A Latent Variable Model of Segregation Analysis for Ordinal Traits

Many health conditions, including cancer and psychiatric disorders, are believed to have a complex genetic basis, and genes and environmental factors are likely to interact in the presence and severity of these conditions. Assessing familial aggregation and inheritability of disease is a classic topic of genetic epidemiology, commonly referred to as segregation analysis. Although today it is routine to conduct such analyses for quantitative and dichotomous traits, methods and software that accommodate ordinal traits do not exist. To this end, we propose a latent variable model by extending the work of Zhang and Merikangas, who examined binary traits. The advantage of this latent variable model lies in its flexibility to include environmental factors (usually represented by covariates) and its potential to allow gene-environment interactions. The model building uses the EM algorithm for maximization and a peeling algorithm for computational efficiency. We provide asymptotic theory for statistical inference, and conduct simulation studies to confirm that the asymptotic theory is adequate in practical applications. We also apply our model to examine the familial transmission of alcoholism, which is categorized into three ordinal levels: normal control, alcohol abuse, and alcohol dependence. Our analysis not only confirms that alcoholism is familial, but also suggests that the transmission may have a major gene component not revealed by previous analyses using dichotomous traits.