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Spatial modeling of regional variables. (English) Zbl 1248.62211
Summary: Accumulated sudden infant death syndrome (SIDS) data, from 1974-1978 and 1979-1984 for the counties of North Carolina, are analyzed. After a spatial exploratory data analysis, Markov random-field models are fit to the data. The (spatial) trend is meant to capture the large-scale variation in the data, and the variance and spatial dependence are meant to capture the small-scale variation. The trend could be a function of other explanatory variables or could simply be modeled as a function of spatial location. Both models are fit and compared. The results give an excellent illustration of a phenomenon already well-known in time series, that autocorrelation in data can be due to an undiscovered explanatory variable. Indeed, for 1974-1978 we confirm a dependence of SIDS rate on proportion of non-white babies born, along with insignificant spatial correlation. Without this regressor variable, however, the spatial correlation is significant. In 1979-1984, perhaps due to reporting bias or the effect of public-education programs in infant health, the proportion of non-white babies born is no longer an important explanatory variable. SIDS is currently a leading category of postneonatal death, yet its cause is still a mystery. It accounts for about 7,000 deaths a year in the United States, taking the lives of about two infants per 1,000 live births. In contrast to the usual pathologic and physiologic studies of SIDS, this article takes an epidemiologic approach, using data available at the county level. The SIDS data analyzed are in a form that is representative of many problems encountered in the health and social sciences. Counts of individuals from a known or estimated base occur in epidemiologic studies (e.g., consider cancer incidence in a particular year, from the base of population years at risk, for U.S. counties), census surveys (e.g., for assessing undercount consider the dual-system estimate of uncounted people in a decennial census, from the base of total number of people, for U.S. states), and so forth. It is hoped that the spatial methods presented will prove useful in a variety of such problems.

62P10 Applications of statistics to biology and medical sciences; meta analysis
62M40 Random fields; image analysis
92C50 Medical applications (general)
Full Text: DOI Link
[1] Atkinson D., ”Epidemiology of Sudden Infant Death in North Carolina: Do Cases Tend to Cluster?” (1978)
[2] Besag J. E., Journal of the Royal Statistical Society 35 pp 192– (1974)
[3] Clayton D., Biometrics 43 pp 671– (1987) · doi:10.2307/2532003
[4] Cliff A. D., Spatial Processes: Models and Applications (1981) · Zbl 0598.62120
[5] Cressie N., Journal of the International Association for Mathematical Geology 17 pp 693– (1985) · doi:10.1007/BF01031611
[6] Cressie N., Journal of the American Statistical Association 81 pp 625– (1986)
[7] Cressie N., Statistics for Spatial Data · Zbl 0799.62002
[8] Cressie N., ”Spatial Modeling of Regional Variables,” (1986) · Zbl 1248.62211
[9] Cressie, N. and Guo, R. ”Mapping Variables,”. Proceedings of the National Computer Graphics Association Conference: Computer Graphics ’87. Vol. 3, pp.521–530. McLean, VA: National Computer Graphics Association.
[10] Cressie N., Biometrical Journal pp 31–
[11] Emerson J. D., Understanding Robust and Exploratory Data Analysis pp 166– (1983)
[12] Fogerty A. C., American Journal of Clinical Nutrition 39 pp 201– (1984)
[13] Giulian G. G., The New England Journal of Medicine 316 pp 1122– (1987) · doi:10.1056/NEJM198704303161804
[14] Goldberg J., Lancet 8080 pp 107– (1978) · doi:10.1016/S0140-6736(78)91423-X
[15] Journel A. G., Mining Geostatistics (1978)
[16] Kindermann R., Markov Random Fields and Their Applications (1980) · Zbl 1229.60003 · doi:10.1090/conm/001
[17] McCullagh P., The Annals of Statistics 11 pp 59– (1983) · Zbl 0507.62025 · doi:10.1214/aos/1176346056
[18] Ord J. K., Journal of the American Statistical Association 70 pp 120– (1975)
[19] Peters T. J., Statistics in Medicine 5 pp 113– (1986) · doi:10.1002/sim.4780050203
[20] Steinschneider A., Pediatrics 50 pp 646– (1972)
[21] Symons M. J., Biometrics 39 pp 193– (1983) · doi:10.2307/2530819
[22] Whittle P., Biometrika 41 pp 434– (1954)
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