Varying Coefficient Models for Mapping Quantitative Trait Loci Using Recombinant Inbred Intercrosses

Abstract

There has been a great deal of interest in the development of methodologies to map quantitative trait loci (QTL) using experimental crosses in the last 2 decades. Experimental crosses in animal and plant sciences provide important data sources for mapping QTL through linkage analysis. The Collaborative Cross (CC) is a renewable mouse resource that is generated from eight genetically diverse founder strains to mimic the genetic diversity in humans. The recombinant inbred intercrosses (RIX) generated from CC recombinant inbred (RI) lines share similar genetic structures of F 2 individuals but with up to eight alleles segregating at any one locus. In contrast to F 2 mice, genotypes of RIX can be inferred from the genotypes of their RI parents and can be produced repeatedly. Also, RIX mice typically do not share the same degree of relatedness. This unbalanced genetic relatedness requires careful statistical modeling to avoid false-positive findings. Many quantitative traits are inherently complex with genetic effects varying with other covariates, such as age. For such complex traits, if phenotype data can be collected over a wide range of ages across study subjects, their dynamic genetic patterns can be investigated. Parametric functions, such as sigmoidal or logistic functions, have been used for such purpose. In this article, we propose a flexible nonparametric time-varying coefficient QTL mapping method for RIX data. Our method allows the QTL effects to evolve with time and naturally extends classical parametric QTL mapping methods. We model the varying genetic effects nonparametrically with the B-spline bases. Our model investigates gene-by-time interactions for RIX data in a very flexible nonparametric fashion. Simulation results indicate that the varying coefficient QTL mapping has higher power and mapping precision compared to parametric models when the assumption of constant genetic effects fails. We also apply a modified permutation procedure to control overall significance level.

Contrasting genetic architectures in different mouse reference populations used for studying complex traits

“…These strains have the advantage of generating additional unique genotypes, extending the phenotypic diversity, and supporting studies of epigenetic effects . Specialized statistical methods have been developed to analyze this unique population (Gong and Zou 2012). A striking example of the power of CC-RIX strains is illustrated by their markedly different response to infection by a mouse-adapted strain of the Ebola virus, thus providing among the first and best mouse models for studying Ebola infection, and in particular the associated hemorrhagic fever (Rasmussen et al 2014).…”

A Bayesian Nonparametric Approach for Mapping Dynamic Quantitative Traits

“…Yang et al 2009;R. Yang et al 2009;Xiong et al 2011;Gong and Zou 2012;Xing et al 2012). In addition, the residual terms of these models were often assumed to share a certain covariance structure such as an autoregressive process (Ma et al 2002).…”

“…Most of the existing frequentist approaches (Ma et al 2002;Lin and Wu 2006;Xiong et al 2011;Gong and Zou 2012) follow single-locus functional mapping, which maps the dynamic traits to each marker one at a time and uses either likelihood methods or least-squares-estimating equations approaches (with independent residual covariance structure). These approaches typically construct a test statistic (e.g., log-likelihood ratio or Wald statistic) to screen the important variables (QTL) through a multiple-testing procedure (e.g., adjusting the P-value by permutation or by Bonferroni correction).…”

“…First, with Bsplines, our focus is on automatic adaptive determination of the degree of smoothness (i.e., number of knots), which is a crucial problem in B-splines modeling. In the earlier works of Xiong et al (2011) and Gong and Zou (2012), the degree of smoothness of B-splines was chosen explicitly by cross-validation or the Akaike information criterion (AIC). While here we estimate the degree of smoothness implicitly by assigning second-order penalty priors (Fahrmeir and Kneib 2011) to the time-varying parameters.…”

Bayesian longitudinal low-rank regression models for imaging genetic data from longitudinal studies

“…This assumption can be relaxed by modeling the effects as more flexible functions of age, e.g., polynomial functions and nonparametric functions, which is known as the varying-coefficient models (Hastie and Tibshirani, 1993; Fan and Zhang, 1999, 2008). Varying-coefficient models have been used to study the time-dependent genetic effects and gene-environment interactions (Gong and Zou, 2012; Wu and Cui, 2013; Li et al, 2015). Compared to L2R2, these studies only modeled univariate response variables.…”