Statistical inference for familial disease clusters

In many epidemiologic studies, the first indication of an environmental or genetic contribution to the disease is the way in which the diseased cases cluster within the same family units. The concept of clustering is contrasted with incidence. We assume that all individuals are exchangeable except for their disease status. This assumption is used to provide an exact test of the initial hypothesis of no familial link with the disease, conditional on the number of diseased cases and the distribution of the sizes of the various family units. New parametric generalizations of binomial sampling models are described to provide measures of the effect size of the disease clustering. We consider models and an example that takes covariates into account. Ascertainment bias is described and the appropriate sampling distribution is demonstrated. Four numerical examples with real data illustrate these methods.