Odds ratio for a single 2 × 2 table with correlated binomials for two margins |
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Authors: | Jing-Shiang Hwang Atanu Biswas |
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Institution: | (1) Institute of Statistical Science, Academia Sinica, Taipei, 11529, Taiwan;(2) Applied Statistics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, 700108, India |
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Abstract: | While analyzing 2 × 2 contingency tables, the log odds ratio for measuring the strength of association is often approximated
by a normal distribution with some variance. We show that the expression of that variance needs to be modified in the presence
of correlation between two binomial distributions of the contingency table. In the present paper, we derive a correlation-adjusted
variance of the limiting normal distribution of log odds ratio. We also propose a correlation adjusted test based on the standard
odds ratio for analyzing matched-pair studies and any other study settings that induce correlated binary outcomes. We demonstrate
that our proposed test outperforms the classical McNemar’s test. Simulation studies show the gains in power are especially
manifest when sample size is small and strong correlation is present. Two examples of real data sets are used to demonstrate
that the proposed method may lead to conclusions significantly different from those reached using McNemar’s test. |
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Keywords: | Bivariate binomial distribution Log-odds ratio McNemar’ s test Normal approximation |
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