Modelling the Effects of Penetrance and Family Size on Rates of Sporadic and Familial Disease

<i>Background/Aims:</i> Many complex diseases show a diversity of inheritance patterns ranging from familial disease, manifesting with autosomal dominant inheritance, through to simplex families in which only one person is affected, manifesting as apparently sporadic disease. The role of ascertainment bias in generating apparent patterns of inheritance is often overlooked. We therefore explored the role of two key parameters that influence ascertainment, penetrance and family size, in rates of observed familiality. <i>Methods:</i> We develop a mathematical model of familiality of disease, with parameters for penetrance, mutation frequency and family size, and test this in a complex disease: amyotrophic lateral sclerosis. <i>Results:</i> Monogenic, high-penetrance variants can explain patterns of inheritance in complex diseases and account for a large proportion of those with no apparent family history. With current demographic trends, rates of familiality will drop further. For example, a variant with penetrance 0.5 will cause apparently sporadic disease in 12% of families of size 10, but 80% of families of size 1. A variant with penetrance 0.9 has only an 11% chance of appearing sporadic in families of a size similar to those of Ireland in the past, compared with 57% in one-child families like many in China. <i>Conclusions:</i> These findings have implications for genetic counselling, disease classification and the design of gene-hunting studies. The distinction between familial and apparently sporadic disease should be considered artificial.