×

Autoregressive spatial smoothing and temporal spline smoothing for mapping rates. (English) Zbl 1209.62309

Summary: This article proposes generalized additive mixed models for the analysis of geographic and temporal variability of mortality rates. This class of models accommodates random spatial effects and fixed and random temporal components. Spatiotemporal models that use autoregressive local smoothing across the spatial dimension and B-spline smoothing over the temporal dimension are developed. The objective is the identification of temporal trends and the production of a series of smoothed maps from which spatial patterns of mortality risks can be monitored over time. Regions with consistently high rate estimates may be followed for further investigation. The methodology is illustrated by analysis of British Columbia infant mortality data.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M30 Inference from spatial processes
62J12 Generalized linear models (logistic models)
92D30 Epidemiology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bernardinelli, Empirical Bayes versus fully Bayesian analysis of geographical variation in disease risk, Statistics in Medicine 11 pp 983– (1992) · doi:10.1002/sim.4780110802
[2] Besag, Bayesian image restoration, with two applications in spatial statistics, Annals of the Institute of Statistical Mathematics 43 pp 1– (1991) · Zbl 0760.62029 · doi:10.1007/BF00116466
[3] Breslow, Approximate inference in generalized linear mixed models, Journal of the American Statistical Association 88 pp 9– (1993) · Zbl 0775.62195 · doi:10.2307/2290687
[4] Clayton, Geographical and Environmental Epidemiology: Methods for Small-Area Studies pp 205– (1992)
[5] Boor, A Practical Guide to Splines (1978) · doi:10.1007/978-1-4612-6333-3
[6] Diggle, Model based geostatistics (with discussion), Applied Statistics 47 pp 229– (1998) · Zbl 0904.62119
[7] Markov Chain Monte Carlo in Practice (1996) · Zbl 0832.00018
[8] Disease Mapping and Risk Assessment for Public Health (1999) · Zbl 0942.00010
[9] Lee, Hierarchical generalized linear models (with discussion), Journal of the Royal Statistical Society, Series B 58 pp 619– (1996) · Zbl 0880.62076
[10] Leroux, Statistical Models in Epidemiology, the Environment and Clinical Trials pp 135– (1999)
[11] Lin, Bias correction in generalized linear mixed models with multiple components of dispersion, Journal of the American Statistical Association 91 pp 1007– (1993) · Zbl 0882.62059 · doi:10.2307/2291720
[12] Lin, Inference in generalized additive mixed models by using smoothing splines, Journal of the Royal Statistical Society, Series B 61 pp 381– (1999) · Zbl 0915.62062 · doi:10.1111/1467-9868.00183
[13] MacNab , Y. C. 1999 Spatio-temporal modeling of rates Department of Mathematics and Statistics, Simon Eraser University, Burnaby, British Columbia, Canada
[14] MacNab, Parametric bootstrap and penalized quasi-likelihood inference in conditional autoregressive models, Statistics in Medicine 19 (17/18) pp 2421– (2000) · doi:10.1002/1097-0258(20000915/30)19:17/18<2421::AID-SIM579>3.0.CO;2-C
[15] McCulloch, Maximum likelihood algorithms for generalized linear mixed models, Journal of the American Statistical Association 92 pp 162– (1997) · Zbl 0889.62061 · doi:10.2307/2291460
[16] Verbyla, The analysis of designed experiments and longitudinal data by using smoothing splines (with discussion), Applied Statistics 48 pp 269– (1999) · Zbl 0956.62062
[17] Wakefield, Bayesian Statistics 6 pp 657– (1999)
[18] Waller, Hierarchical spatio-temporal mapping of disease rates, Journal of the American Statistical Association 92 pp 607– (1997) · Zbl 0889.62094 · doi:10.2307/2965708
[19] White, Invited Papers, 19th International Biometrics Conference pp 57– (1998)
[20] Yasui, A regression method for spatial disease rates: An estimating function approach, Journal of the American Statistical Association 92 pp 21– (1997) · Zbl 0889.62096 · doi:10.2307/2291446
[21] Zeger, A regression model for time series of counts, Biometrika 75 pp 621– (1988) · Zbl 0653.62064 · doi:10.1093/biomet/75.4.621
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.