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Bayesian non-parametric models for regional prevalence estimation

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  • Adam Branscum
  • Timothy Hanson
  • Ian Gardner

Abstract

We developed a flexible non-parametric Bayesian model for regional disease-prevalence estimation based on cross-sectional data that are obtained from several subpopulations or clusters such as villages, cities, or herds. The subpopulation prevalences are modeled with a mixture distribution that allows for zero prevalence. The distribution of prevalences among diseased subpopulations is modeled as a mixture of finite Polya trees. Inferences can be obtained for (1) the proportion of diseased subpopulations in a region, (2) the distribution of regional prevalences, (3) the mean and median prevalence in the region, (4) the prevalence of any sampled subpopulation, and (5) predictive distributions of prevalences for regional subpopulations not included in the study, including the predictive probability of zero prevalence. We focus on prevalence estimation using data from a single diagnostic test, but we also briefly discuss the scenario where two conditionally dependent (or independent) diagnostic tests are used. Simulated data demonstrate the utility of our non-parametric model over parametric analysis. An example involving brucellosis in cattle is presented.

Suggested Citation

  • Adam Branscum & Timothy Hanson & Ian Gardner, 2008. "Bayesian non-parametric models for regional prevalence estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(5), pages 567-582.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:5:p:567-582
    DOI: 10.1080/02664760701835862
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    References listed on IDEAS

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    1. Hanson, Timothy E., 2006. "Inference for Mixtures of Finite Polya Tree Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1548-1565, December.
    2. 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.
    3. 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.
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    Cited by:

    1. Haydar Demirhan & Kamil Demirhan, 2016. "A Bayesian approach for the estimation of probability distributions under finite sample space," Statistical Papers, Springer, vol. 57(3), pages 589-603, September.
    2. Giancarlo Manzi & David J. Spiegelhalter & Rebecca M. Turner & Julian Flowers & Simon G. Thompson, 2011. "Modelling bias in combining small area prevalence estimates from multiple surveys," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(1), pages 31-50, January.
    3. Joscha Krause & Jan Pablo Burgard & Domingo Morales, 2022. "$$\ell _2$$ ℓ 2 -penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 459-489, May.

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