Division of Biostatistics, Department of Community Medicine, University of Connecticut School of Medicine, Farmington, CT 060306325, USA. E-mail: MartinK{at}neuron.uchc.edu
In this issue of the International Journal of Epidemiology Huillard d'Aignaux et al.1 present a very interesting geographical analysis of sporadic Creutzfeldt-Jakob Disease in France. A number of non-traditional statistical methods are used, and here we offer some comments regarding their purpose and interpretation.
Tests for Spatial Randomness
An important first step in any geographical investigation of disease is to present a descriptive map, such as the one provided by Huillard d'Aignaux et al.1 in Figure 1. Whether or not there are true geographical differences in risk, there will always be some geographical patterns apparent to the naked eye. For example, in the aforementioned map, there are three apparent low-risk regions in the south, north and west, respectively. As in all medical research, it is important to evaluate whether observed patterns/results are likely to be due to chance or not. For geographical data, this is done using a test for spatial randomness, adjusting for the geographical distribution of the population at risk, as well as covariates such as age. Such tests are not a replacement for the maps, but an important complement. If the null hypothesis of spatial randomness is rejected, it means that there is likely to be predictors that are geographically unevenly distributed. If the null hypothesis is not rejected, the geographical pattern observed is less likely to provide important information, and we should watch out not to spend a lot of time trying to interpret random spatial noise.
Different tests for spatial randomness have different purposes, and Huillard-d'Aignaux et al.1 are at the forefront of the field by evaluating their data using more than one test statistic. Mantel-Bailar's Test,2 used in Analysis 1, is a global clustering test.3 It evaluates whether clustering exists as a global phenomena throughout the map, without pinpointing the location of specific clusters. This may occur through two different types of random processes.4 It could be that initial cases generate other cases close by, as when a disease is infectious. It could also be that there are a number of health hazards, each creating an increased risk for the disease in a limited surrounding area.
Other global clustering tests that have recently been proposed include Cuzick-Edwards' k-Nearest Neighbor Test5 and Tango's Maximized Excess Events Test.6 Mantel and Bailar6 use a fixed geographical distance to define the scale of clustering, that is, the maximum distance at which two cases are considered to be close. As a contrast, Cuzick and Edwards' test defines the scale in terms of the number of neighbours, so that one case is close to another if it is among the k nearest neighbours. This means that two cases 4 km apart may be considered close in a rural area but not in a city. In comparing the two methods, Mantel-Bailar's test is therefore expected to have higher statistical power if the clustering is stronger in urban areas while Cuzick-Edwards' test will have higher power if the clustering is stronger in rural areas. Both methods require the user to specify a parameter representing the scale of clustering, and as the scale is typically unknown, it is good to perform the test for multiple parameter values. Tango's Maximized Excess Events Test6 deals with this issue directly, evaluating the test statistic for multiple parameter values but providing one single P-value adjusted for multiple testing.
The spatial scan statistic,7 used in Analysis 3, is a cluster detection test, which determines the location and statistical significance of specific clusters. If the null hypothesis is rejected, that rejection is dependent on the number of cases inside versus outside the detected cluster, but independent of their specific locations. This means that no matter how the outside cases are distributed we will still reject the null hypothesis, and hence, we can attribute both the rejection and the P-value to the detected cluster.3,7
Besag-Newell's method,8 used in Analysis 2, is also designed for cluster detection, being one of the forerunners to the spatial scan statistic. The main difference is that it provides one P-value for each cluster location and size, not adjusted for multiple testing, while the spatial scan statistic adjusts the P-values for the multiple testing inherent in the many potential cluster locations and sizes.
Data Quality and Interpretation
For the population at risk, Huillard d'Aignaux et al.1 used data from the 1995 census, and the fact that this lies in the middle of the 19921998 study interval makes migration bias unlikely in the place of residence analyses.
As pointed out by the authors, a more troubling aspect is the lack of age-specific population numbers, making it impossible to adjust the geographical analyses for age, irrespectively of what statistical method is used. While the significant global clustering results in Analysis 1 could be due to a geographically uneven age distribution,1 the lack of age adjustment cannot explain the cluster with three cases in the southwest. This is because the P-value is very small (P = 0.001) and a slight change in the population-based denominator will not make a big difference when the relative risk is high. Larger clusters with lower relative risk are more prone to be caused by inadequate age adjustments. The lack of age adjustment may also have the opposite effect, leading to false-negative results where a test fails to find clustering that would have been apparent in an age-adjusted analysis.
The fact that one test statistic provides a significant result, while another does not, is not a cause for concern. Rather, the difference in results should be viewed as information on the type of clustering present in the data. Such information must be used with flexibility, and it is sometimes appropriate to investigate non-significant clusters, as Huillard d'Aignaux et al.1 have done with respect to the cluster in northern France.
Geographical analyses and tests for spatial randomness can provide important clues about a disease, but rarely any definite answers. That requires detailed case histories, searching for the presence of known or potential risk factors, and often, the design of traditional non-geographical epidemiological studies to evaluate newly generated hypotheses. It is my hope that the thorough and excellent geographical study by Huillard d'Aignaux et al.1 will result in such further studies, be it in France or other countries.
References
1
Huillard d'Aignaux J, Cousens SN, Delasnerie-Lauprêtre N et al. Analysis of the geographical distribution of sporadic Creutzfeldt-Jakob disease in France between 1992 and 1998. Int J Epidemiol 2002;31:49095.
2 Mantel N, Bailar JC. A class of permutational and multinomial tests arising in epidemiological research. Biometrics 1970;26:687700.[ISI][Medline]
3 Kulldorff M. Statistical methods for spatial epidemiology: tests for randomness. In: Gatrell and Löytönen (eds). GIS and Health. London: Taylor & Francis, 1998, pp.4962.
4 Haining R. Spatial statistics and the analysis of health data. In: Gatrell and Löytönen (eds). GIS and Health. London: Taylor & Francis, 1998, pp.2947.
5 Cuzick J, Edwards R. Spatial clustering for inhomogeneous populations. J R Statist Soc 1990;B52:73104.[ISI]
6 Tango T. A test for spatial disease clustering adjusted for multiple testing. Stat Med 2000;19:191204.[CrossRef][ISI][Medline]
7 Kulldorff M. A spatial scan statistic. Comm Stat: Theory Meth 1997, 26:148196.[ISI]
8 Besag J, Newell J. The detection of clusters in rare diseases. J R Statist Soc 1991;A154:14355.[ISI]
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