A new confidence interval for the difference between two binomial proportions of paired data |
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| Affiliation: | 1. Biostatistics Unit, HSR & D Center of Excellence, VA Puget Sound Health Care System, 1660 S. Columbian Way, Seattle, WA 98108-1597, USA;2. Department of Biostatistics, University of Washington, F-600 Health Sciences Building, Campus MS 357232, Seattle, WA 98195-7232, USA;3. Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, USA;1. Department of Cardiac Surgery, Klinikum Nürnberg, Paracelsus Medizinischen Privatuniversität, Nuremberg, Germany;2. Department of Cardiac Surgery, Universitätsklinikum Münster, Münster, Germany;1. Institute for Biostatistics, Hannover Medical School, Carl-Neuberg-Str. 1, 30625 Hannover, Germany;2. Department of Medical Statistics, University Göttingen, Humboldtallee 32, 37073 Göttingen, Germany;3. National Reference Centre for TSE, Department for Neurology, University Göttingen, Robert-Koch-Str. 40, 37075 Göttingen, Germany;4. Department of Epidemiology, Helmholtz Centre for Infection Research, Inhoffenstr. 7, 38124 Braunschweig, Germany;5. German Center for Infection Research, Hannover-Braunschweig Site, Feodor-Lynen-Str. 7, 30625 Hannover, Germany;1. Division of Nephrology, Hypertension and Endocrinology, Department of Internal Medicine, Nihon University School of Medicine, Tokyo, Japan;2. Department of Nephrology, Keiai Hospital, Tokyo, Japan;3. Department of Nephrology, Meirikai Chuo General Hospital, Tokyo, Japan;4. Department of Nephrology, Yujin Clinic, Tokyo, Japan |
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| Abstract: | Motivated by a study on comparing sensitivities and specificities of two diagnostic tests in a paired design when the sample size is small, we first derived an Edgeworth expansion for the studentized difference between two binomial proportions of paired data. The Edgeworth expansion can help us understand why the usual Wald interval for the difference has poor coverage performance in the small sample size. Based on the Edgeworth expansion, we then derived a transformation based confidence interval for the difference. The new interval removes the skewness in the Edgeworth expansion; the new interval is easy to compute, and its coverage probability converges to the nominal level at a rate of O(n−1/2). Numerical results indicate that the new interval has the average coverage probability that is very close to the nominal level on average even for sample sizes as small as 10. Numerical results also indicate this new interval has better average coverage accuracy than the best existing intervals in finite sample sizes. |
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