스크리닝 검사로부터 불량률 추정에 관한 연구 = A Study on the Estimation for Defect Rate from Screening Test

다국어 초록 (Multilingual Abstract)

The estimation problem of defect rate in a specified population has been received much attention in various fields, assessing the products or the process. This problem is intrinsically very simple. However it could become very complex problem when the decision process of defect is done by screening process, because the screening test depends on sensitivity and specificity of the test, and theses are usually less perfect.
Recently the estimation problem of defect rate with perfect specificity and unknown sensitivity was studied by Parker(1996). He proposed a Bayesian method of constructing the confidence interval of defect rate and compared the performances his estimator with Noether(1957)'s estimator, Bailey(1987)'s one and Score method by Gart and Nam(1988). Park et al.(1999) also discussed the same problem and proposed the bootstrap method of constructing a confidence interval.
This paper focuses on the estimation of defect rate when both values of the sensitivity and specificity of the test are unknown. We consider the current available methods, Rogan and Gladden(1978)'s method and Fieller type method, and proposed the more general version of Rogan and Gladden's method, which is based on second order Taylor expansion of Rogan and Gladden's estimator.
In order to compare the performance of the discussed estimators, we conduct the simulation study by using SAS IML. The simulation study is based on 2,000 repetitions and calculate 95% confidence interval. We obtain the approximate coverage probabilities and average interval lengths under the various parameter configurations in order to compare the performances of the discussed estimators.
The simulation study shows that the performances of the estimators highly depends on the sample sizes of three independent groups, especially when defect rate is low. The current available methods do not even maintain the given nominal level, but the proposed method does maintain the given level, even though the method tends to be a little conservative.
In clusion, we recommend the Taylor 2nd expansion method for the estimation for defect rate from screening test.

목차 (Table of Contents)

• 제 1 장 서 론 = 1
• 제 2 장 스크리닝 검사 = 3
• 2.1. 스크리닝 검사의 정의 = 3
• 2.2. 스크리닝 검사에서 용어정의 = 4
• 2.3. 불량발생률 = 5
• 2.4. 스크리닝 검사에서 불량발생률 추정 = 5
• 제 3 장 알려지지 않은 민감도와 특이도를 가진 불량률의 신뢰구간 추정방법 = 7
• 3.1. Taylor 1차 전개방법 = 7
• 3.2. Taylor 2차 전개방법 = 9
• 3.3 Fieller 방법 = 11
• 제 4 장 알려지지 않은 민감도와 완벽한 특이도를 가진 불량률의 신뢰구간 추정방법 = 13
• 4.1 Noether 방법 = 13
• 4.2. Bailey 방법 = 13
• 4.3 Score 방법 = 14
• 제 5 장 모의실험 = 15
• 제 6 장 결론 = 21
• 참고문헌 = 22
• 부 록 = 23
• ABSTRACT = 32