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Test for Homogeneity of Odds Ratios Using <i>U</i>-Statistics
Surgery Core Research, Baylor College of Medicine, Houston, USA
Department of Biostatistics and Data Science, School of Public Health, The University of Texas Health Science Center at Houston, Houston, USA
- 1 Surgery Core Research, Baylor College of Medicine, Houston, USA
- 2 Department of Biostatistics and Data Science, School of Public Health, The University of Texas Health Science Center at Houston, Houston, USA
Open Journal of Statistics·Volume 09 (2019)·Pages 347–360·Published 17 June 2019·DOI10.4236/ojs.2019.93024
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Abstract
There are a few statistics testing the homogeneity of odds ra t ios across strata. Asymptotic statistics los e their power in the “sparse-data” setting. Both asymptotic statistics and exact tests have low power when the sample sizes are small. We created a set of U statistics and compared them with some existing statistics in testing homogeneity of OR at different data settings. We evaluated their performance in terms of the empirical size and power via Monto Carlo simulations. Our results showed that two of the U-statistics under our study had higher power for testing homogeneity of odds ratios for 2 by 2 con tingency tables. The application of the tests was illustrated in two real examples.
KeywordsHomogeneity TestOdds Ratio<i>U</i>-Statistics
- Liang, K.Y. and Self, S.G. (1985) Tests of Homogeneity of Odds Ratio When the Data Are Sparse. Biometrika, 72, 353-358. https://doi.org/10.1093/biomet/72.2.353
- Paul, S.R. and Donner, A. (1992) Small Sample Performance of Tests of Homogeneity of Odds Ratios in k 2 × 2 Tables. Statistics in Medicine, 11, 159-165. https://doi.org/10.1002/sim.4780110203
- Jones, M.P., O’Gorman, T.W., Lemke, J.H. and Woolson, R.F. (1989) A Monte Carlo Investigation of Homogeneity Tests of the Odds Ratio under Various Sample Size Configurations. Biometrics, 45, 171-181. https://doi.org/10.2307/2532043
- Zelen, M. (1971) The Analysis of Several 2 × 2 Contingency Tables. Biometrika, 58, 129-137. https://doi.org/10.1093/biomet/58.1.129
- Halperin, M., Ware, J.H., Byar, D.P., Mantel, M., Brown, C.C., Koziol, J., Jail, M. and Green, S.B. (1977) Testing for Interaction in an I × J × K Contingency Table. Biometrika, 64, 271-275. https://doi.org/10.1093/biomet/64.2.271
- Thomas, D.G. (1975) Exact and Asymptotic Methods for the Combination of 2 × 2 Tables. Computers and Biomedical Research, 8, 423-446. https://doi.org/10.1016/0010-4809(75)90048-8
- Pagano, M. and Tritchler, D. (1983). Algorithms for the Analysis of Several 2 × 2 Contingency Tables. SIAM Journal of Scientific and Statistical Computing, 4, 302-309. https://doi.org/10.1137/0904024
- Metha, C.R., Patel, N.R. and Wei, L.J. (1988) Computing Exact Significance Tests with Restricted Randomization Rules. Biometrika, 75, 295-302. https://doi.org/10.1093/biomet/75.2.295
- Thomas, D.G. and Gart, J.J. (1992) Improved and Extended Exact and Asymptotic Methods for the Combination of 2 × 2 Tables. Computers and Biometrical Research, 25, 75-84. https://doi.org/10.1016/0010-4809(92)90036-A
- Hirji, K.F., Vollset, S.E., Reis, I.M. and Afifi, A.A. (1996) Exact Tests for Interaction in Several 2 × 2 Tables. Journal of Computational and Graphical Statistics, 5, 209-224. https://doi.org/10.1080/10618600.1996.10474706
- Reis, I. M., Hirji, K.F. and Afifi, A.A. (1999) Exact and Asymptotic Tests for Homogeneity in Several 2 × 2 Tables. Statistics in Medicine, 18, 893-906. https://doi.org/10.1002/(SICI)1097-0258(19990430)18:8 3.0.CO;2-5
- Bagheri, Z., Ayatollahi, S.M.T. and Jafari, P. (2011) Comparison of Three Tests of Homogeneity of Odds Ratios in Multicenter Trials with Unequal Sample Sizes within and among Centers. BMC Medical Research Methodology, 11, 58. https://doi.org/10.1186/1471-2288-11-58