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st: sample size for equivalence tests
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.
At 08:24 PM 8/02/2003 +0000, you wrote:
On 8-2-03 2:08 pm, "Philip Ryan" <firstname.lastname@example.org> wrote:
> Remember this simple program uses normal approximations, so when dealing
> with proportions less than about 0.2 you are on shaky ground.
Unfortunately I am dealing with proportions of the order of 0.01.
Department of Public Health
University of Adelaide
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