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

Author

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  • M. Rosário Oliveira

    (Department of Mathematics and CEMAT, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
    These authors contributed equally to this work.)

  • Ana Subtil

    (Department of Mathematics and CEMAT, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
    These authors contributed equally to this work.)

  • Luzia Gonçalves

    (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)

Abstract

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.

Suggested Citation

  • M. Rosário Oliveira & Ana Subtil & Luzia Gonçalves, 2020. "Common Medical and Statistical Problems: The Dilemma of the Sample Size Calculation for Sensitivity and Specificity Estimation," Mathematics, MDPI, vol. 8(8), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1258-:d:393091
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    References listed on IDEAS

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    1. Nandini Dendukuri & Elham Rahme & Patrick Bélisle & Lawrence Joseph, 2004. "Bayesian Sample Size Determination for Prevalence and Diagnostic Test Studies in the Absence of a Gold Standard Test," Biometrics, The International Biometric Society, vol. 60(2), pages 388-397, June.
    2. Luzia Gonçalves & M. Rosário de Oliveira & Cláudia Pascoal & Ana Pires, 2012. "Sample size for estimating a binomial proportion: comparison of different methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2453-2473, July.
    3. Vos, Paul W. & Hudson, Suzanne, 2005. "Evaluation Criteria for Discrete Confidence Intervals: Beyond Coverage and Length," The American Statistician, American Statistical Association, vol. 59, pages 137-142, May.
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