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Analysis of the ratio of marginal probabilities in a matched‐pair setting
Author(s) -
Nam Junmo,
Blackwelder William C.
Publication year - 2002
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1017
Subject(s) - statistics , wald test , mathematics , sample size determination , likelihood ratio test , equivalence (formal languages) , score test , statistic , nuisance parameter , null hypothesis , type i and type ii errors , confidence interval , statistical hypothesis testing , nominal level , statistical power , econometrics , discrete mathematics , estimator
Statistical methods for testing and interval estimation of the ratio of marginal probabilities in the matched‐pair setting are considered in this paper. We are especially interested in the situation where the null value is not one, as in one‐sided equivalence trials. We propose a Fieller‐type statistic based on constrained maximum likelihood (CML) estimation of nuisance parameters. For a series of examples, the significance level of the CML test is satisfactorily close to the nominal level, while a Wald‐type test is anticonservative for reasonable sample sizes. We present formulae for approximate power and sample size for the CML and Wald tests. The matched design is seen to have a clear advantage over the unmatched design in terms of asymptotic efficiency when the two responses of the pair are highly positively correlated. We recommend the CML method over the Wald method, especially for small or moderate sample sizes. Published in 2002 by John Wiley & Sons, Ltd.