# PharmPK Discussion - Statistical test for three sequence three period BE test

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• On 11 Feb 2005 at 19:34:32, Shruti Agrawal (shrutiagrawal02.aaa.yahoo.co.in) sent the message
`Dear allWe have developed two formulations and want to test the bioequivalenceof both the products in coparison to marketed product. the study designwould be three sequence three period (two tests and one reference) BEstudy.What would be the appropriate statistical test to determine BE of boththe formulations from this study design?Thanks in advanceShrutiDr. Shruti AgrawalDepartment of PharmaceuticsErnest Mario School of PharmacyRutgers, The State University of New Jersey160 Frelinghyusen roadPiscataway NJ 08854`
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• On 11 Feb 2005 at 15:40:34, "Labadie, Robert" (robert.labadie.at.pfizer.com) sent the message
`The following message was posted to: PharmPKShruti,You need to do a six sequence Williams square (special Latin square)designfor your study which is balanced for carryover effects.  Run all yourdatathrough the same statistical model as your classic 2x2 crossover butuse theappropriate contrast statements to obtain your unbiased treatmentestimatesand CIs.Regards.Rob`
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• On 14 Feb 2005 at 17:07:32, =?ISO-8859-1?Q?Helmut_Sch=FCtz?= (helmut.schuetz.aaa.bebac.at) sent the message
`The following message was posted to: PharmPKDear Shruti,as Robert already pointed out, you need a six-sequence Williams' design(a three sequence simply will not work, because it's not balanced bothfortreatment and carry-over).Bellow you will find the six sequences (T1 and T2 are the testformulations, R is the reference)S#|P1|P2|P3------------#1|T1|T2|R#2|T2|R |T1#3|R |T1|T2#4|T1|R |T2#5|T2|T1|R#6|R |T2|T1Since Williams' design is balanced, you are also able to extractpairwisecomparisons - which you may need for nonparametric testing of Tmax ;-)One Caveat:According to my experience, such a design is only acceptable forregulatory applications if you _drop_ one of the formulations in thelater drug development process, i.e., only one of the formulationswill actually be marketed - the study helped you in deciding, which one.If you want to use both formulations (e.g., two different galenicforms should _both_ show BE to the reference) you will run intomultiplicity issues: two simultaneous tests at alpha=0.05 lead to anincreased patient's risk of 1-(1-0.05)^2=0.0975!The calculation of a Bonferroni-corrected 95% confidence interval -instead of the 90% CI - is needed to keep the overall alpha-risk at 5%:alpha-adj=1-(1-0.05/2)^2=0.0494, which is <0.05.You will have to adjust the sample size in study planning accordingly.RegardsHelmut--Helmut SchutzBEBACConsultancy Services for Bioequivalence and Bioavailability StudiesNeubaugasse 36/11A-1070 Vienna/Austriatel/fax +43 1 2311746http://BEBAC.at Bioequivalence/Bioavailability Forum athttp://forum.bebac.athttp://www.goldmark.org/netrants/no-word/attach.html`
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