Elsevier

Health & Place

Volume 9, Issue 3, September 2003, Pages 273-277
Health & Place

Visualization of the spatial scan statistic using nested circles

https://doi.org/10.1016/S1353-8292(02)00060-6Get rights and content

Abstract

We propose a technique for the display of results of Kulldorff's spatial scan statistic and related cluster detection methods that provides a greater degree of informational content. By simultaneously considering likelihood ratio and relative risk, it is possible to identify focused sub-clusters of higher (or lower) relative risk among broader regional excesses or deficits. The result is a map with a nested or contoured appearance. Here the technique is applied to prostate cancer mortality data in counties within the contiguous United States during the period 1970–1994. The resulting map shows both broad and localized patterns of excess and deficit, which complements a choropleth map of the same data.

Introduction

The choropleth (value-by-area) map is the most common method of depicting disease rates geographically (Walter and Birnie, 1991; Le et al., 1995; Pickle et al., 1996; Devesa et al., 1999). One problem associated with this method is that extreme values are most commonly found in sparsely populated areas, and these areas account for a disproportionate amount of the total map area. Because of this, novice map users are often erroneously drawn to what appear to be areas of high disease rates in large, sparsely populated states such as Wyoming or Nevada, while experienced users may be just as likely to discount a statistically important trend in such areas. This situation underscores the importance of incorporating statistical information into choropleth maps so that genuine excesses can be distinguished from random noise (Pickle et al., 1996; MacEachren et al., 1998; Kulldorff, 1999a).

There are a variety of general cluster detection methods that can help to make this distinction, by defining contiguous areas of excess or deficit that are not likely to have arisen by chance (Openshaw et al., 1987; Turnbull et al., 1990; Besag and Newell, 1991; Kulldorff and Nagarwalla, 1995; Fotheringham and Zhan, 1996; Kulldorff, 1997). These methods involve the generation and comparison of large numbers of circular areas (other shapes are theoretically possible), and tend to identify many similar, closely overlapping circles. Some researchers have opted to display all of these circles, with their density suggestive of the areas with the greatest statistical power (Openshaw et al., 1987; Turnbull et al., 1990; Fotheringham and Zhan, 1996; Timander and McLafferty, 1998). This apparent relationship, however, is biased by the underlying geography of the areas involved. A cluster in Manhattan, for example, would tend to contain more circles, and thus be more visually prominent, than a statistically identical cluster in rural upstate New York, simply as a result of their differing population densities.

Those following Kulldorff's approach, in contrast, have typically reported only the circles with the highest likelihood ratio that are non-overlapping, provided these circles meet some threshold for statistical significance (Kulldorff and Nagarwalla, 1995; Kulldorff, 1997; Jemal et al., 2000; Gregorio et al., 2001; Sankoh et al., 2001; Forand et al., 2002). While this approach reduces the graphic complexity considerably, it tends to identify large areas with large populations but small elevations in risk, since such areas have the highest statistical power. Smaller clusters contained within these areas that have higher elevations in risk but lower, though statistically significant, likelihood ratios, are ignored. Such sub-clusters might be expected, for example, in the case of a dose–response relationship from an environmental point source, or may arise for many other reasons. In any case, the knowledge of these sub-clusters would certainly contribute to the generation of possible explanatory hypotheses. There have been several examples where sub-clusters have been reported; these have depended on sequential limitation of the maximum allowable circle size (Kulldorff et al., 1997) and an isotonic regression function (Kulldorff, 1999b). Neither of these approaches have been operationalized in the freeware SaTScan computer program employing Kulldorff's method (Kulldorff et al., 1998; Kulldorff and Information Management Systems Inc., 2002).

We use the results of Kulldorff's spatial scan statistic to propose a method of selecting clusters for display that is straightforward and as least as informative as any of the above approaches. While our approach is applicable to any of the general cluster detection methods cited above, we chose Kulldorff's spatial scan statistic because it confers advantages not shared by all of the other methods: it identifies circular clusters of any size, located anywhere within a study area, while controlling for multiple hypothesis testing; it is conceptually straightforward; and is emerging as a widespread tool for identifying areas of unusual disease patterns. Our approach involves stratifying the set of statistically significant circles by relative risk. Within each relative risk stratum, the nonoverlapping circles with highest likelihood are displayed, creating a nested or contoured effect.

Section snippets

Methods

In our analysis, we used 522,994 observed and expected prostate cancer deaths among white males from 1970–1989 in 3053 counties in the contiguous 48 states. These data are available through the National Cancer Institute Cancer Mortality Maps and Graphs web site (National Cancer Institute, 2001). For the purposes of calculating distances between counties and defining groupings of counties, county geographic centroids were used. A grid of over 18,000 points was constructed, consisting of each

Results

The method identified statistically significant excesses in mortality in a number of regions of the country, including much of the West, Upper Midwest, and Northeast (Fig. 1). Also identified were numerous sub-areas of higher relative risk that are significant under their own power, including three areas with a relative risk above 1.4, in Vermont, Iowa, and Wyoming-Idaho. In all, a total of 37 distinct elevated areas were mapped, nine of which would have been identified by SaTScan using the

Discussion

Our approach provides more visual information than the results from SaTScan, while avoiding the visual chaos resulting from attempting to display millions of mostly similar circles. Comparable results could have been obtained through consideration of variable maximum allowable circle sizes or isotonic regression functions, but relative risk is a more familiar concept than either of these two approaches.

Comparing our statistical summary map with a conventional choropleth map of the same data as

References (35)

  • Devesa, S.S., Grauman, D.J., Blot, W.J., Pennello, G.A., Hoover, R.N., Fraumeni, J.F., 1999. Atlas of cancer mortality...
  • E.J. Feuer et al.

    Cancer surveillance seriesinterpreting trends in prostate cancer—part II: cause of death misclassification and the recent rise and fall in prostate cancer mortality

    Journal of the National Cancer Institute

    (1999)
  • S.M. Fincham et al.

    Patterns and risks of cancer in farmers in Alberta

    Cancer

    (1992)
  • A.S. Fotheringham et al.

    A comparison of three exploratory methods for cluster detection in spatial point patterns

    Geographic Analysis

    (1996)
  • A. Gelman et al.

    All maps of parameter estimates are misleading

    Statistics in Medicine

    (1999)
  • D.I. Gregorio et al.

    Geographical differences in primary therapy for early stage breast cancer

    Annals of Surgical Oncology

    (2001)
  • A.W. Hsing et al.

    Trends and patterns of prostate cancerwhat do they suggest?

    Epidemiologic Reviews

    (2001)
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