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 健康保健與用藥安全是近代社會兩個重要的課題，故在臨床醫學研究上對藥物控制研究特別受到重視，常需藉由比較不同劑量的藥劑或不同藥劑產生的影響作進一步的討論，用以增進生活的品質。本文針對兩相關變量三元反應配對資料邊際機率相關問題作深入的研究，提出常用之統計方法以比較不同樣本間的差異，並透過統計方法比較與數值模擬的過程找尋較簡易且適當的統計方法，供實務應用者方便使用。
 The health care and drug safety are two important subjects for modern society. Recently, clinical medical research is especially paid attention to pharmacy control. In order to improve quality of life, it is necessary to investigate the difference between dosages or drugs. The goal of this paper is to test the marginal homogeneity having two dependent variables of matched pair data with three responses. Some well-known statistic methods are studied. Comparisons between those methods are conducted by simulation studies, and simple and suitable methods are recommended for practical applications.
 目錄............................................................................................................................................I表目錄...................................................................................................................................... II第一章 緒論............................................................................................................................11-1 前言...............................................................................................................................11-2 背景、動機與目的........................................................................................................3第二章 文獻探討....................................................................................................................5第三章 研究方法....................................................................................................................73-1 邊際同質性檢定............................................................................................................73-1-1 華德和分數型態統計量.....................................................................................103-1-2 概似比例和皮爾森卡方統計量.........................................................................123-1-3 Cochran-Mantel-Haenszel 統計量......................................................................133-2 三元反應之特定反應邊際機率檢定..........................................................................15第四章 資料分析與數值模擬..............................................................................................174-1 邊際同質性檢定..........................................................................................................194-2 特定反應之邊際機率檢定..........................................................................................25第五章 結論與未來研究......................................................................................................28附錄.........................................................................................................................................29A. 三元反應邊際同質性檢定-華德與分數型態統計量...................................................29B. 二元反應邊際同質性檢定-華德與分數型態統計量...................................................32C. 程式碼.............................................................................................................................34參考文獻.................................................................................................................................43
 1. Agresti, A. (2002). Categorical data analysis. Wiley, New York.2. Agresti, A. and Klingenberg, B. (2005). Multivariate tests comparing binomialprobabilities, with application to safety studies for drugs. Applied Statistics 54, 691-816.3. Agresti, A. and Klingenberg, B. (2006). Multivariate extensions of McNemar’s test. Biometrics 45, 629-636.4. Agresti, A. and Min, Y. (2005). Simple improved confidence intervals for comparing matched proportions. Statistics in Medicine 24, 729–740.5. Becker, M. P. and Balagtas, C. C. (1993). Marginal modeling of binary cross-over data.Biometrics 49, 997-1009.6. Connett, J. E., Smith, J. A., and McHugh, R. B. (1987). Sample size and power for pair-matched case-control studies. Statistics in Medicine 6, 53-59.7. Connor, R. J. (1987). Sample size for testing differences in proportions for the paired-sample design. Biometrics 43, 207-211.8. Eliasziw, M. and Donner, A. (1991). Application of the McNemar test to non-independentmatched pair data. Statistics in Medicine 10, 1981-1991.9. Feuer, E. J. and Kessler, L. J. (1989). Test statistic and sample size for a two-sample McNemar test. Biometrics 45, 629-636.10. Ireland, C. T., Ku, H. H., and Kullback, S. (1969). Symmetry and marginal homogeneity of an r × r contingency table. Journal of the American Statistical Association 64, 1323-1341.11. Landis, J. R., Heyman, E. R., and Koch, G. G. (1978). Average partial association inthree-way contingency tables：A review and discussion of alternative tests. International Statistical Review 46, 237-254.12. Lang, J. B. (2004). Multinomial-poisson homogeneous models for contingency table.Annals of Statistics 32, 340-383.13. Lang, J. B. and Agresti, A. (1994). Simultaneously modeling joint and marginaldistributions of multivariate categorical responses. Journal of the American StatisticalAssociation 89, 625-632.14. McNemar, S. (1947). Note on the sampling error of the differences between corrected proportions or percentages. Psychometrzka 12, 153-157.15. Nam, J. M. (1997). Establishing equivalence of two treatments and sample size requirements in matched-pairs design. Biometrics 53, 1422-1430.16. Newcombe, R. (1998). Improved confidence intervals for the difference between binomial proportions based on paired data. Statistics in Medicine 17, 2635–2650.17. Obuchowski, N. (1998). On the comparison of correlated proportions for clustered data.Statistics in Medicine 17, 1495-1507.18. Tango, T. (1998). Equivalence test and confidence interval for the difference inproportions for the paired-sample design. Statistics in Medicine 17, 891-908.
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