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.

##### MSC:

62P10 | Applications of statistics to biology and medical sciences |

62M40 | Statistics of random fields; image analysis |

92C50 | Medical applications of mathematical biology |