Bivariate survival models for analysis of genetic and environmental effects in twins

Classic methods in genetics for the analysis of binary attributes, based on an assumption of a “threshold” on a normally distributed latent variable called “liability,” estimate the strength of genetic and environmental effects from differences in correlations between relatives of differing genetic relatedness. Two problems that are not easily addressed by these methods are the need to take the age of onset into account (particularly in chronic diseases in which incidence rates vary considerably with age and the lengths of time at risk can vary between individuals) and the desirability of incorporating measured covariates (genetic or environmental). The standard methods of cohort analysis used in epidemiology allow for both of these features, but until recently have been restricted to independent individuals. Recent developments in survival analysis have extended the widely used “proportional hazards” model of Cox by the addition of latent variable, ε, reflecting the shared susceptibility of related subjects because of their shared genes or shared environment. We show how this approach can be combined with more traditional models of gene–environment interaction to allow the main effects of measured genetic markers and environmental variables to be estimated, as well as the residual variance of genetic and environment and their interactions. The approaches are applied to a cohort of female twin births in Sweden from 1886 to 1958, linked with the Swedish cancer registry from 1961 to 1982.