Computation of reference Bayesian inference for variance components in longitudinal studies

Annals of Human Genetics

Hsiao

Wen

2008

Multiple markers in linkage disequilibrium (LD) are usually used to localize the disease gene location. These markers may contribute to the disease etiology simultaneously. In contrast to the single-locus tests, we propose a genetic random effects model that accounts for the dependence between loci via their spatial structures. In this model, the locus-specific random effects measure not only the genetic disease risk, but also the correlations between markers. In other words, the model incorporates this relation in both mean and covariance structures, and the variance components play important roles. We consider two different settings for the spatial relations. The first is our proposal, relative distance function (RDF), which is intuitive in the sense that markers nearby are likely to correlate with each other. The second setting is a common exponential decay function (EDF). Under each setting, the inference of the genetic parameters is fully Bayesian with Markov chain Monte Carlo (MCMC) sampling. We demonstrate the validity and the utility of the proposed approach with two real datasets and simulation studies. The analyses show that the proposed model with either one of two spatial correlations performs better as compared with the single locus analysis. In addition, under the RDF model, a more precise estimate for the disease locus can be obtained even when the candidate markers are fairly dense. In all simulations, the inference under the true model provides unbiased estimates of the genetic parameters, and the model with the spatial correlation structure does lead to greater confidence interval coverage probabilities.

Section: Discussionmentioning

confidence: 99%

A Bayesian Spatial Multimarker Genetic Random‐Effect Model for Fine‐Scale Mapping

Annals of Human Genetics

Hsiao

Wen

2008

“…Similarly, the constant * n is Pr Z 1 ∈ R + q+1 , where Z 1 ∼ N * * and is the submatrix of 1 , the inverse observed information matrix under H 1 , for . For non normal response variables, the MLE is intractable and a direct approach is to apply the penalized quasi-likelihood estimate (PQL; Breslow and Clayton, 1993) However, this approximation may not work well because the PQL estimates can be substantially biased (Lin and Breslow, 1996;Tsai and Hsiao, 2008). Here, we propose a hybrid approximation combining a simulated version of Laplace's method and an importance sampling approach.…”

Section: Bayes Factors For Variance Components In Glmmsmentioning

confidence: 97%

“…Next, the log B L−I us , log B L−I unit , and log B L−I W were compared with log B to derive their observed significance levels, respectively. The reason for choosing log B L−I J and log B as the references is because the posterior estimates under the modified approximate Downloaded by [Central Michigan University] (Tsai and Hsiao, 2008). Similarly, the log B Chib us , log B Chib unit , and log B Chib W were compared with log B * that was the standard cutoff value corresponding to the considered by the percentile of log B Chib J .…”

Section: Poisson Data With Moderate Sample Sizementioning

confidence: 99%

A Hybrid Approximation Bayesian Test of Variance Components for Longitudinal Data

Communications in Statistics - Theory and Methods

2010

Self Cite

The test of variance components of possibly correlated random effects in generalized linear mixed models (GLMMs) can be used to examine if there exists heterogeneous effects. The Bayesian test with Bayes factors offers a flexible method. In this article, we focus on the performance of Bayesian tests under three reference priors and a conjugate prior: an approximate uniform shrinkage prior, modified approximate Jeffreys' prior, half-normal unit information prior and Wishart prior. To compute Bayes factors, we propose a hybrid approximation approach combining a simulated version of Laplace's method and importance sampling techniques to test the variance components in GLMMs.

“…Breslow and Clayton [2] proposed penalized quasi-likelihood (PQL) that utilizes a Gaussian approximation and is easily implemented for different types of data. However, the estimates via PQL are substantially biased for variance components if the cluster size is small [3,19,35]. Even the correction for penalized quasi-likelihood (CPQL) proposed by Breslow and Lin [3] and Lin and Breslow [19] suffers from some biases.…”

Section: Introductionmentioning

confidence: 97%

Extended Bayesian model averaging for heritability in twin studies

Journal of Applied Statistics

2010

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Family studies are often conducted to examine the existence of familial aggregation. Particularly, twin studies can model separately the genetic and environmental contribution. Here we estimate the heritability of quantitative traits via variance components of random-effects in linear mixed models (LMMs). The motivating example was a myopia twin study containing complex nesting data structures: twins and siblings in the same family and observations on both eyes for each individual. Three models are considered for this nesting structure. Our proposal takes into account the model uncertainty in both covariates and model structures via an extended Bayesian model averaging (EBMA) procedure. We estimate the heritability using EBMA under three suggested model structures. When compared with the results under the model with the highest posterior model probability, the EBMA estimate has smaller variation and is slightly conservative. Simulation studies are conducted to evaluate the performance of variance-components estimates, as well as the selections of risk factors, under the correct or incorrect structure. The results indicate that EBMA, with consideration of uncertainties in both covariates and model structures, is robust in model misspecification than the usual Bayesian model averaging (BMA) that considers only uncertainty in covariates selection.Bayesian model averaging, boundary Laplace approximation, heritability, linear mixed models, model uncertainty,