小樣本具相關0-1資料比例差的信賴區間之比較研究

A Comparison of the Confidence Intervals for the Proportions Difference Based on Small Sample Correlated Binary Data

李怡華(YI-HUA,LI)

指導教授 ： 王鴻龍

國立臺北大學/商學院/統計學系/碩士(2008年)

摘要

在醫學上為了能夠準確檢驗出人類所罹患的疾病，研發出新的醫學檢測方法，透過新的醫學檢測方法和現行的醫學檢測方法比較，希望能研發出高度準確率的醫學檢測法，讓病患能早期發現，及早做進一步的治療。要比較檢驗方法的反應比率，以兩種檢驗法來說，檢驗結果為成對二元0-1的資料形式，而兩種不同醫學診斷程序的相等性問題屬於兩相關母體比例差檢定。兩相關母體， McNemar(1947) 提出在大樣本之下以近似卡方檢定來比較兩比例差是否相等。

本研究以小樣本之下成對資料二項比例差為一定值的檢定為基礎建構信賴區間，並探討數個檢定統計量，其信賴區間的表現。我們比較了?-投影z統計量、概似比統計量、修正的概似比統計量等檢定統計量，以 Chan 及Zhang(1999)提出的檢定基礎法，找出各種不同統計量反應比例差的信賴區間上下界，最後使用平均覆蓋機率(mean coverage probability)及平均信賴寬度(mean confidence width)，來比較各統計量的信賴區間表現。
結果顯示，樣本數為5-12時以修正的概似比檢定統計量為最適合適用；樣本數為13-20時以?-投影z統計量為最適合使用。

關鍵字

信賴區間 ； 基礎法 ； 小樣本 ； 平均覆蓋機率 ； 平均信賴寬度

並列摘要

In order to improve the inspection rate in clinical trials, researchers develop new inspection method and compared with the current inspection method. These comparisons belong to the testing of two correlated proportions. Under large sample, McNemar (1947) proposed an asymptotic chi-square to test the equality of two correlated proportions.
In the paper, we focused on the test-based confidence intervals under small sample, compared the performances under various testing statistics. Adapting the test based method, proposed by Chan and Zhang (1999), we constructed confidence intervals under various testing statistics, such as ?-projected z statistics, Likelihood ratio statistics and Modified Likelihood ratio statistics. We use the mean coverage probability and mean confidence width to compare the performance of the 95% confidence intervals based on these testing statistics. The result shows that Modified Likelihood ratio statistics performs better when sample size is 5-12; And??-projected z statistics is adaptable to use when sample?size is 13-20.

並列關鍵字

confidence interval ； test based method ； small sample ； mean coverage probability,mean confidence width

參考文獻

Chan, I.S.F. and Zhang, Z. (1999), Test-based Exact confidence intervals for the difference of binomail proportions. Biomtrics 55, 1202-1209.

Chen, X.(2002), Aquasi-exact method for the confidence intervals of the difference of independent binomail proportions in small sample cases. Statistics in Medicine 21, 943-956.

Clopper, C. J. and Pearson, E. S. (1934), The use of confidence or fiducial limits illustrated

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