簡易檢索 / 詳目顯示
| 研究生： |
吳晨瑄 CHEN-HSUAN WU |
|---|---|
| 論文名稱： |
多項分布 2 × 2 列聯表勝算比之區間估計 Interval estimation for the odds ratio of a 2 × 2 contingency table from multinomial distribution |
| 指導教授： |
楊明宗
Ming-Chung Yang |
| 口試委員: | |
| 學位類別： |
碩士 Master |
| 系所名稱： |
理學院 - 統計研究所 Graduate Institute of Statistics |
| 畢業學年度： | 96 |
| 語文別： | 中文 |
| 論文頁數： | 60 |
| 中文關鍵詞： | 區間估計 、正確非條件方法 、正確條件方法 、多項式分布 、勝算比 |
| 外文關鍵詞： | Interval estimation, Multinomial distribution, Exact conditional approach, Exact unconditional approach, Odds ratio |
| 相關次數： | 點閱：13 下載：0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
在多項抽樣模型下得到的 2 × 2列聯表，欲想了解兩變數間的關聯強度，通常是對勝算比做區間估計，因此模型抽樣會存在兩個干擾參數，常用正確條件法及正確非條件法來解決。由於正確條件法是給定條件下建構信賴區間，在小樣本下樣本空間會有高度離散的情形，所以區間常具有保守性；正確非條件法是利用最大化條件法來消除干擾參數，其建構出的正確非條件信賴區間會有最短的區間長度，且覆蓋機率至少能達到並接近給定的名目信賴係數，且即使在小樣本至中小樣本中其表現亦如此。
For a 2 × 2 contingency table sampled from multinomial distribution, we are interested in measuring strength of association between two variables by the odds ratio. Also constructing a confidence interval for the odds ratio is primarily of concerned in practice. For the multinomial sampling, there are two nuisance parameters except for the odds ratio. Hence we usually take the exact conditional approach to obtain a confidence interval for the odds. However, the exact conditional confidence interval can be very conservative because the exact conditional approach may use a high discrete conditional distribution when the sample size is small. On the other hand, the exact unconditional approach eliminates the nuisance parameters by taking the maximal p-value over all possible values of the nuisance parameters. In this paper, we take the unconditional approach to obtain a modified confidence interval. For small to moderate sample sizes, numerical studies show that comparing to other interval the modified confidence interval usually has shorter length, and its actual confidence coefficient is closer to and at least the nominal confidence coefficient.
1. Agresti, A. (2007). An introduction to categorical data analysis, 2nd edition. John Wiley and Sons, INC., Publication.
2. Agresti, A. and Min, Y. (2002). Unconditional small-sample confidence intervals for the odds ratio. Biostatistics 3, 379-386.
3. Agresti, A. and Min, Y. (2001). On a small-sample confidence intervals for parameters in discrete distributions. Biometrics 57, 963-971.
4. Blaker, H. (2000). Condence curves and improved exact condence intervals for discrete distributions. Canadian Journal of Statistics 28, 783-798.
5. Berger, R.L. and Boos, D.D. (1994). P-values maximized over a confidence set for the nuisance parameter. Journal of the American Statistical Association 89, 1012-1016.
6. Baptista, J. and Pike, M.C. (1977). Exact two-sided confidence limits for the odds ratio in a 2 × 2 table. Journal of the Royal Statistical Society, Series C 26, 214-220.
7. Cornfield, J. (1956). A statistical problem arising from retrospective studies. In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability (ed. Neyman, J.), 4, 135-148.University of California Press, Berkeley.
8. Casella, G. and Berger, R.L. (2002). Statistical inference, 2nd edition. Duxbury Press, Pascic Grove, California
9. Crozier, K.S, Graziani, V., Ditunno, J.F. J.r. and Herbison, G.J. (1991). Spinal cord injury: prognosis for ambulation based on sensory examination in patients who are initially motor complete. Archives of physical Medicine and Rehabilitation 72, 119-121.
10. Fisher, R. A. (1935). The logic of inductive inference. Journal of the Royal Statistical Society Series A 98, 39-54.
11. Hwang J.T. and Yang, M.C. (2001). An optimality theory for mid p-values in 2 × 2 contingency tables. Statistica Sinica 11, 807-826.
12. Lancaster, H.O. (1961). Significance tests in discrete distributions. Journal of the American Statistical Association 56, 223-234.
13. Lin, C.Y. (2006). The study of the improved p-value test in discrete distributions. Ph.D.Thesis of Graduate Institute of Statistics at National Central University.
14. Lin, C.Y. and Yang, M.C. (2005). Improved p-value tests for c omparing two independent binomial proportions. Graduate Institute of Statistics National Central University Technical Report.
15. Lin, C.Y. and Yang, M.C. (2006). Improved exact confidence intervals for the odds ratio in two independent binomial samples. Biometrical Journal 48, 1008-1019.
16. Suissa, S. and Shuster, J.J. (1985). Exact unconditional sample sizes for the 2 × 2 binominal trial. Journal of the Royal Statistical Society Series A 148, 317-327.
17. Troendle, J.F. and Frank, J. (2001). Unbiased condence intervals for the odds ratio of two independent binomial samples with application to case-control data. Biometrics 57, 484-489.
