A Bayes factor approach with informative prior for rare genetic variant analysis from next generation sequencing data

The discovery of rare genetic variants through next generation sequencing is a very challenging issue in the field of human genetics. We propose a novel region‐based statistical approach based on a Bayes Factor (BF) to assess evidence of association between a set of rare variants (RVs) located on the same genomic region and a disease outcome in the context of case‐control design. Marginal likelihoods are computed under the null and alternative hypotheses assuming a binomial distribution for the RV count in the region and a beta or mixture of Dirac and beta prior distribution for the probability of RV. We derive the theoretical null distribution of the BF under our prior setting and show that a Bayesian control of the false Discovery Rate can be obtained for genome‐wide inference. Informative priors are introduced using prior evidence of association from a Kolmogorov‐Smirnov test statistic. We use our simulation program, sim1000G, to generate RV data similar to the 1000 genomes sequencing project. Our simulation studies showed that the new BF statistic outperforms standard methods (SKAT, SKAT‐O, Burden test) in case‐control studies with moderate sample sizes and is equivalent to them under large sample size scenarios. Our real data application to a lung cancer case‐control study found enrichment for RVs in known and novel cancer genes. It also suggests that using the BF with informative prior improves the overall gene discovery compared to the BF with noninformative prior.     

Transient Acceleration of Epidermal Growth Factor Receptor Dynamics Produces Higher-Order Signaling Clusters

Cell signaling depends on spatiotemporally regulated molecular interactions. Although the movements of signaling proteins have been analyzed with various technologies, how spatial dynamics influence the molecular interactions that transduce signals is unclear. Here, we developed a single-molecule method to analyze the spatiotemporal coupling between motility, clustering, and signaling. The analysis was performed with the epidermal growth factor receptor (EGFR), which triggers signaling through its dimerization and phosphorylation after association with EGF. Our results show that the few EGFRs isolated in membrane subdomains were released by an EGF-dependent increase in their diffusion area, facilitating molecular associations and producing immobile clusters. Using a two-color single-molecule analysis, we found that the EGF-induced state transition alters the properties of the immobile clusters, allowing them to interact for extended periods with the cytoplasmic protein, GRB2. Our study reveals a novel correlation between this molecular interaction and its mesoscale dynamics, providing the initial signaling node.     

Efficient screening of predictive biomarkers for individual treatment selection

The development of molecular diagnostic tools to achieve individualized medicine requires identifying predictive biomarkers associated with subgroups of individuals who might receive beneficial or harmful effects from different available treatments. However, due to the large number of candidate biomarkers in the large‐scale genetic and molecular studies, and complex relationships among clinical outcome, biomarkers, and treatments, the ordinary statistical tests for the interactions between treatments and covariates have difficulties from their limited statistical powers. In this paper, we propose an efficient method for detecting predictive biomarkers. We employ weighted loss functions of Chen et al. to directly estimate individual treatment scores and propose synthetic posterior inference for effect sizes of biomarkers. We develop an empirical Bayes approach, namely, we estimate unknown hyperparameters in the prior distribution based on data. We then provide efficient screening methods for the candidate biomarkers via optimal discovery procedure with adequate control of false discovery rate. The proposed method is demonstrated in simulation studies and an application to a breast cancer clinical study in which the proposed method was shown to detect the much larger numbers of significant biomarkers than existing standard methods.     

Comparison of Bayesian and empirical ranking approaches to visual perception

Much current vision research is predicated on the idea--and a rapidly growing body of evidence--that visual percepts are generated according to the empirical significance of light stimuli rather than their physical characteristics. As a result, an increasing number of investigators have asked how visual perception can be rationalized in these terms. Here, we compare two different theoretical frameworks for predicting what observers actually see in response to visual stimuli: Bayesian decision theory and empirical ranking theory. Deciding which of these approaches has greater merit is likely to determine how the statistical operations that apparently underlie visual perception are eventually understood.     

Testing for group effect in a 2 x k heteroscedastic ANOVA model

It is natural to want to relax the assumption of homoscedasticity and Gaussian error in ANOVA models. For a two-way ANOVA model with 2 x k cells, one can derive tests of main effect for the factor with two levels (referred to as group) without assuming homoscedasticity or Gaussian error. Empirical likelihood can be used to derive testing procedures. An approximate empirical likelihood ratio test (AELRT) is derived for the test of group main effect. To approximate the distributions of the test statistics under the null hypothesis, simulation from the approximate empirical maximum likelihood estimate (AEMLE) restricted by the null hypothesis is used. The homoscedastic ANOVA F -test and a Box-type approximation to the distribution of the heteroscedastic ANOVA F -test are compared to the AELRT in level and power. The AELRT procedure is shown by simulation to have appropriate type I error control (although possibly conservative) when the distribution of the test statistics are approximated by simulation from the constrained AEMLE. The methodology is motivated and illustrated by an analysis of folate levels in the blood among two alcohol intake groups while accounting for gender.     

Use of proton Nuclear Overhauser Effects for the determination of the conformations of amino acid residues in oligopeptides

The use of the Nuclear Overhauser Effect to determine backbone and side-chain conformations of oligopeptides is discussed. The distance between the H^α proton of a given residue and the amide proton of the following residue depends only on the dihedral angle ψ. A calibration curve is given for the determination of ψ from the Nuclear Overhauser Effect involving these protons. In amino acids with branched side chains, e.g., threonine, isoleucine, and valine, the Nuclear Overhauser Effect involving the H^β proton and the amide proton in either the same or the following residue gives limited information about both χ¹ and either or ψ. The Nuclear Overhauser Effect involving the H^α and H^γ protons in leucine gives information about χ¹ and χ².     

Bayesian Hierarchical Functional Data Analysis Via Contaminated Informative Priors

Summary .  A variety of flexible approaches have been proposed for functional data analysis, allowing both the mean curve and the distribution about the mean to be unknown. Such methods are most useful when there is limited prior information. Motivated by applications to modeling of temperature curves in the menstrual cycle, this article proposes a flexible approach for incorporating prior information in semiparametric Bayesian analyses of hierarchical functional data. The proposed approach is based on specifying the distribution of functions as a mixture of a parametric hierarchical model and a nonparametric contamination. The parametric component is chosen based on prior knowledge, while the contamination is characterized as a functional Dirichlet process. In the motivating application, the contamination component allows unanticipated curve shapes in unhealthy menstrual cycles. Methods are developed for posterior computation, and the approach is applied to data from a European fecundability study.     

Bayesian Model Selection for Incomplete Data Using the Posterior Predictive Distribution

Summary We explore the use of a posterior predictive loss criterion for model selection for incomplete longitudinal data. We begin by identifying a property that most model selection criteria for incomplete data should consider. We then show that a straightforward extension of the Gelfand and Ghosh (1998, Biometrika, 85 , 1–11) criterion to incomplete data has two problems. First, it introduces an extra term (in addition to the goodness of fit and penalty terms) that compromises the criterion. Second, it does not satisfy the aforementioned property. We propose an alternative and explore its properties via simulations and on a real dataset and compare it to the deviance information criterion (DIC). In general, the DIC outperforms the posterior predictive criterion, but the latter criterion appears to work well overall and is very easy to compute unlike the DIC in certain classes of models for missing data.     

From NMR chemical shifts to amino acid types: Investigation of the predictive power carried by nuclei

An approach to automatic prediction of the amino acid type from NMR chemical shift values of its nuclei is presented here, in the frame of a model to calculate the probability of an amino acid type given the set of chemical shifts. The method relies on systematic use of all chemical shift values contained in the BioMagResBank (BMRB). Two programs were designed, one (BMRB stats) for extracting statistical chemical shift parameters from the BMRB and another one (RESCUE2) for computing the probabilities of each amino acid type, given a set of chemical shifts. The Bayesian prediction scheme presented here is compared to other methods already proposed: PROTYP RESCUE and PLATON and is found to be more sensitive and more specific. Using this scheme, we tested various sets of nuclei. The two nuclei carrying the most information are C(beta) and H(beta), in agreement with observations made in Grzesiek and Bax, 1993. Based on four nuclei: H(beta), C(beta), C(alpha) and C', it is possible to increase correct predictions to a rate of more than 75%. Taking into account the correlations between the nuclei chemical shifts has only a slight impact on the percentage of correct predictions: indeed, the largest correlation coefficients display similar features on all amino acids.     

From Africa via Europe to South America: migrational route of a species‐rich genus of Neotropical lowland rain forest trees (Guatteria,Annonaceae)

Aim Several recent studies have suggested that a substantial portion of today’s plant diversity in the Neotropics has resulted from the dispersal of taxa into that region rather than by vicariance. In general, three routes have been documented for the dispersal of taxa onto the South American continent: (1) via the North Atlantic Land Bridge, (2) via the Bering Land Bridge, or (3) from Africa directly onto the continent. Here a species‐rich genus of Neotropical lowland rain forest trees (Guatteria, Annonaceae) is used as a model to investigate these three hypotheses. Location The Neotropics. Methods The phylogenetic relationships within the long‐branch clade of Annonaceae were reconstructed (using maximum parsimony, maximum likelihood and Bayesian inference) in order to gain insight in the phylogenetic position of Guatteria. Furthermore, Bayesian molecular dating and Bayesian dispersal–vicariance (Bayes‐DIVA) analyses were undertaken. Results Most of the relationships within the long‐branch clade of Annonaceae were reconstructed and had high support. However, the relationship between the Duguetia clade, the Xylopia–Artabotrys clade and Guatteria remained unclear. The stem node age estimate of Guatteria ranged between 49.2 and 51.3 Ma, whereas the crown node age estimate ranged between 11.4 and 17.8 Ma. For the ancestral area of Guatteria and its sister group, the area North America–Africa was reconstructed in 99% of 10,000 DIVA analyses, while South America–North America was found just 1% of the time. Main conclusions The estimated stem to crown node ages of Guatteria in combination with the Bayes‐DIVA analyses imply a scenario congruent with an African origin followed by dispersal across the North Atlantic Land Bridge in the early to middle Eocene and further dispersal into North and Central America (and ultimately South America) in the Miocene. The phylogenetically and morphologically isolated position of the genus is probably due to extinction of the North American and European stem lineages in the Tertiary.