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Birth Defects Registered by Double Sampling: A Bayesian Approach Incorporating Covariates and Model Uncertainty

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  • Jeremy York
  • David Madigan
  • Ivar Heuch
  • Rolv Terje Lie

Abstract

In double‐sampling schemes, a large sample is classified by using one method, and a sub‐sample is also classified with a supplementary method. In the application discussed here, we are attempting to identify infants in Norway born with Down's syndrome by using both a national birth registry and a regional registry. Usual methods for analysing such data assume that one classification method is perfect, which is not the case here. We develop a Bayesian approach that allows for error in both registries, includes covariates (here, the age of the mother) and explicitly accounts for our lack of knowledge about the complexity of the relationships between the variables considered. Markov chain Monte Carlo methods are used to approximate the posterior. In the data considered here, the error rates of the two registries appear to be substantial. Despite a strong relationship between maternal age and risk of Down's syndrome, the inclusion of the maternal age covariate does not substantially change the overall estimates.

Suggested Citation

  • Jeremy York & David Madigan & Ivar Heuch & Rolv Terje Lie, 1995. "Birth Defects Registered by Double Sampling: A Bayesian Approach Incorporating Covariates and Model Uncertainty," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(2), pages 227-242, June.
    • Handle: RePEc:bla:jorssc:v:44:y:1995:i:2:p:227-242
    DOI: 10.2307/2986347
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    Cited by:

    1. Rahardja, Dewi & Young, Dean M., 2011. "Likelihood-based confidence intervals for the risk ratio using double sampling with over-reported binary data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 813-823, January.
    2. Rahardja, Dewi & Young, Dean M., 2010. "Credible sets for risk ratios in over-reported two-sample binomial data using the double-sampling scheme," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1281-1287, May.
    3. Boese, Doyle H. & Young, Dean M. & Stamey, James D., 2006. "Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3369-3385, August.
    4. Xavier Sala-I-Martin & Gernot Doppelhofer & Ronald I. Miller, 2004. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," American Economic Review, American Economic Association, vol. 94(4), pages 813-835, September.
    5. K. Chitakasempornkul & G. J. M. Rosa & A. Jager & N. M. Bello, 2020. "Hierarchical Modeling of Structural Coefficients for Heterogeneous Networks with an Application to Animal Production Systems," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(4), pages 1-22, December.
    6. Housila Singh & Mariano Ruiz Espejo, 2007. "Double Sampling Ratio-product Estimator of a Finite Population Mean in Sample Surveys," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(1), pages 71-85.
    7. Nandram, Balgobin & Zelterman, Daniel, 2007. "Computational Bayesian inference for estimating the size of a finite population," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2934-2945, March.
    8. Gyuhyeong Goh & Jae Kwang Kim, 2021. "Accounting for model uncertainty in multiple imputation under complex sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 930-949, September.

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