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Biometrika 1985 72(2):353-358; doi:10.1093/biomet/72.2.353
© 1985 by Biometrika Trust
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Tests for homogeneity of odds ratio when the data are sparse

KUNG YEE LIANG and STEVEN G. SELF

Department of Biostatistics, Johns Hopkins University Baltimore, Maryland 21205, U.S.A.

Three tests for homogeneity of odds ratio for a series of 2 x 2 tables when the data are sparse are studied by means of Monte Carlo experiments. A score test, based on the assumption that the log odds ratios are generated from some unknown distribution, is shown to be more powerful than the other two. The original test of Zelen (1971), later corrected by Halperin, Ware, Byar et al. (1977), is also examined. It tends to be too liberal under the sparse data situation; however, it has approximately the nominal size when there are as many as ten tables with as few as ten observations per table.

Key Words: Binary data • Conditional maximum likelihood • Odds ratio • Score test • Sparse data • Tests cf homogeneity


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