 
Summary: Genetic Epidemiology 35 : 291302 (2011)
Genetic Variance Components Estimation for Binary Traits Using
Multiple Related Individuals
Charalampos Papachristou,1,2Ã Carole Ober,2
and Mark Abney2
1
Department of Mathematics, Physics, and Statistics, University of the Sciences, Philadelphia, Pennsylvania
2
Department of Human Genetics, University of Chicago, Chicago, Illinois
Understanding and modeling genetic or nongenetic factors that influence susceptibility to complex traits has been the focus
of many genetic studies. Large pedigrees with known complex structure may be advantageous in epidemiological studies
since they can significantly increase the number of factors whose influence on the trait can be estimated. We propose a
likelihood approach, developed in the context of generalized linear mixed models, for modeling dichotomous traits based
on data from hundreds of individuals all of whom are potentially correlated through either a known pedigree or an
estimated covariance matrix. Our approach is based on a hierarchical model where we first assess the probability of each
individual having the trait and then formulate a likelihood assuming conditional independence of individuals. The
advantage of our formulation is that it easily incorporates information from pertinent covariates as fixed effects and at the
same time takes into account the correlation between individuals that share genetic background or other random effects.
The high dimensionality of the integration involved in the likelihood prohibits exact computations. Instead, an automated
Monte Carlo expectation maximization algorithm is employed for obtaining the maximum likelihood estimates of the model
