Date: Wed, 18 Oct 2006 05:24:11 0400
ReplyTo: Jim Groeneveld <jim2stat@YAHOO.CO.UK>
Sender: "SAS(r) Discussion" <SASL@LISTSERV.UGA.EDU>
From: Jim Groeneveld <jim2stat@YAHOO.CO.UK>
Subject: Re: Sample size in clinical trial
Hi Madan,
Instead of your "inferiority trial" I would say:
For noninferiority trial,
Ho : Mu(r)  Mu(t) < Delta
H1 : Mu(r)  Mu(t) >= Delta (Delta negative)
With usual superiority tests you test with Delta=0, i.e. whether the
difference is significantly larger than 0. If you want to show a significant
difference of say 30, your Delta should be 30, a supersuperiority. If you
want to show noninferiority, like above, you set Delta to e.g. 30. This
would show a significant difference of certainly 30, meaning that the
difference actually is around 0 or positive.
This is the way to test noninferiority and equivalence: you choose
reasonable Delta values close to 0 (positive and negative), that you regard
conceptually or clinically just unequal to 0 and test with those. An
equivalence test would imply two noninferiority tests in either direction.
In quite some software calculating sample size you may enter the difference
to test for. This is mostly 0, but may be specified positive
(supersuperiority) or negative (noninferiority).
I don't know about the alternative formulas by head, but you may find them
quite well on the internet.
Regards  Jim.

Jim Groeneveld, Netherlands
Statistician, SAS consultant
home.hccnet.nl/jim.groeneveld
On Wed, 18 Oct 2006 12:54:22 +0530, Madan Gopal Kundu
<Madan.Kundu@RANBAXY.COM> wrote:
>Hi ALL,
>
>
>
>I have question regarding sample size calculation in Clinical trial. How
>does the sample size calculation differ for Superiority, Noninferiority
>and Equivalence trials?
>
>
>
>Suppose we want to compare population mean (with respect to some
>character) of Test drug with that of Reference drug. Then our hypothesis
>will be:
>
>For superiority trial,
>
>Ho : Mu(t)  Mu(r) <= Delta
>
>H1 : Mu(t)  Mu(r) > Delta
>
>
>
>For inferiority trial,
>
>Ho : Mu(r)  Mu(t) > Delta
>
>H1 : Mu(r)  Mu(t) <= Delta
>
>
>
>For equivalence trial,
>
>Ho : Mu(t)  Mu(r) > Delta or Mu(r)  Mu(t) > Delta
>
>H1 : Delta<= Mu(t)  Mu(r) <= Delta
>
>
>
>Here, Mu(t) and Mu(r) are means of test drug and reference drug
>populations respectively, Delta being the clinically meaningful
>significance difference.
>
>
>
>Now for the following hypothesis and given alpha level of significance
>and (1beta)*100% power
>
>Ho : Mu(t)  Mu(r) =Delta
>
>H1 : Mu(t)  Mu(r) ^= Delta
>
>Sample size formula will be: n = 2*variance*((z(alpha/2) +
>z(1beta)/Delta)**2 (with certain assumptions)
>
>
>
>Now how can I use this formula for Superiority, Inferiority and
>Equivalence trials?
>
>Is there any reference paper that can help me in this regard?
>
>
>
>Thanks in advance.
>
>Regards
>
>MADAN
>
>
>
>
>
>
>
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