本文考慮根據條件勝算比針對二元配對資料進行受測和對照處理的非劣性檢定。首先利用已有的近似檢定推導此一勝算比的近似信賴界限，但是這些近似信賴界限的最小覆蓋機率低於名目信賴水準。本文進一步利用Buehler (1957)的方法修正上述的近似信賴界限，得到條件勝算比的正確信賴界限，並且得到兩種處理的正確非劣性檢定。本文計算上述非劣性檢定的型I誤差率和檢定力，評估近似及正確非劣性檢定的表現。最後，利用一筆資料說明所提正確非劣性檢定的應用。

This article considers testing against the noninferiority of a testing treatment to a reference treatment based on the conditional odds ratio for matched-pair data. Approximated confidence bounds for the odds ratio are first derived from existed approximate tests. However, the minimum coverage probabilities of the approximate confidence bounds lose to maintain their nominal level. Therefore, the approximate confidence bounds are modified based on the results in Buehler (1957), and the exact noninferiority tests are obtained. The type I error rates and power are then computed to evaluate the performance of the approximate and exact noninferiority tests. Finally, the exact tests are illustrated by using a real data set.

1. Bartlett, M.S. (1953). Approximate Confidence Intervals. II: More Than One Unknown Parameter. Biometrika 40, 306-317.
2. Buehler, R.J. (1957). Confidence Intervals for the Product of Two Binomial Parameters. Journal of the American Statistical Association 52, 482-493.
3. Chan, I.S.F, Tang, N.S., Tang, M.L. and Chan, P.S. (2003). Statistical Analysis of Noninferiority Trials with a Rate Ratio in Small-Sample Matched-Pair Designs. Biometrics 59, 1170-1177.
4. Hsueh, H.M., Liu, J.P. and Chen, J.J. (2001). Unconditional Exact Tests for Equivalence or Noninferiority for Paired Binary Endpoints. Biometrics 57, 478-483.
5. Jobe, J.M. and David, H.T. (1992). Buehler Confidence Bounds for a Reliability- Maintainability Measure. Technometrics 34, 214-222.
6. Lachenbruch, P.A. and Lynch, C.J. (1998). Assessing Screening Tests: Extensions of McNemar’s Test. Statistics in Medicine 17, 2207-2217.
7. Lachin, J.M. (2000). Biostatistical Methods: The Assessment of Relative Risks. John Wiley and Sons, New York.
8. Liu, J.P., Fan, H.Y. and Ma, M.C. (2005). Tests for Equivalence Based on Odds Ratio for Matched-Pair Design. Journal of Biopharmaceutical Statistics 15, 889-901.
9. Liu, J.P., Hsueh, H.M., Hsieh, E. and Chen, J.J. (2002). Tests for Equivalence or Non-Inferiority for Paired Binary Data. Statistics in Medicine 21, 231-245.
10. Lloyd, C.J. and Kabaila, P. (2003). On the Optimality and Limitations of Buehler Bounds. Australian and New Zealand Journal of Statistics 45, 167-174.
11. Lloyd, C.J. and Moldovan, M.V. (2007). Exact One-Sided Confidence Limits for the Difference Between Two Correlated Proportions. Statistics in Medicine 26, 3369-3384.
12. Lu, Y. and Bean, J.A. (1995). On the Sample Size for One-Sided Equivalence of Sensitivities Based upon McNemar’s Test. Statistics in Medicine 14, 1831- 1839.
13. Mack, T.M., Pike, M.C., Henderson, B.E., Pfeffer, R.I., Gerkins, V.R., Arthus, B.S. and Brown, S.E. (1976). Estrogens and Endometrial Cancer in a Retirement Community. New England Journal of Medicine 294, 1262-1267.
14. McNemar, Q. (1947). Note on the Sampling Error of the Difference Between Corrected Proportions or Percentages. Psychometrika 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. Nam, J.M. and Blackwelder, W.C. (2002). Analysis of the Ratio of Marginal Probabilities in a Matched-Pair Setting. Statistics in Medicine 21, 689-699.
17. Serfling, R.J. (1980). Approximation Theorems of Mathematics Statistics. John Wiley and Sons, New York.
18. Tang, M.L., Tang, N.S., Chan, I.S.F. and Chan, B.P.S. (2002). Sample Size Determination for Establishing Equivalence /Noninferiority via Ratio of Two Proportions in Matched-Pair Design. Biometrics 58, 957-963.
19. Tang, N.S., Tang, M.L. and Chen, I.S.F. (2003). On Tests of Equivalence via Non-Unity Relative Risk for Matched-Pair Design. Statistics in Medicine 22, 1217-1233.
20. 蘇峻德(民國98年)。「二元配對資料邊際機率比率之正確信賴下界」，國立中央大學，碩士論文。