Spatial statistics in environmental epidemiology

The planet earth is rich in carbon, oxygen, and hydrogen; it is third from the sun in an orbit that delivers just the right amount of heat and light; and it travels through space with a thin shell of protective ozone that has been crucial to the evolution of terrestrial-based organisms. Our environment has in recent times been seen as delicate and not to be taken for granted. The study of the interaction of one or many organisms with its environment is known as ecology. In this entry, we shall concentrate on one organism, the species Homo sapiens, which is unique in its ability to modify the environment of all organisms on this planet. Changes in the environment, anthropogenic or natural (see Global environmental change), can have deleterious effects on humans. The study of these effects can range in scale from the molecular to the demographic. This entry is concerned with the demographic scale, where the study of disease and its progression through the population of H. sapiens is known as epidemiology. Environmental epidemiology is a discipline that relies to a large extent on observational studies; even the case–control studies that are a standard tool of epidemiologists [3] (see Deviance function) do not approach the rigor of the design of agricultural field trials [14]. There is a very real tension in environmental epidemiology between the desire to establish a network of causation and the lack of experimental control available in observational studies. However, when the ‘signal’ is strong enough, sometimes it is possible to establish causative relationships. One of the earliest success stories in environmental epidemiology is the study by Snow [26] that related the street addresses of cholera victims to putative pollution sources, water supply pumps. Through the use of maps and the careful study of each case of a cholera epidemic in London in 1848, John Snow discovered that cholera is a waterborne infectious disease (see Disease mapping). This is all the more amazing because it was done some 20 years before Koch and Pasteur established the beginnings of microbiology as we know it today. To make progress with noisy data and vaguely formulated hypotheses, statistical models have been developed that allow inference even down to individual levels, such as in frailty models [4]. Many of these models are hierarchical and some are spatial, and it is on these we shall concentrate in this entry. Methods of longitudinal data analysis [18], which emphasize changes in disease state over time, are not addressed here; see instead the entry on longitudinal studies.