Sample size determination for matched-pair equivalence trials using rate ratio

Biostatistics, Jul 2007

In this article, we compare Wald-type, logarithmic transformation, and Fieller-type statistics for the classical 2-sided equivalence testing of the rate ratio under matched-pair designs with a binary end point. These statistics can be implemented through sample-based, constrained least squares estimation and constrained maximum likelihood (CML) estimation methods. Sample size formulae based on the CML estimation method are developed. We consider formulae that control a prespecified power or confidence width. Our simulation studies show that statistics based on the CML estimation method generally outperform other statistics and methods with respect to actual type I error rate and average width of confidence intervals. Also, the corresponding sample size formulae are valid asymptotically in the sense that the exact power and actual coverage probability for the estimated sample size are generally close to their prespecified values. The methods are illustrated with a real example from a clinical laboratory study.

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Sample size determination for matched-pair equivalence trials using rate ratio

NIAN-SHENG TANG 0 1 0 Department of Statistics, Yunnan University , Kunming 650091, China 1 Department of Mathematics, Hong Kong Baptist University , Kowloon, Hong Kong MAN-LAI TANG SHUN-FANG WANG c The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: . 1. INTRODUCTION 2. PROCEDURES FOR EQUIVALENCE HYPOTHESIS TESTS 2.1 Interval hypothesis New Total Reference procedure Concordant (1) Not concordant (0) Total procedures can be described by the following interval hypotheses: H0g: p1+g/ p+1g where 0g < 1g are predetermined clinically meaningful lower and upper equivalence limits. To test the interval hypothesis H0g in (2.1), we adopt the widely used two one-sided tests (TOST) approach. This consists of testing the following 1-sided hypotheses (see, Dunnett and Gent, 1977; Schuirmann, 1987): H0lg: p1+g/ p+1g H0ug: p1+g/ p+1g and taking the p value of the equivalence test for (2.1) to be the maximum of the p values of the TOST for (2.2) and (2.3) (Berger and Hsu, 1996). Asymptotic equivalence tests T1lg = T1ug = T2ug = T2lg = T3lg = T3ug = Tests based on the confidence interval approach k lg = inf{0g: Tk lg < z/2} and k ug = sup{1g: Tk ug > z/2}, with k = 1, 2, 3. 3. SAMPLE SIZE FORMULAE 4. ANALYSIS OF THE LABORATORY STUDY H0g: p1+g/ p+1g Penicillin allergy Concordant BPO-SP Concordant Not concordant Concordant Not concordant 17 2 p11d = p1+d 0.3 p11d = p1+d 0.2 5. CONCLUSION ACKNOWLEDGMENTS REFERENCES BERGER, J. R. AND HSU, J. (1996). Bioequivalence trials, intersection union tests and equivalence confidence sets (with discussion). Statistical Science 11, 283319. FARRINGTON, C. P. AND MANNING, G. (1990). Test statistics and sample size formulae for comparative binomial trials with null hypothesis of non-zero risk difference or non-unity relative risk. Statistics in Medicine 9, 14471454. (...truncated)


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Nian-Sheng Tang, Man-Lai Tang, Shun-Fang Wang. Sample size determination for matched-pair equivalence trials using rate ratio, Biostatistics, 2007, pp. 625-631, 8/3, DOI: 10.1093/biostatistics/kxl034