The point location maps of all and infected herds in Figure
6
clearly show the spatialheterogeneity of the distribution of both EBL positive as well as all dairy herds in New Zealand. Yet, it is difficult to identify any patterns within dense clusters of overlaying points. Using kernel density estimation it is possible to generate a smooth surface map. The influence of the choice of bandwidth on the appearance of the resulting smoothed
map is shown in Figures
9
to 1 2 . With bandwidths of 1 0 and 1 5 km, the resulting mapsshow many spikes resulting from high estimated density values. Increasing the
bandwidth to 20 km resulted in a smooth map that still reflected the detail of local as
well as large scale variation. Using the largest bandwidth estimated by the ArcView software, a very smooth map was generated which does not show local variation of population but offers a general impression of the overall distribution of EBL positive herd occurrence. This shows that the choice of bandwidth for kernel density estimation is a largely subjective process and that it has a strong influence of the resulting map
presentations. Therefore, a decision with respect to bandwidth should consider whether
the focus of the investigation is on large or small scale processes, or both. In this study,
our emphasis was more on local processes and thus the application of a narrower bandwidth was appropriate. At the same time care had to be taken to ensure that the bandwidth chosen was not too small as this would result in data noise dominating the
density estimates.
The EBL herd prevalence map produced on the basis of the ratio of kernel density estimates for EBL positive herds and all dairy cattle herds as the population at risk does provide a useful visual representation of spatial variation in disease occurrence particularly at the regional level. For example, in Northland herd prevalence is
consistently less than
5%
whereas in the Bay of Plenty region it varies between5
and1 5%.
These figures are within the range reported by the New Zealand Dairy IndustryEBL Control Scheme (Hayes, unpublished paper). Figures 1 3 and
1 4
demonstrate how70
On the basis of the visual inspection of EBL herd prevalence maps it was possible to tentatively identify potential clusters on the basis of observed local peaks in EBL prevalence. However, estimates produced by this technique where data is sparse may be unreliable. Estimation of confidence limits could be used to highlight these areas. Bailey and Gatrell ( 1 995) suggest using a larger bandwidth to ensure a reasonable size denominator. Adaptive kernel estimation allows for local adjustment of bandwidth which does preserve detail in high density areas and smoothes out spurious noise in sparse data areas (see the right maps of Figure 1 3 and 1 4).
This analysis has shown that examination of kernel density maps represents a useful step in the search for clusters which often begins as an 'exploratory spatial analysis' without any prior assumptions or specific hypotheses. However, it should not be seen as an end in itself (Rushton and Lolonis, 1 996 ).
Statistical of s patial cl usteri ng of EBL positive herds
The only significant cluster detected in this analysis consists of 498 herds in the Bay of Plenty area. Another possible cluster was identified in the northern part of the South Island. B oth clusters have estimated risks for EBL positive herd status that are 2.5 times greater than that of the area outside the cluster. In the case of the Bay of Plenty cluster it is interesting to note that it is on a relatively narrow strip of coastal land, and in comparison with the one in the South Island, it is relatively compact. While it is not possible to develop any causal hypotheses on the basis of these results, it would appear worthwhile to follow up these findings with a more in-depth investigation of affected herds in both areas, but particularly in the case of the Bay of Plenty cluster. The cluster in the South Island was significant at the p=0.08 level and, therefore, may be due to chance.
Cluster investigations involving the use of statistical methods are easy to conduct, yet they are often difficult to interpret. The results can be used to guide further investigations, but it should be kept in mind that failure to identify clusters in the data does not necessarily mean that they are not there, because the techniques are known to have limited statistical power. The objectivity resulting from the use of a statistical analysis approach such as the spatial scan statistic without involving a post-hoc hypothesis generation will make it possible though that the use of resources for more in-depth investigations can be more easily justified (Kulldorff and Nagarwalla, 1 995).
7 1
The analytical approach described i n this paper provides a general framework for the detection of spatial clusters in animal populations. Both, kernel density maps of disease risk and the spatial scan statistic could become part of a disease surveillance system which would allow identification of unusual occurrences of high disease density. It does not provide information about etiological or causal mechanisms of the underlying disease process, but rather can indicate areas that should be examined more closely through specific epidemiological investigations.
Reference List
Bailey, T.C. , Gatrell, A.C., 1 995. Interactive spatial data analysis. Longman Scientific
& Technical, New York, U.S.A.
Burton, L., Allen, G., Hayes, D., Pfeiffer, D., Morris, R. , 1 997.
A
novel approach to disease control. An industry operated programme for bovine leukaemia virus in New Zealand. 3 1 -32. 08.08.1 - 08.08.3.Ferrer, J., F., 1 980. Bovine Lymphosarcoma. In : Advances in veterinary science and
comparative medicine. Academic Press, 1 -68.
Hayes, D., 1 998. Enzootic bovine leucosis eradication scheme. Surveillance, 25. 3-5. Hilbink, F., 1 993 . Penrose, M. , Prevalence of enzootic bovine leukosis in the New
Zealand dairy cattle population. 20. 1 1 - 1 3 .
Jacquez, G.M., 1 993. The statistical description of disease clusters. Statistics m
Medicine, 1 2 : 1 967-8.
Kulldorff, M., Nagarwalla, N., 1 995. Spatial disease clusters: detection and inference. Statistics in Medicine, 14. 799-8 1 0.
Marshall, R.J., 1 99 1 . A review of methods for statistical analysis of spatial patterns of disease. J oumal of the Royal Statistical Society Series A, 1 54. 4 2 1 -44 1 .
Rushton, G., Lolonis, P., 1 996. Exploratory spatial analysis of birth defect rates in an urban population. Statistics in Medicine, 1 5 . 7 1 7-26.
Silverman, B.W., 1 9 86. Density estimation for statistics and data analysis. Chapman and Hall, New York
72