Odds Ratio Estimation for Small Proportion in Binomial Distribution
Keywords:
Odds Ratio, Empirical Bayes, Modified Maximum Likelihood EstimatorAbstract
In this study, we introduce the new estimator of odds ratio using Empirical Bayes (EB) for small proportions of success in a 2x2 table. The proposed estimate of odds ratio based on EB is then compared to conventional method, modified maximum likelihood estimator (MMLE), using the Estimated Relative Error (ERE) as a criterion of comparison. The result indicated that the EB estimator is more efficient than MMLE.
References
Agresti, A., Categorical Data Analysis, 3rd Etd., John Willey and Sons, USA, 2013.
Haldane, J.B.S., The estimation and Significance of the Logarithm of a ratio frequencies. Annals of Human Genetics, 1955; 20: 309-311.
Gart, J.J., and Zweifel, J.R., On the bias of various estimations of the logit and its variance with application
Bishop, Y.M.M., Fienberg, S.E., and Holland, P.W., Discrete multivariate analysis. Theory and Practice, Cambridge, MA:MIT press.
Agresti, A., and Yang, M., An empirical investigation some effects of sparseness in contingency tables. Computational Statistics and Data Analysis, 1987; 5: 9-21.
Minka, T.P, Estimating a Dirichlet Distribution. Technical report. MIT, 2000.
Parzen, M., Lipsitz, S., Ibrahim, J., and Klar, N., An estimation of the odds ratio that always exists. Journal of Computation and Graphical Statistics, 2002; 11: 420-436.
Downloads
Issue
Section
License
Copyright © The Author(s). This article is published under the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
