Spatial Epidemics

240

RESEARCH

WORKSHOP

SPATIAL EPIDEMICS MEASURING THE SEVERITY USING TANGO’S INDEX DICK KRYSCIO, University (with Claude Lefevre)

OF DISEASE

of Kentucky,

Lexington,

CLUSTERING

Kentucky

Tango (1984) proposed a test for disease clustering applicable to grouped data obtained from a population that remains fairly uniform over the study period. A number of investigators have examined the properties of this test. Whittemore et al. (1977) proposed a normal approximation for the distribution of the test statistic under randomness. Raubertas (1988) showed how to generalize Tango’s test statistic to detect clustering in both space and time even when the population does not remain uniform over the study period, and Tango (1990) showed that, at least for detecting clustering in time, a chi-square approximation is almost always superior to a normal approximation for those cases routinely encountered in data analysis. In this paper we consider the related question of measuring the severity of the clustering once it has been determined that cases are not randomly distributed, In particular, we propose an alternative to randomness that is defined in terms of a parameter that measures the severity of the disease clustering and a sufficient statistic for this parameter, which is Tango’s test statistic. For the special case of temporal clustering as defined by Tango, an unbiased estimator of this clustering parameter and its sampling variance is derived; a particularly simple interpretation of this estimator is presented. Applications to the trisomy data given by Tango (1990) are discussed. Raubertas,

R. F., Spatial

and temporal

analysis

clustering, Biometrics 44:112-129 (1988). Tango, T., The detection of disease clustering Tango, T., Asymptotic distribution of an 46:351-357 (1990). Whittemore, A. S., N. Friend, disease,

Biometrika

B. W. Brown,

74:631-635

of disease

occurrence

in time, Biometrics index for disease

KGNIG,

Mining Academy,

of

40~15-26 (1984). clustering, B~mefr~cs

and E. A. Holly, A test to detect

clusters

of

(1987).

MARRED POINT PROCESSES FOR STOCHASTIC OF THE SPREAD OF EPIDEMIC DIETER

for detection

Freiberg,

MODELING

East Germany

Planar point processes and their statistics are suitable tools for modeling and analyzing dependences in the spread of diseases in different areas and to quantify correlations and directional and other effects. On the basis of