Using entropy distance measures for testing odds ratio parameters under logistic regression models based on case–control data |
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Affiliation: | 1. Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing of Ministry of Education, Shanghai 200240, China;2. School of Biomedical Engineering Shanghai Jiao Tong University, Shanghai 200240, China;3. Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box 400743, Charlottesville, VA 22904-4743, USA |
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Abstract: | We propose two retrospective test statistics for testing the vector of odds ratio parameters under the logistic regression model based on case–control data by exploiting the density ratio structure under a two-sample semiparametric model, which is equivalent to the assumed logistic regression model. The proposed test statistics are based on Kullback–Leibler entropy distance and are particularly relevant to the case–control sampling plan. These two test statistics have identical asymptotic chi-squared distributions under the null hypothesis and identical asymptotic noncentral chi-squared distributions under local alternatives to the null hypothesis. Moreover, the proposed test statistics require computation of the maximum semiparametric likelihood estimators of the underlying parameters, but are otherwise easily computed. We present some results on simulation and on the analysis of two real data sets. |
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