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.