Analytical relationship between family history and genetic and environmental risks, with application to female breast cancer

It is well established in genetic epidemiology that family history is an important indicator of familial aggregation of disease in a family. A strong genetic risk factor or an environmental risk factor with high familial correlation can result in a strong family history. In this paper, family history refers to the number of first-degree relatives affected with the disease. Cui and Hopper (Journal of Epidemiology and Biostatistics 2001; 6: 331-342) proposed an analytical relationship between family history and relevant genetic parameters. In this paper we expand the relationship to both genetic and environmental risk factors. We established a closed-form formula for family history as a function of genetic and environmental parameters which include genetic and environmental relative risks, genotype frequency, prevalence and familial correlation of the environmental risk factor. The relationship is illustrated by an example of female breast cancer in Australia. For genetic and environmental relative risks less than 10, most of the female breast cancer cases occur between the age of 40 and 60 years. A higher genetic or environmental relative risk will move the peak of the distribution to a younger age. A more common disease allele or more prevalent environmental risk factor will move the peak to an older age. For a proband with breast cancer, it is most likely (with probability ge80%) that none of her first-degree relatives is affected with the disease. To enable the probability of having a positive family history to reach 50%, the environmental relative risks must be extremely as high as 100, the familial correlation as high as 0.8 and the prevalence as low as 0.1. For genetic risk alone, even the relative risk is as high as 100, the probability of having a positive family history can only reach about 30%. This suggests that the environmental risk factor seems to play a more important role in determining a strong family history than the genetic risk factor.