Confidence intervals for proportion difference from two independent partially validated series.
Partially validated series are common when a gold-standard test is too expensive to be applied to all subjects, and hence a fallible device is used accordingly to measure the presence of a characteristic of interest. In this article, confidence interval construction for proportion difference between two independent partially validated series is studied. Ten confidence intervals based on the method of variance estimates recovery (MOVER) are proposed, with each using the confidence limits for the two independent binomial proportions obtained by the asymptotic, Logit-transformation, Agresti-Coull and Bayesian methods. The performances of the proposed confidence intervals and three likelihood-based intervals available in the literature are compared with respect to the empirical coverage probability, confidence width and ratio of mesial non-coverage to non-coverage probability. Our empirical results show that (1) all confidence intervals exhibit good performance in large samples; (2) confidence intervals based on MOVER combining the confidence limits for binomial proportions based on Wilson, Agresti-Coull, Logit-transformation, Bayesian (with three priors) methods perform satisfactorily from small to large samples, and hence can be recommended for practical applications. Two real data sets are analysed to illustrate the proposed methods.
Department of Statistics, Chongqing University of Technology, Chongqing, China sfqiu@cqut.edu.cn.
Shi-Fang
SF
Qiu
Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China.
Wai-Yin
WY
Poon
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China.
Man-Lai
ML
Tang
D000063:Accidents, Traffic / Q000706:statistics & numerical data; D000741:Anemia, Aplastic / Q000453:epidemiology; D001336:Automobiles; D001499:Bayes Theorem; D016010:Binomial Distribution; D016001:Confidence Intervals; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008297:Male; D015995:Prevalence; D015203:Reproducibility of Results; D055815:Young Adult
Bayesian confidence interval; method of variance estimates recovery; partially validated series; proportion difference