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Experimental design and statistical methods for classical and bioequivalence hypothesis testing with an application to dairy nutrition studies¹

Department of Animal Science, Michigan State University, East Lansing 48824-1225

² Correspondence: 1205 Anthony Hall (phone: 517-355-8445; e-mail: tempelma{at}msu.edu).

Genetically modified (GM) corn hybrids have been recently compared against their isogenic reference counterparts in order to establish proof of safety as feedstuffs for dairy cattle. Most such studies have been based on the classical hypothesis test, whereby the null hypothesis is that of equivalence. Because the null hypothesis cannot be accepted, bioequivalence-testing procedures in which the alternative hypothesis is specified to be the equivalence hypothesis are proposed for these trials. Given a Type I error rate of 5%, this procedure is simply based on determining whether the 90% confidence interval on the GM vs. reference hybrid mean difference falls between two limits defining equivalence. Classical and bioequivalence power of test are determined for 4 x 4 Latin squares and double-reversal designs, the latter of which are ideally suited to bioequivalence studies. Although sufficient power likely exists for classical hypothesis testing in recent GM vs. reference hybrid studies, the same may not be true for bioequivalence testing depending on the equivalence limits chosen. The utility of observed or retrospective power to provide indirect evidence of bioequivalence is also criticized. Design and analysis issues pertain to Latin square and crossover studies in dairy nutrition studies are further reviewed. It is recommended that future studies should place greater emphasis on the use of confidence intervals relative to P-values to unify inference in both classical and bioequivalence-testing frameworks.

Key Words: Bioequivalence Testing • Dairy Science • Experimental Design • Genetically Modified Feedstuffs • Sample Size

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