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A Bayesian Superpopulation Approach to Inference for Finite Populations Based on Imperfect Diagnostic Outcomes

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  • Geoffrey Jones

    (Massey University)

  • Wesley O. Johnson

    (University of California)

Abstract

Common approaches to the analysis of diagnostic outcome data in the absence of a gold standard test employ binomial distributions for the number of infected individuals in each sample, implicitly assuming that the populations are infinite or at least large in relation to the sample size. We present a theoretical framework within which this approach can be justified even for small populations, and describe how this framework can be used to make inferences pertaining to the actual finite populations sampled. The general approach is quite well known in the sample survey literature, but perhaps not outside of it. We show how this approach can be adapted and extended to the modeling of imperfect diagnostic outcomes.

Suggested Citation

  • Geoffrey Jones & Wesley O. Johnson, 2016. "A Bayesian Superpopulation Approach to Inference for Finite Populations Based on Imperfect Diagnostic Outcomes," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(2), pages 314-327, June.
    • Handle: RePEc:spr:jagbes:v:21:y:2016:i:2:d:10.1007_s13253-015-0239-9
    DOI: 10.1007/s13253-015-0239-9
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    References listed on IDEAS

    as
    1. Marios P. Georgiadis & Wesley O. Johnson & Ian A. Gardner & Ramanpreet Singh, 2003. "Correlation‐adjusted estimation of sensitivity and specificity of two diagnostic tests," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 63-76, January.
    2. Little R.J., 2004. "To Model or Not To Model? Competing Modes of Inference for Finite Population Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 546-556, January.
    3. Geoffrey Jones & Wesley O. Johnson & Timothy E. Hanson & Ronald Christensen, 2010. "Identifiability of Models for Multiple Diagnostic Testing in the Absence of a Gold Standard," Biometrics, The International Biometric Society, vol. 66(3), pages 855-863, September.
    4. Nandini Dendukuri & Lawrence Joseph, 2001. "Bayesian Approaches to Modeling the Conditional Dependence Between Multiple Diagnostic Tests," Biometrics, The International Biometric Society, vol. 57(1), pages 158-167, March.
    5. Geoffrey Jones & Wesley O. Johnson, 2014. "Prior Elicitation: Interactive Spreadsheet Graphics With Sliders Can Be Fun, and Informative," The American Statistician, Taylor & Francis Journals, vol. 68(1), pages 42-51, February.
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