A statistical test for detection of ancestral genetic contributions to disease occurrence in finite populations

We have been investigating cancer patterns in the Hutterites, a religious isolate residing on communal farms [Martin et al, 1980a,b,c]. Advantages of this population include extensive and accurate genealogies, essentially complete case ascertainment, and relatively uniform environmental background with regard to geographic location, lifestyle, and diet. However, application of the common epidemiological approach to familial risk assessment based on incidence in relatives of index cases [Haenszel, 1959] posed difficulties because all cases are probands. We also planned to employ matching to control for important confounders and thus had to deal with the problems of the matching of cases and controls as well as the existence of complex inbreeding [Hauck and Martin, 1982]. Our basic approach was to compare coefficients of kinship (Fm, a measure of coancestry) of cases with each other to coefficients between cases and matched controls drawn from the same population. We have developed a paired t-type statistic to assess the significance of observed differences. We present, as examples, application of our methods to the analysis of Hutterite data on neurofibromatosis, known to be inherited in autosomal dominant fashion, and on cancer. Neurofibromatosis showed significant familial aggregation, as expected. Breast, colon-rectal, and stomach cancer did not. We then show how to evaluate power and to determine appropriate sample sizes for detecting specified increases in kinship.