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Bayesian sample size determination for estimating binomial parameters from data subject to misclassification

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  • E. Rahme
  • L. Joseph
  • T. W. Gyorkos

Abstract

We investigate the sample size problem when a binomial parameter is to be estimated, but some degree of misclassification is possible. The problem is especially challenging when the degree to which misclassification occurs is not exactly known. Motivated by a Canadian survey of the prevalence of toxoplasmosis infection in pregnant women, we examine the situation where it is desired that a marginal posterior credible interval for the prevalence of width w has coverage 1−α, using a Bayesian sample size criterion. The degree to which the misclassification probabilities are known a priori can have a very large effect on sample size requirements, and in some cases achieving a coverage of 1−α is impossible, even with an infinite sample size. Therefore, investigators must carefully evaluate the degree to which misclassification can occur when estimating sample size requirements.

Suggested Citation

  • E. Rahme & L. Joseph & T. W. Gyorkos, 2000. "Bayesian sample size determination for estimating binomial parameters from data subject to misclassification," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 49(1), pages 119-128.
    • Handle: RePEc:bla:jorssc:v:49:y:2000:i:1:p:119-128
    DOI: 10.1111/1467-9876.00182
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    Cited by:

    1. Stamey, James & Gerlach, Richard, 2007. "Bayesian sample size determination for case-control studies with misclassification," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2982-2992, March.
    2. Sander Greenland, 2005. "Multiple‐bias modelling for analysis of observational data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(2), pages 267-306, March.
    3. Bollinger, Christopher R. & van Hasselt, Martijn, 2017. "A Bayesian analysis of binary misclassification," Economics Letters, Elsevier, vol. 156(C), pages 68-73.
    4. T. Pham-Gia & N. Turkhan, 2005. "Bayesian decision criteria in the presence of noises under quadratic and absolute value loss functions," Statistical Papers, Springer, vol. 46(2), pages 247-266, April.
    5. Martin Ladouceur & Elham Rahme & Christian A. Pineau & Lawrence Joseph, 2007. "Robustness of Prevalence Estimates Derived from Misclassified Data from Administrative Databases," Biometrics, The International Biometric Society, vol. 63(1), pages 272-279, March.
    6. Martijn van Hasselt & Christopher R. Bollinger & Jeremy W. Bray, 2022. "A Bayesian approach to account for misclassification in prevalence and trend estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 351-367, March.
    7. Zhuoyu Wang & Nandini Dendukuri & Madhukar Pai & Lawrence Joseph, 2017. "Taking Costs and Diagnostic Test Accuracy into Account When Designing Prevalence Studies: An Application to Childhood Tuberculosis Prevalence," Medical Decision Making, , vol. 37(8), pages 922-929, November.
    8. Wesley O. Johnson & Chun-Lung Su & Ian A. Gardner & Ronald Christensen, 2004. "Sample Size Calculations for Surveys to Substantiate Freedom of Populations from Infectious Agents," Biometrics, The International Biometric Society, vol. 60(1), pages 165-171, March.
    9. Singh, Saroja Kumar & Acharya, Sarat Kumar & Cruz, Frederico R.B. & Quinino, Roberto C., 2021. "Bayesian sample size determination in a single-server deterministic queueing system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 17-29.
    10. Paul Gustafson, 2006. "Sample size implications when biases are modelled rather than ignored," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(4), pages 865-881, October.
    11. 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.
    12. Boris G. Zaslavsky, 2013. "Bayesian Hypothesis Testing in Two-Arm Trials with Dichotomous Outcomes," Biometrics, The International Biometric Society, vol. 69(1), pages 157-163, March.
    13. Paul Gustafson & Nhu D. Le & Refik Saskin, 2001. "Case–Control Analysis with Partial Knowledge of Exposure Misclassification Probabilities," Biometrics, The International Biometric Society, vol. 57(2), pages 598-609, June.

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