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Equivalence test and confidence interval for the difference in proportions for the paired‐sample design
Author(s) -
Tango Toshiro
Publication year - 1998
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/(sici)1097-0258(19980430)17:8<891::aid-sim780>3.0.co;2-b
Subject(s) - mcnemar's test , confidence interval , statistics , equivalence (formal languages) , mathematics , sample size determination , coverage probability , nominal level , robust confidence intervals , cdf based nonparametric confidence interval , monte carlo method , discrete mathematics
This paper considers a model for the difference of two proportions in a paired or matched design of clinical trials, case‐control studies and also sensitivity comparison studies of two laboratory tests. This model includes a parameter indicating both interpatient variability of response probabilities and their correlation. Under the proposed model, we derive a one‐sided test for equivalence based upon the efficient score. Equivalence is defined here as not more than 100Δ per cent inferior. McNemar's test for significance is shown to be a special case of the proposed test. Further, a score‐based confidence interval for the difference of two proportions is derived. One of the features of these methods is applicability to the 2×2 table with off‐diagonal zero cells; all the McNemar type tests and confidence intervals published so far cannot apply to such data. A Monte Carlo simulation study shows that the proposed test has empirical significance levels closer to the nominal α‐level than the other tests recently proposed and further that the proposed confidence interval has better empirical coverage probability than those of the four published methods. © 1998 John Wiley & Sons, Ltd.