Multivariate Binary Phenotypes

1. Complex diseases are caused by multiple phenotypes that are correlated. In many clinical or psychological settings, diagnoses are made through a set of binary phenotypes. Currently, there are several statistical methods available to analyze multiple phenotypes, such as comparing the results from single phenotype analyses, and performing multivariate analysis for quantitative phenotypes. These methods can be extended for related samples. The authors proposed new approach to jointly evaluate a set of binary phenotypes for related samples because of the following motivations. First, joint analysis of multiple phenotypes may provide a gain in power and an increased precision of estimates compared to the univariate analysis. Second, unlike a
The authors used one type of model called Rasch model in item response theory (IRT) to obtain a latent variable as a measure to summarize the multivariate binary phenotypes for related samples. The latent variable can be incorporated with information on individuals as fixed or random effects into the model (called multilevel IRT model). They used the five metabolic syndrome (MetS) components (waist circumference, fasting glucose levels, HDL-cholesterol, triglycerides, and blood pressure) as the multivariate binary phenotypes. The Rasch model has one location parameter b_i for ith item affection jth individuals from the kth family with latent trait θ_jk. The response probability (i.e., the prevalence) for ith item is modeled as a logistic function of the difference between the latent trait θ_jk and the location parameter b_i so that the response probability becomes 0.5 for individuals whose latent trait equals to the location parameter. Then the latent trait θ_jk is defined as the dependent variable in the mixed linear model with the genetic random effect expressed as
The correlation of latent traits between jth and lth individuals in the kth family can be expressed