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An Exact Trend Test for Correlated Binary Data
Author(s) -
Corcoran Chris,
Ryan Louise,
Senchaudhuri Pralay,
Mehta Cyrus,
Patel Nitin,
Molenberghs Geert
Publication year - 2001
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2001.00941.x
Subject(s) - exact test , binary data , binary number , mathematics , exponential family , statistics , binomial (polynomial) , exact statistics , negative binomial distribution , score test , likelihood ratio test , poisson distribution , arithmetic
Summary. The problem of testing a dose‐response relationship in the presence of exchangeably correlated binary data has been addressed using a variety of models. Most commonly used approaches are derived from likelihood or generalized estimating equations and rely on large‐sample theory to justify their inferences. However, while earlier work has determined that these methods may perform poorly for small or sparse samples, there are few alternatives available to those faced with such data. We propose an exact trend test for exchangeably correlated binary data when groups of correlated observations are ordered. This exact approach is based on an exponential model derived by Molenberghs and Ryan (1999) and Ryan and Molenberghs (1999) and provides natural analogues to Fisher's exact test and the binomial trend test when the data are correlated. We use a graphical method with which one can efficiently compute the exact tail distribution and apply the test to two examples.