Using Item Response Theory to Model Multiple Phenotypes and Their Joint Heritability in Family Data

Abstract

Many important complex diseases are composed of a series of phenotypes, which makes the disease diagnosis and its genetic dissection difficult. The standard procedures to determine heritability in such complex diseases are either applied for single phenotype analyses or to compare findings across phenotypes or multidimensional reduction procedures, such as principal components analysis using all phenotypes. However each method has its own problems and the challenges are even more complex for extended family data and categorical phenotypes. In this paper, we propose a methodology to determine a scale for complex outcomes involving multiple categorical phenotypes in extended pedigrees using item response theory (IRT) models that take all categorical phenotypes into account, allowing informative comparison among individuals. An advantage of the IRT framework is that a straightforward joint heritability parameter can be estimated for categorical phenotypes. Furthermore, our methodology allows many possible extensions such as the inclusion of covariates and multiple variance components. We use Markov Chain Monte Carlo algorithm for the parameter estimation and validate our method through simulated data. As an application we consider the metabolic syndrome as the multiple phenotype disease using data from the Baependi Heart Study consisting of 1,696 individuals in 95 families. We adjust IRT models without covariates and include age and age squared as covariates. The results showed that adjusting for covariates yields a higher joint heritability (ĥ2=0.53) than without co variates (ĥ2=0.21) indicating that the covariates absorbed some of the error variance.

Cohort profile: the Baependi Heart Study—a family-based, highly admixed cohort study in a rural Brazilian town

“…Using the cohort data the groups were able to propose empirically guided statistical methodologies which account for all categorical phenotypes, allowing informative comparison among individuals. 30 Strengths and limitations Over the last decade, the Baependi cohort study has begun to fulfil its potential of making significant contributions to our understanding of the heritability across a variety of different health conditions. A number of study attributes make this study population unique, including the substantial admixture, the conservative and cohesive lifestyle patterns, and the increasingly rich tapestry of both cardiovascular and other variables extracted at baseline and follow-up.…”

Bayesian Variable Selection in Multilevel Item Response Theory Models with Application in Genomics

“…Fragoso et al. [] adapted the data augmentation approach described in Fu et al. [] to the multilevel IRT model, which relies on formulating the dataset as just a part of the complete dataset.…”

“…Recently, Fragoso et al. [] proposed a multilevel model from item response theory (IRT), which is capable of summarizing multiple individual dichotomous characteristics taking fixed and random effects into consideration, providing an interpretable model for the complex disease studied through a family‐based association study.…”

“…Item response models accomplish this goal by modeling the complex disease as an unobserved construct affecting the diagnosis of individuals on each feature, each interpreted as items in the IRT setting [Fragoso et al., ]. The probability of each observation is modeled as a function of characteristics of each item and individual parameters, denominated latent traits in the IRT literature.…”

“…This step is made possible by the insertion of a Metropolis‐Hastings step into the Gibbs sampler proposed in Fragoso et al. []. Given the massive genetic data we aimed to integrate into the model, we sought to propose a variable selection step that was robust to high dimensional challenges, which is obtained by adapting the proposal distribution used in Baragatti [] for the multilevel IRT model, and implementing the resulting Markov Chain Monte Carlo (MCMC) procedure in fast algorithms allowing for feasible computing times.…”