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Mixture models in measurement error problems, with reference to epidemiological studies

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  • Sylvia Richardson
  • Laurent Leblond
  • Isabelle Jaussent
  • Peter J. Green

Abstract

Summary. The paper focuses on a Bayesian treatment of measurement error problems and on the question of the specification of the prior distribution of the unknown covariates. It presents a flexible semiparametric model for this distribution based on a mixture of normal distributions with an unknown number of components. Implementation of this prior model as part of a full Bayesian analysis of measurement error problems is described in classical set‐ups that are encountered in epidemiological studies: logistic regression between unknown covariates and outcome, with a normal or log‐normal error model and a validation group. The feasibility of this combined model is tested and its performance is demonstrated in a simulation study that includes an assessment of the influence of misspecification of the prior distribution of the unknown covariates and a comparison with the semiparametric maximum likelihood method of Roeder, Carroll and Lindsay. Finally, the methodology is illustrated on a data set on coronary heart disease and cholesterol levels in blood.

Suggested Citation

  • Sylvia Richardson & Laurent Leblond & Isabelle Jaussent & Peter J. Green, 2002. "Mixture models in measurement error problems, with reference to epidemiological studies," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 165(3), pages 549-566, October.
    • Handle: RePEc:bla:jorssa:v:165:y:2002:i:3:p:549-566
    DOI: 10.1111/1467-985X.00252
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    References listed on IDEAS

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    1. Murray Aitkin, 1999. "A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 55(1), pages 117-128, March.
    2. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    3. Daniel W. Schafer & Jay H. Lubin & Elaine Ron & Marilyn Stovall & Raymond J. Carroll, 2001. "Thyroid Cancer Following Scalp Irradiation: A Reanalysis Accounting for Uncertainty in Dosimetry," Biometrics, The International Biometric Society, vol. 57(3), pages 689-697, September.
    4. Raymond J. Carroll & Kathryn Roeder & Larry Wasserman, 1999. "Flexible Parametric Measurement Error Models," Biometrics, The International Biometric Society, vol. 55(1), pages 44-54, March.
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    10. Arana, Jorge E. & Leon, Carmelo J., 2005. "Flexible mixture distribution modeling of dichotomous choice contingent valuation with heterogenity," Journal of Environmental Economics and Management, Elsevier, vol. 50(1), pages 170-188, July.
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