Distribution of family history of a disease as a function of mode of inheritance, genetic relative hazard, allele frequency and disease status of the proband, with application to female breast cancer.

Abstract

This paper aims to determine the family history distribution of a particular disease as a result of its specific genetic aetiology, defined by the mode of inheritance (dominant or recessive), allele frequency, and increased risk in carriers of the genetic risk (genetic relative hazard). Here, 'family history' is the number of affected first-degree relatives of a defined index person (termed the proband), who may be either affected or unaffected with the disease in question. We consider model parameters relevant for female breast cancer in Australia. Breast cancer affects one sex only, although the extension of the model to both sexes is straightforward. Contour plots of the relationships between family history distribution and genetic parameters, for both dominant and recessive inheritance, are displayed for the proband being either affected or unaffected. Under dominant inheritance and an allele frequency of 0.005 (as may be appropriate for mutations in the genes BRCA1 and BRCA2), the proportion of affected probands diagnosed with breast cancer before age 50 years and who have no family history is stable as the genetic relative hazard increases from 5 to 20, decreasing from 89% to 85%. The probability that a proband has a family history is higher when the proband is affected compared with when she is not. For allele frequency 0.005 and relative hazard 10, the ratio of the probability of i (i = 1, 2, 3 or more) affected relatives for an affected proband compared with an unaffected proband is 1.2, 2 and 4.5 respectively, under dominant inheritance. Under recessive inheritance with allele frequency 0.35 and relative hazard 3 (as may be the case for a common polymorphism in the CYP17 gene), the corresponding ratios are 1.1, 1.3 and 1.5, respectively.