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Test procedure and sample size determination for a proportion study using a double-sampling scheme with two fallible classifiers.

Authors
  • Qiu, Shi-Fang1
  • Zeng, Xiao-Song1
  • Tang, Man-Lai2
  • Poon, Wai-Yin3
  • 1 1 Department of Statistics, Chongqing University of Technology, Chongqing, China. , (China)
  • 2 2 Department of Mathematics and Statistics, Hang Seng Management College, Hong Kong, China. , (China)
  • 3 3 Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China. , (China)
Type
Published Article
Journal
Statistical Methods in Medical Research
Publisher
SAGE Publications
Publication Date
Apr 01, 2019
Volume
28
Issue
4
Pages
1019–1043
Identifiers
DOI: 10.1177/0962280217744239
PMID: 29233082
Source
Medline
Keywords
Language
English
License
Unknown

Abstract

Double sampling is usually applied to collect necessary information for situations in which an infallible classifier is available for validating a subset of the sample that has already been classified by a fallible classifier. Inference procedures have previously been developed based on the partially validated data obtained by the double-sampling process. However, it could happen in practice that such infallible classifier or gold standard does not exist. In this article, we consider the case in which both classifiers are fallible and propose asymptotic and approximate unconditional test procedures based on six test statistics for a population proportion and five approximate sample size formulas based on the recommended test procedures under two models. Our results suggest that both asymptotic and approximate unconditional procedures based on the score statistic perform satisfactorily for small to large sample sizes and are highly recommended. When sample size is moderate or large, asymptotic procedures based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic, log- and logit-transformation statistics based on both models generally perform well and are hence recommended. The approximate unconditional procedures based on the log-transformation statistic under Model I, Wald statistic with the variance being estimated under the null hypothesis, log- and logit-transformation statistics under Model II are recommended when sample size is small. In general, sample size formulae based on the Wald statistic with the variance being estimated under the null hypothesis, likelihood rate statistic and score statistic are recommended in practical applications. The applicability of the proposed methods is illustrated by a real-data example.

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