Abstract

This paper proposes a unified framework for the analysis of incidence or mortality data in space and time. The problem with such analysis is that the number of cases and the corresponding population at risk in any single unit of space \Theta time are too small to produce a reliable estimate of the underlying disease risk without "borrowing strength" from neighbouring cells. The goal here could be described as one of smoothing, in which both spatial and non--spatial considerations may arise, and spatio--temporal interactions may become an important feature. Based on an extended version of the main effects model proposed in KnorrHeld and Besag (1998), four generic types of space \Theta time interactions are introduced. Each type implies a certain degree of prior (in)dependence for interaction parameters, and corresponds to the product of one of the two spatial main effects with one of the two temporal main effects. Data analysis is implemented via Markov chain Monte Carlo methods. The methodology is illustrated by an analysis of Ohio lung cancer data 1968-88. We compare the fit and the complexity of each model by the DIC criterion, recently proposed in Spiegelhalter et al. (1998).

Citations

295	Bayesian computations via the Gibbs sampler and related Markov chain Monte Carlo methods - Smith, Roberts - 1993
174	Bayesian image restoration, with two applications in spatial statistics. Ann Inst Stat Math 43(1):1–59 - Besag, York, et al. - 1991
121	Polynomial Splines and their Tensor Products in Extended Linear Modeling (with discussion - Stone, Hansen, et al. - 1997
110	Bayesian computation and stochastic Systems (with discussion - Besag, Green, et al. - 1995
100	Kaldor J: Empirical Bayes estimates of age-standardized relative risks for use in disease mapping - DG - 1987
98	Generalized linear models.2nd edition - McCullagh, JA - 1989
86	Bayesian Forecasting and Dynamic Models, 2nd edn - West, Harrison - 1997
40	Hierachical spatio-temporal mapping of disease rates - Waller, Carlin, et al. - 1997
27	Conditional prior proposals in dynamic models - Knorr-Held - 1999
27	Montomoli C: Bayesian estimates of disease maps: How important are prior - Bernardinelli, Clayton - 1995
24	Modelling risk from a disease in time and space - Knorr-Held, Besag - 1998
24	Bayesian Deviance, the Effective Number of Parameters, and the Comparison of Arbitrarily Complex Models - SPIEGELHALTER, BEST, et al. - 1998
23	Bayesian methods for mapping disease risk - Clayton, Bernardinelli - 1992
18	Generalized linear mixed models - Clayton - 1996
16	Bayesian models for spatially correlated disease and exposure data - Best, Arnold, et al. - 1999
9	Dynamic and semiparametric models - Fahrmeir, Knorr-Held - 2000
7	Bayesian analysis of survival on multiple time scales - Berzuini, Clayton - 1994
6	Bayesian analysis of space-time variation in disease risk - Bernardinelli, Clayton, et al. - 1995
2	Urbanization and cancer mortality - Greenberg - 1983
2	Dynamic discrete time duration models: estimation via Markov chain Monte Carlo - Fahrmeir, Knorr-Held - 1997
2	cancer rates: a simple adjustment for urbanization - Kafadar, Tukey - 1993