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The mapping of quantitative trait loci (QTL) is to identify molecular markers or genomic loci that influence the variation of complex traits. The problem is complicated by the facts that QTL data usually contain a large number of markers across the entire genome and most of them have little or no effect on the phenotype. In this article, we propose several Bayesian hierarchical models for mapping multiple QTL that simultaneously fit and estimate all possible genetic effects associated with all markers. The proposed models use prior distributions for the genetic effects that are scale mixtures of normal distributions with mean zero and variances distributed to give each effect a high probability of being near zero. We consider two types of priors for the variances, exponential and scaled inverse-x 2 distributions, which result in a Bayesian version of the popular least absolute shrinkage and selection operator (LASSO) model and the well-known Student's t model, respectively. Unlike most applications where fixed values are preset for hyperparameters in the priors, we treat all hyperparameters as unknowns and estimate them along with other parameters. Markov chain Monte Carlo (MCMC) algorithms are developed to simulate the parameters from the posteriors. The methods are illustrated using well-known barley data.

The problem of identifying complex epistatic quantitative trait loci (QTL) across the entire genome continues to be a formidable challenge for geneticists. The complexity of genome-wide epistatic analysis results mainly from the number of QTL being unknown and the number of possible epistatic effects being huge. In this article, we use a composite model space approach to develop a Bayesian model selection framework for identifying epistatic QTL for complex traits in experimental crosses from two inbred lines. By placing a liberal constraint on the upper bound of the number of detectable QTL we restrict attention to models of fixed dimension, greatly simplifying calculations. Indicators specify which main and epistatic effects of putative QTL are included. We detail how to use prior knowledge to bound the number of detectable QTL and to specify prior distributions for indicators of genetic effects. We develop a computationally efficient Markov chain Monte Carlo (MCMC) algorithm using the Gibbs sampler and MetropolisHastings algorithm to explore the posterior distribution. We illustrate the proposed method by detecting new epistatic QTL for obesity in a backcross of CAST/Ei mice onto M16i. M ANY complex human diseases and traits of biotive corrections for multiple testing. Non-Bayesian model logical and/or economic importance are deterselection methods combine simultaneous search with a mined by multiple genetic and environmental influsequential procedure such as forward or stepwise selecences (Lynch and Walsh 1998). Mounting evidence tion and apply criteria such as P-values or modified Bayesuggests that interactions among genes (epistasis) play sian information criterion (BIC) to identify well-fitting an important role in the genetic control and evolumultiple-QTL models (Kao et al. 1999; Carlborg et al. tion of complex traits (Cheverud 2000; Carlborg and 2000;Reifsnyder et al. 2000; Bogdan et al. 2004). These Haley 2004). Mapping quantitative trait loci (QTL) is methods, although appealing in their simplicity and popa process of inferring the number of QTL, their genoularity, have several drawbacks, including: (1) the uncermic positions, and genetic effects given observed phenotainty about the model itself is ignored in the final intype and marker genotype data. From a statistical perference, (2) they involve a complex sequential testing spective, two key problems in QTL mapping are model strategy that includes a dynamically changing null hysearch and selection (e.g., Broman and ful and conceptually simple approach to mapping multiExtensions of this approach can allow for main and epiple QTL (Satagopan et al. 1996; Hoeschele 2001; Sen static effects at two or perhaps a few QTL at a time and and Churchill 2001). The Bayesian approach proemploy a multidimensional scan to detect QTL. Howceeds by setting up a likelihood function for the phenoever, such an approach neglects potential confoundtype and assigning prior distributions to all unknowns ing effects from additional QTL and requires prohibiin the prob...

Background:There is clinical evidence that very low and safe levels of amplitude-modulated electromagnetic fields administered via an intrabuccal spoon-shaped probe may elicit therapeutic responses in patients with cancer. However, there is no known mechanism explaining the anti-proliferative effect of very low intensity electromagnetic fields.Methods:To understand the mechanism of this novel approach, hepatocellular carcinoma (HCC) cells were exposed to 27.12 MHz radiofrequency electromagnetic fields using in vitro exposure systems designed to replicate in vivo conditions. Cancer cells were exposed to tumour-specific modulation frequencies, previously identified by biofeedback methods in patients with a diagnosis of cancer. Control modulation frequencies consisted of randomly chosen modulation frequencies within the same 100 Hz–21 kHz range as cancer-specific frequencies.Results:The growth of HCC and breast cancer cells was significantly decreased by HCC-specific and breast cancer-specific modulation frequencies, respectively. However, the same frequencies did not affect proliferation of nonmalignant hepatocytes or breast epithelial cells. Inhibition of HCC cell proliferation was associated with downregulation of XCL2 and PLP2. Furthermore, HCC-specific modulation frequencies disrupted the mitotic spindle.Conclusion:These findings uncover a novel mechanism controlling the growth of cancer cells at specific modulation frequencies without affecting normal tissues, which may have broad implications in oncology.

BackgroundRecent advances in next-generation sequencing (NGS) technology enable researchers to collect a large volume of metagenomic sequencing data. These data provide valuable resources for investigating interactions between the microbiome and host environmental/clinical factors. In addition to the well-known properties of microbiome count measurements, for example, varied total sequence reads across samples, over-dispersion and zero-inflation, microbiome studies usually collect samples with hierarchical structures, which introduce correlation among the samples and thus further complicate the analysis and interpretation of microbiome count data.ResultsIn this article, we propose negative binomial mixed models (NBMMs) for detecting the association between the microbiome and host environmental/clinical factors for correlated microbiome count data. Although having not dealt with zero-inflation, the proposed mixed-effects models account for correlation among the samples by incorporating random effects into the commonly used fixed-effects negative binomial model, and can efficiently handle over-dispersion and varying total reads. We have developed a flexible and efficient IWLS (Iterative Weighted Least Squares) algorithm to fit the proposed NBMMs by taking advantage of the standard procedure for fitting the linear mixed models.ConclusionsWe evaluate and demonstrate the proposed method via extensive simulation studies and the application to mouse gut microbiome data. The results show that the proposed method has desirable properties and outperform the previously used methods in terms of both empirical power and Type I error. The method has been incorporated into the freely available R package BhGLM (http://www.ssg.uab.edu/bhglm/ and http://github.com/abbyyan3/BhGLM), providing a useful tool for analyzing microbiome data.

Empirical evidence supporting the commonality of gene × gene interactions, coupled with frequent failure to replicate results from previous association studies, has prompted statisticians to develop methods to handle this important subject. Nonparametric methods have generated intense interest because of their capacity to handle high-dimensional data. Genome-wide association analysis of large-scale SNP data is challenging mathematically and computationally. In this paper, we describe major issues and questions arising from this challenge, along with methodological implications. Data reduction and pattern recognition methods seem to be the new frontiers in efforts to detect gene × gene interactions comprehensively. Currently, there is no single method that is recognized as the ‘best’ for detecting, characterizing, and interpreting gene × gene interactions. Instead, a combination of approaches with the aim of balancing their specific strengths may be the optimal approach to investigate gene × gene interactions in human data.

BackgroundObesity has been shown to increase breast cancer risk. FTO is a novel gene which has been identified through genome wide association studies (GWAS) to be related to obesity. Our objective was to evaluate tissue expression of FTO in breast and the role of FTO SNPs in predicting breast cancer risk.MethodsWe performed a case-control study of 354 breast cancer cases and 364 controls. This study was conducted at Northwestern University. We examined the role of single nucleotide polymorphisms (SNPs) of intron 1 of FTO in breast cancer risk. We genotyped cases and controls for four SNPs: rs7206790, rs8047395, rs9939609 and rs1477196. We also evaluated tissue expression of FTO in normal and malignant breast tissue.ResultsWe found that all SNPs were significantly associated with breast cancer risk with rs1477196 showing the strongest association. We showed that FTO is expressed both in normal and malignant breast tissue. We found that FTO genotypes provided powerful classifiers to predict breast cancer risk and a model with epistatic interactions further improved the prediction accuracy with a receiver operating characteristic (ROC) curves of 0.68.ConclusionIn conclusion we have shown a significant expression of FTO in malignant and normal breast tissue and that FTO SNPs in intron 1 are significantly associated with breast cancer risk. Furthermore, these FTO SNPs are powerful classifiers in predicting breast cancer risk.

We develop hierarchical generalized linear models and computationally efficient algorithms for genomewide analysis of quantitative trait loci (QTL) for various types of phenotypes in experimental crosses. The proposed models can fit a large number of effects, including covariates, main effects of numerous loci, and gene-gene (epistasis) and gene-environment (G 3 E) interactions. The key to the approach is the use of continuous prior distribution on coefficients that favors sparseness in the fitted model and facilitates computation. We develop a fast expectation-maximization (EM) algorithm to fit models by estimating posterior modes of coefficients. We incorporate our algorithm into the iteratively weighted least squares for classical generalized linear models as implemented in the package R. We propose a model search strategy to build a parsimonious model. Our method takes advantage of the special correlation structure in QTL data. Simulation studies demonstrate reasonable power to detect true effects, while controlling the rate of false positives. We illustrate with three real data sets and compare our method to existing methods for multiple-QTL mapping. Our method has been implemented in our freely available package R/qtlbim (www.qtlbim.org), providing a valuable addition to our previous Markov chain Monte Carlo (MCMC) approach. MOST complex traits are influenced by interacting networks of multiple quantitative trait loci (QTL) and environmental factors (Carlborg and Haley 2004). Mapping QTL is to infer which genomic loci are strongly associated with the complex trait and to estimate genetic effects of these loci, i.e., main effects and gene-gene (epistasis) and gene-environment (G 3 E) interactions. Due to the multilocus nature of complex traits, it is desirable to simultaneously analyze multiple loci rather than one locus (or a few loci) at a time. However, QTL mapping studies usually genotype hundreds or thousands of genomic loci (markers), leading to numerous variables and a huge number of possible models, and the dependence of genotypes on a chromosome results in many correlated variables. Therefore, mapping multiple QTL requires sophisticated methods that can handle problems with high-dimensional correlated variables.The popular approaches to mapping multiple QTL are some form of variable selection. Such techniques involve identifying a subset of all possible genetic effects (a multiple-QTL model) that best explains the phenotypic variation. Classical variable selection methods use forward or stepwise search procedures and selection criteria such as Bayesian information criteria (BIC) or modified versions to find a multiple-QTL model (Kao et al. 1999;Broman and Speed 2002;Bogdan et al. 2004;Baierl et al. 2006). Bayesian methods proceed by setting up a likelihood function for observed data and prior distributions on unobserved quantities. Two types of prior distributions have been suggested for multiple-QTL mapping. The first assumes a two-component mixture distribution for each genetic effect, ty...