Impact of Cliff and Ord (1969, 1981) on Spatial Epidemiology

Article excerpt

The influence in spatial epidemiology of the seminar work on autocorrelation by Cliff and Ord is discussed. Quantifying the evidence of spatial clustering was an important step in the development of modern statistical methods for analyzing spatial variations of diseases. Autocorrelation is nowadays mostly accounted for at a latent level within a hierarchical framework to small area disease mapping. The importance of accounting for autocorrelation in geographical correlation studies is also reviewed.

Introduction

As defined by Elliott and Wartenberg (2004), spatial epidemiology is the description and analysis of geographic variations in disease with respect to demographic, environmental, behavioral, socioeconomic, genetic, and infectious risk factors. Spatial analyses abound in the epidemiological literature, with an early example found in the monograph edited by Doll (1984) about the geography of disease, in which large-scale geographical variations of mortality for a number of chronic diseases were used to formulate hypotheses about the potential influence of life style and environment. The article on testing spatial autocorrelation by Cliff and Ord (1969) was highly instrumental in encouraging researchers to go beyond the simple display of disease maps and environmental atlases. It gave impetus to the development of a more formal statistical analysis framework, aimed at precisely characterizing the scale of spatial dependence and the type of geographical patterns, whether in the disease rates themselves or in the residuals of geographical correlation studies. Recent books, containing Spatial Epidemiology in their titles, by Elliott et al. (2000), Lawson (2006, 2008), and Pfeiffer et al. (2008) discuss the central concept of autocorrelation formalized in Cliff and Ord (1969) in order to lay the foundations for more sophisticated analyses. They also describe a series of recent examples, which show how the field has moved on from large-scale descriptive studies toward more powerful small area studies that take advantage of the advances in geographical information systems.

Characterization of spatial disease patterns

Before computing any autocorrelation index, paying attention to the geographical scale and resolution of data is important, both of which influence autocorrelation measures, as shown in Griffith, Wong, and Whitfield (2003). Moreover, spatial gradients, analogous to the trend observed in many time series, influence the autocorrelation indices considered in Cliff and Ord (1969, 1981), because they capture many nonstationary patterns of variation. In spatial epidemiology, the influence of gradient-like contrasts on the epidemiological interpretation of association results is highlighted in the early work of Lazar (1982) and Pocock, Cook, and Shaper (1982), in which strong regional contrasts were shown for both disease and environmental variables, resulting in fewer degrees of freedom for interpretation than if substantial local heterogeneity is observed.

Following on from their 1969 article, Cliff and Ord (1981) introduced a useful general definition of spatial autocorrelation of a variable [Y.sub.i] as [[SIGMA].sub.i,j] [w.sub.ij][A.sub.ij], with weights [w.sub.ij] chosen to measure spatial closeness of areas i and j, and [A.sub.ij] denoting a function quantifying the dependence between the values of [Y.sub.i] and [Y.sub.j]. Their discussion highlights two important interlinked aspects: first, that space has to be treated quite differently from time because it has no natural ordering; and, second, that a need exists to characterize a priori the form of spatial dependence of interest. Indeed, the chosen form of the weights [w.sub.ij] is related to the scale and the type of dependence one is trying to measure, with binary weights based on adjacency being the most commonly used to study local dependence of disease outcomes, whereas distance-based weights are more appropriate when a smoothly varying dependence is hypothesized, such as could be observed for an environmental pollutant. …