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A Comparison of Several Point Estimators of the Odds Ratio in a Single 2 X 2 Contingency Table

S. D. Walter and R. J. Cook
Biometrics
Vol. 47, No. 3 (Sep., 1991), pp. 795-811
DOI: 10.2307/2532640
Stable URL: http://www.jstor.org/stable/2532640
Page Count: 17
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Comparison of Several Point Estimators of the Odds Ratio in a Single 2 X 2 Contingency Table
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Abstract

The relative performance of the unconditional maximum likelihood estimators (UMLEs), conditional MLEs (CMLEs), and Jewell-type estimators of the odds ratio (OR) and its logarithm were investigated in sets of single 2 x 2 contingency tables. The tables were generated by complete enumeration of all possible cell frequencies consistent with a single fixed margin. The bias, mean squared error (MSE), and average absolute error (AAE) were computed for all estimators using the individual table probabilities as weights. The results showed that, for the OR, Jewell's estimator usually had smaller bias, MSE, and AAE than either of the MLEs. While the differences were often slight for MSE and AAE, for bias it was sometimes substantial. For the log(OR), the UMLE usually had the lowest bias, and its MSE and AAE were only slightly greater than those for the other estimators. Overall we recommend estimation on the log scale using the UMLE. If OR is to be estimated, Jewell's method had strong merit, although it is nonsymmetric with respect to the table orientation. In view of this, the UMLE may again be favoured in some situations.

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