  83033570
fax: +61 8 82234075

philip.ryan@adelaide.edu.au
http://www.public-health.adelaide.edu.au/

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