```Date: Wed, 18 Oct 2006 05:24:11 -0400 Reply-To: Jim Groeneveld Sender: "SAS(r) Discussion" From: Jim Groeneveld Subject: Re: Sample size in clinical trial Comments: To: Madan Kundu Hi Madan, Instead of your "inferiority trial" I would say: For non-inferiority 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 super-superiority. If you want to show non-inferiority, 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 non-inferiority 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 non-inferiority 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 (super-superiority) or negative (non-inferiority). 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 wrote: >Hi ALL, > > > >I have question regarding sample size calculation in Clinical trial. How >does the sample size calculation differ for Superiority, Non-inferiority >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 (1-beta)*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(1-beta)/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 > > > > > > > >(i) The information contained in this e-mail message is intended only for the confidential use of the recipient(s) named above. This message is privileged and confidential. If the reader of this message is not the intended recipient or an agent responsible for delivering it to the intended recipient, you are hereby notified that you have received this document in error and that any review, dissemination, distribution, or copying of this message is strictly prohibited. If you have received this communication in error, please notify us immediately by e-mail, and delete the original message. > > > (ii) The sender confirms that Ranbaxy shall not be responsible if this email message is used for any indecent, unsolicited or illegal purposes, which are in violation of any existing laws and the same shall solely be the responsibility of the sender and that Ranbaxy shall at all times be indemnified of any civil and/ or criminal liabilities or consequences there. ```

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