Threshold model in the genetics of age-dependent disease in twins: I. General principles as applied to Alzheimer disease

In the context of the etiology and pathogenesis of Alzheimer disease (AD), we discuss assumptions under which categorical data on the phenotypes of twin pairs may be used to estimate standardized characteristics (correlation and the critical threshold) for an age-dependent multinomial process. Important topics include Erlangian, gamma, and Poisson processes, tetrachoric and trichoric functions, and degrees of freedom and how they relate to estimation from both an abstract and a practical standpoint. Under plausible assumptions about the age-dependence of a heritable trait, it is possible to generate sufficient degrees of freedom to test the genetic model and to explore age- dependence and the impact of environmental factors that may influence it systematically. Though general in scope, the model is focused on data from twin pairs. The statistical strategy is briefly outlined, but its properties are not examined in detail.