Computing the distribution of the maximum in balls-and-boxes problems with application to clusters of disease cases

We present a rapid method for the exact calculation of the cumulative distribution function of the maximum of multinomially distributed random variables. The method runs in time O(mn), where m is the desired maximum and n is the number of variables. We apply the method to the analysis of two situations in which an apparent clustering of cases of a disease in some locality has raised epidemiological concerns, and these concerns have been discussed in the recent literature. We conclude that one of these clusters may be explained on purely random grounds, namely the leukemia cluster in Niles, IL, in 1956-1960; whereas the other, a leukemia cluster in Fallon, NV, in 1999-2001, may not.

Clinical implications of cytogenetic abnormalities in melanoma

Unlike leukemia, in which specific reciprocal translocations are frequently observed, melanomas involve complex recurring chromosome anomalies. Analysis of the constituted genome of melanoma patients should identify cancer susceptibility genes and at-risk individuals in families with a history of melanoma. The first of these genes to be cloned is the cell cycle regulatory protein inhibitor--the p16 gene-- and a second gene locus for melanoma predisposition has been linked to the chromosome 1p36 band region. Detection of the most common somatic genetic alterations in melanoma enhances our understanding of molecular mechanisms of melanoma development and may lead to genetic markers in melanoma. Some alterations may be used to identify interesting subpopulations. Others may be of prognostic value when they are considered in tandem with clinical data.

Disease clusters, exact distributions of maxima, and P-values

This paper presents combinatorial (exact) methods that are useful in the analysis of disease cluster data obtained from small environments, such as buildings and neighbourhoods. Maxwell-Boltzmann and Fermi-Dirac occupancy models are compared in terms of appropriateness of representation of disease incidence patterns (space and/or time) in these environments. The methods are illustrated by a statistical analysis of the incidence pattern of bone fractures in a setting wherein fracture clustering was alleged to be occurring. One of the methodological results derived in this paper is the exact distribution of the maximum cell frequency in occupancy models.