The scale-invariant spatial clustering of leukemia in San Francisco.
This study tests the hypothesis of scale-invariant self-similar clustering of childhood leukemia cases over the San Francisco spatial area. The spatial distribution of leukemia cases has been investigated over seven scales of observation. A power-law relation of the variance to the mean of aggregates (quadrats) was used to detect possible scale-invariant self-similar clustering. The spatial distribution of leukemia cases (incidence from 1946 to 1964) was well fitted by a power-law function. The follow-up of clustering from the first years of case notification (1946) confirmed a scale-invariant self-similar spatial pattern with a stable power-law slope from 1952 onward. This pattern was shown to pertain specifically to school-age leukemia cases. Younger cases had a random distributional pattern over space. Observation and simulations of the distributional patterns revealed memory-keeping of historical (the pre-1953 era) fractal-like conditions. Based on a comparison of the leukemia fractal dimension with that of the city residential data, it is speculated that the current scale-invariant self-similar spatial clustering of the leukemia cases reflects the onset of the historical fractal patterning of the city residences at a particular time point in the past.
Philippe
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Faculty of Medicine, University of Montreal, M. d'Youville Bldg, Montreal, QC, H3C 3J7, Canada.
D002648:Child; D017709:Fractals; D006801:Humans; D015233:Models, Statistical; D054198:Precursor Cell Lymphoblastic Leukemia-Lymphoma / Q000453:epidemiology*; D012495:San Francisco; D013029:Space-Time Clustering; D014505:Urban Population