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Open AccessArticle

Common Medical and Statistical Problems: The Dilemma of the Sample Size Calculation for Sensitivity and Specificity Estimation

1
Department of Mathematics and CEMAT, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
2
Unidade de Saúde Pública Internacional e Bioestatística, Global Health and Tropical Medicine, Instituto de Higiene e Medicina Tropical, Universidade Nova de Lisboa and Centro de Estatística e Aplicações da Universidade de Lisboa, Rua da Junqueira, 100, 1349-008 Lisbon, Portugal
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2020, 8(8), 1258; https://doi.org/10.3390/math8081258
Received: 29 June 2020 / Revised: 25 July 2020 / Accepted: 29 July 2020 / Published: 1 August 2020
(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)
Sample size calculation in biomedical practice is typically based on the problematic Wald method for a binomial proportion, with potentially dangerous consequences. This work highlights the need of incorporating the concept of conditional probability in sample size determination to avoid reduced sample sizes that lead to inadequate confidence intervals. Therefore, new definitions are proposed for coverage probability and expected length of confidence intervals for conditional probabilities, like sensitivity and specificity. The new definitions were used to assess seven confidence interval estimation methods. In order to determine the sample size, two procedures—an optimal one, based on the new definitions, and an approximation—were developed for each estimation method. Our findings confirm the similarity of the approximated sample sizes to the optimal ones. R code is provided to disseminate these methodological advances and translate them into biomedical practice. View Full-Text
Keywords: sample size; sensitivity; specificity; conditional probability; coverage probability sample size; sensitivity; specificity; conditional probability; coverage probability
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MDPI and ACS Style

Oliveira, M.R.; Subtil, A.; Gonçalves, L. Common Medical and Statistical Problems: The Dilemma of the Sample Size Calculation for Sensitivity and Specificity Estimation. Mathematics 2020, 8, 1258.

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