EGIS (1994), copyright EGIS Foundation.
With infectious endemic diseases that possess diffusive, land-spread foci, it is of primary importance to delimitate areas of their significant risk. Herein, spatial statistics of requested clinical cases and GIS have been applied for a systematic disease mapping. A statistical model assumes that the geographical pattern of cases is a realization of an inhomogeneous (Cox) process driven by local risk intensity conditional on an intensity of human population, and a weighted-averages method is exploited for the risk estimation. An example of geostatistical analysis of distribution of clinical cases of Lyme borreliosis and tick-borne encephalitis is given.
For ages, infectious endemic diseases have been persisting in nature independently of humans. A man can acquire the infection when attending some of the places of disease occurrence - the so called disease foci. They are relatively stable, disseminated over a landscape, and their geography is of primary importance for the disease control and planning preventive or prophylactic measures. The methods of disease mapping involve various techniques, the most straightforward one is, of course, based on an analysis of spatial distribution of registered cases. A plot of the localities from which cases were reported into a map is an ordinary way to acquire an impression of the disease spread. For more than an intuitive perception of the disease pattern, however, a method of statistical analysis is needed.
The expanding applications of geographic information systems (GIS) to epidemiology in general (Openshaw et al. 1987, 1988; DeLepper & Scholken 1991 etc. ) and too the control of endemic diseases in particular (Hugh-Jones 1991; Kitron et al. 1991; Clare et al. 1991 etc.) inspired us to design procedures suitable for statistical analysis of such health events which could be implemented in a GIS software.
If the loci of disease contraction are well defined in space, like the places of tick or mosquito attacks, contact with a sick animal, etc., they could be treated as points and the second-moment methods of point pattern analysis can be applied (Ripley 1981; Diggle 1983). The frequency at which clinical cases emerge in a locality can be attributed to a latent risk of infection persisting in a nearby
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environment and to a local population at risk. Accordingly, the basic model expects that the pattern of health events is a realization of an inhomogeneous (Cox) process driven by local risk intensity L(x) conditional on an intensity of human population P(x). The primary goal is then to assess a map of the intensity of the latent risk of infection from an observed geographical pattern of disease contractions, and from a map of an underlying resident population at risk. If we define the local risk as per capita probability of acquiring the infection at a spot of exposition dx before time t, it could be expressed as
R(t;x) = 1 - exp[-L(x)t], (1)
and the expected number of clinical cases C(x) registered at dx during the period t equals to
C(x) = P(x) R(t;x), (2)
from which
L(x) = -ln[1 - C(x)/P(x)]/t. (3)
Two respects that should be involved in an analysis of epidemiological data are (i) an error of spatial location of disease contractions, and (ii) spontaneous motility of human population.
(i) Due to technical limitations of an epidemiological reporting system as well as subjective (physician, patient) way of case allocation, it is evident that the data set on locations of cases X must comprise a vector of error:
X = X[true] + E. (4)
Although particular distribution of E is unknown, relying on Central Limit Theorem one can assume radially symmetrical Gaussian distribution, E(E) = 0 and VAR(E) > d^2/4, where d is mean nearest neighbor distance between elementary reporting units used in the surveillance. Thus, we have to smooth the pattern of whereabouts of reported disease contractions with this PDF to interpolate properly the map of C(x).
(ii) An insight into the motility of a particular population at risk around its residences can easily be achieved from ordinary epidemiological data, which reports both patient residence and a place of contraction, through an observed distribution of locality-to-residence distances. A nonlinear regression model can then be exploited (Ebdon 1977) to interpolate accordingly a coverage of human density P(x), based on an available map of population centroids (e.g. census tracts, settlements etc. ).
In terms of map algebra (Tomlin 1990) we can define the former procedure (i) as 'Focal_Weighing_Function C(x)' and the later one (ii) as 'Focal_Spreading_Function P(x)'. Then, substituting reasonably small pixels of a GIS grid system for the differential dx, a 'layer' of relative local incidence C(x)/P(x) could be generated by means of the respective steps expressed as follows:
WeighedCases = Focal_Weighing_Function C(x) of Cases, PopDispersion = Focal_Spreading_Function P(x) of PopCenters, LocalIncidence= LocalRatio of WeighedCases and PopDispersion.
Consequently, a map of L(x) would be generated by means of another 'Local' function (3). However, if the disease is
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rare and C(x) « P(x), this function could be further reduced to trivial
L(x) ~ C(x)/P(x) (5)
In fact, this is the case in most endemic diseases. Applying an apt scale factor in (5) allows both avoiding fractional numbers in map algebra and expressing the risk in more conventional epidemiological units of 'cases per 10 000 inhabitants'.
We utilized the above approach for mapping the risk of Lyme borreliosis and tick-borne encephalitis (TBE), two serious tick-borne illnesses endemic in Europe, in a highly endemic region. The data was obtained from an epidemiological
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surveillance that routinely gathered reports on geographical location of disease contraction and patient's residence. A digital map of Central Bohemia, Czech Rep., managed by MicroStation PC (Intergraph Co.) serve as a basis of data allocation. A statistical module, operating out of MicroStation and sharing the same database, was written in Turbo-Pascal (Borland International), and enables semiautomatic rasterisation of a selected area, a test of clustering in mapped point patterns, and generating of risk raster files over a study area. Alternatively, MGE-PC Grid Analyst (Intergraph Co. ) has been used for the method (5).
To prove fidelity of the established GIS model, we also compared predicted local risk levels of LB in fifteen map positions with true human-endangering factors at corresponding localities, i.e. tick numbers in environment and Borrelia-infection rates. The correlation of both values was surprisingly good. Although there are indisputable limitations of the map fidelity, GIS-assisted assessments of disease risk maps have great potential as an aid in planning area-wide preventive measures.
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DeLepper, M. & Scholten, H.J. (1991) The application of geographical information systems in public and environmental health. In: Data requirements and methods for analyzing spatial patterns of disease in small areas. WHO EUR/ICP/CEH 087/A/1, pp. 106 - 112.
Diggle, P.J. (1983) Statistical analysis of spatial point patterns. Academic Press: London.
Ebdon, D. (1977) Statistics in geography. Basil Blackwell: Oxford.
Hugh-Jones, M. (1991) Introductory remarks on the application of remote sensing and geographic information systems to epidemiology and disease control, Prev. Vet. Medicine, 11, pp. 159 - 161.
Kitron, U., Bouseman, J.K., Jones, C.J. (1991) Use of the ARC/INFO GIS to study the distribution of Lyme disease ticks in an Illinois county, Prev. Vet. Medicine, 11, pp. 243 - 248.
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Openshaw, S., Craft, M., Charlton, M., Birch, J. M. (1988) Investigation of leukemia clusters by use of geographical analysis machine, Lancet, pp. 272 - 273.
Ripley, B.D. (1981) Spatial statistics. John Wiley & Sons: New York.
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