Analysis of bivariate binary data with possible chances of wrong ascertainment

Abstract

In familial data, ascertainment correction is often necessary to decipher genetic bases of complex human diseases. This is because families usually are not drawn at random or are not selected according to well-defined rules. While there has been much progress in identifying genes associated with a certain phenotype, little attention has been paid so far for familial studies on exploring common genetic influences on different phenotypes of interest. In this study, we develop a powerful bivariate analytical approach that can be used for a complex situation with paired binary traits. In addition, our model has been framed to accommodate the possibility of imperfect diagnosis as traits may be wrongly observed. Thus, the primary focus is to see whether a particular gene jointly influences both phenotypes. We examine the plausibility of this theory in a sample of families ascertained on the basis of at least one affected individual. We propose a bivariate binary mixed model that provides a novel and flexible way to account for wrong ascertainment in families collected with multiple cases. A hierarchical Bayesian analysis using Markov Chain Monte Carlo (MCMC) method has been carried out to investigate the effect of covariates on the disease status. Results based on simulated data indicate that estimates of the parameters are biased when classification errors and/or ascertainment are ignored.