Bayesian Smoothing of Lung Cancer Data in Tirol, Salzburg and Vorarlberg
DOI:
https://doi.org/10.17713/ajs.v28i1.507Abstract
Due to the high variability ofML-estimates of relative risk in low population areas incidence ratios have to be smoothed before mapping. We fit a Bayesian hierarchical model where the posterior distribution of relative risks is simulated via a Markov Chain Monte Carlo technique.References
J. Besag, J. York, and A. Mollié. Bayesian Image Restoration, with two Applications in Spatial Statistics (with discussion). Ann. Inst. Statist. Math., 43(1):1–59, 1991.
A. W. Bowman and A. Azzalini. Applied Smoothing Techniques for Data Analysis. Clarendon Press, Oxford, 1997.
D. Clayton and J. Kaldor. Empirical Bayes Estimates of Age-standardized Relative Risks for Use in Disease Mapping. Biometrics, 43:671–681, 1987.
L. D. Fisher and G. Van Belle. Biostatistics, A Methodology for the Health Sciences. Wiley, New York, 1993.
A. Gelman and D. B. Rubin. Inference from Iterative Simulation Using Multiple Sequences. Statistical Science, 7(4):457–472, 1992.
J. Geweke. Evaluating the accuracy of sampling-based approaches to calculating posterior moments. In J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, editors, Bayesian Statistics, volume 4. Oxford University Press, Oxford, 1992.
W. R. Gilks, S. Richardson, and D. J. Spiegelhalter. Introducing Markov Chain Monte Carlo. In W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, editors, Markov Chain Monte Carlo in Practice, chapter 1. Chapman and Hall, London, 1996.
W. K. Hastings. Monte Carlo sampling methods using Markov Chains and their applications. Biometrika, 57:97–109, 1970.
P. Heidelberger and P. Welch. Simulation run lengths control in the presence of an initial transient. Operations Research, 31:1109–33, 1983.
R. Ihaka and R. Gentleman. R: A Language for Data Analysis and Graphics. Journal of Computational and Graphical Statistics, 5(3):299–314, 1996.
R. Koboltschnig. Anwendung Bayesscher Modelle in der Räumlichen Epidemiologie am Beispiel von Lungen-Karzinomdaten in Westösterreich. Doctoral Thesis, Universität Klagenfurt, 1998.
N.Metropolis, A.W. Rosenbluth,M. N. Rosenbluth, A. H. Teller, and E. Teller. Equations of State Calculations by Fast Computing Machines. Journal of Chemical Physics, 21: 1087–1091, 1953.
A.Mollié. Bayesian mapping of disease. InW. R. Gilks, S. Richardson, and D. J. Spiegelhalter, editors, Markov Chain Monte Carlo in Practice, chapter 20. Chapman and Hall, London, 1996.
W. Oberaigner, H. Cronich, and H. Hausmaninger. Krebsatlas Westösterreich, 1988-1992, Salzburg, Tirol, Vorarlberg. Verein Arbeitsgemeinschaft regionaler Tumorregister Österreichs, Innsbruck, 1998.
B. Pesch, U. Halekoh, M. Richter, and F. Pott. Krebsatlas Nordrhein-Westfalen. Ministerium für Arbeit, Gesundheit und Soziales des Landes Nordrhein-Westfalen, Düsseldorf, 1994.
A. E. Raftery and S. Lewis. How many Iterations in the Gibbs Sampler? In J. M. Bernardo, J. Berger, A. P. Dawid, and A. F. M. Smith, editors, Bayesian Statistics, volume 4, pages 763–773. Oxford University Press, Oxford, 1992.
G. O. Roberts. Markov Chain concepts related to sampling algorithms. In W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, editors, Markov Chain Monte Carlo in Practice, chapter 3. Chapman and Hall, London, 1996.
V. Wirth. Serie Umhausen, 1. Teil: Radon und Krebs. Konzept einer aktiven Tumorprophylaxe. Curriculum Oncologicum, 2, 1994.
W. Zatonski, M. Smans, J. Tyczynski, and P. Boyle. Atlas of Cancer Mortality in Central Europe. International Agency for Research on Cancer, Lyon, 1996.
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