Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham's-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains. © Institute of Mathematical Statistics, 2010.

Homeostatic imbalance of purine catabolism in first-episode neuroleptic-naïve patients with schizophrenia.

BACKGROUND: Purine catabolism may be an unappreciated, but important component of the homeostatic response of mitochondria to oxidant stress. Accumulating evidence suggests a pivotal role of oxidative stress in schizophrenia pathology. METHODOLOGY/PRINCIPAL FINDINGS: Using high-pressure liquid chromatography coupled with a coulometric multi-electrode array system, we compared 6 purine metabolites simultaneously in plasma between first-episode neuroleptic-naïve patients with schizophrenia (FENNS, n = 25) and healthy controls (HC, n = 30), as well as between FENNS at baseline (BL) and 4 weeks (4w) after antipsychotic treatment. Significantly higher levels of xanthosine (Xant) and lower levels of guanine (G) were seen in both patient groups compared to HC subjects. Moreover, the ratios of G/guanosine (Gr), uric acid (UA)/Gr, and UA/Xant were significantly lower, whereas the ratio of Xant/G was significantly higher in FENNS-BL than in HC. Such changes remained in FENNS-4w with exception that the ratio of UA/Gr was normalized. All 3 groups had significant correlations between G and UA, and Xan and hypoxanthine (Hx). By contrast, correlations of UA with each of Xan and Hx, and the correlation of Xan with Gr were all quite significant for the HC but not for the FENNS. Finally, correlations of Gr with each of UA and G were significant for both HC and FENNS-BL but not for the FENNS-4w. CONCLUSIONS/SIGNIFICANCE: During purine catabolism, both conversions of Gr to G and of Xant to Xan are reversible. Decreased ratios of product to precursor suggested a shift favorable to Xant production from Xan, resulting in decreased UA levels in the FENNS. Specifically, the reduced UA/Gr ratio was nearly normalized after 4 weeks of antipsychotic treatment. In addition, there are tightly correlated precursor and product relationships within purine pathways; although some of these correlations persist across disease or medication status, others appear to be lost among FENNS. Taken together, these results suggest that the potential for steady formation of antioxidant UA from purine catabolism is altered early in the course of illness.

Neutralization activity in a geographically diverse East London cohort of human immunodeficiency virus type 1-infected patients: clade C infection results in a stronger and broader humoral immune response than clade B infection.

The array of human immunodeficiency virus (HIV) subtypes encountered in East London, an area long associated with migration, is unusually heterogeneous, reflecting the diverse geographical origins of the population. In this study it was shown that viral subtypes or clades infecting a sample of HIV type 1 (HIV-1)-positive individuals in East London reflect the global pandemic. The authors studied the humoral response in 210 treatment-naïve chronically HIV-1-infected (>1 year) adult subjects against a panel of 12 viruses from six different clades. Plasmas from individuals infected with clade C, but also plasmas from clade A, and to a lesser degree clade CRF02_AG and CRF01_AE, were significantly more potent at neutralizing the tested viruses compared with plasmas from individuals infected with clade B. The difference in humoral robustness between clade C- and B-infected patients was confirmed in titration studies with an extended panel of clade B and C viruses. These results support the approach to develop an HIV-1 vaccine that includes clade C or A envelope protein (Env) immunogens for the induction of a potent neutralizing humoral response.

Latent Stick-Breaking Processes.

We develop a model for stochastic processes with random marginal distributions. Our model relies on a stick-breaking construction for the marginal distribution of the process, and introduces dependence across locations by using a latent Gaussian copula model as the mechanism for selecting the atoms. The resulting latent stick-breaking process (LaSBP) induces a random partition of the index space, with points closer in space having a higher probability of being in the same cluster. We develop an efficient and straightforward Markov chain Monte Carlo (MCMC) algorithm for computation and discuss applications in financial econometrics and ecology. This article has supplementary material online.

Delimiting species without nuclear monophyly in Madagascar's mouse lemurs.

BACKGROUND: Speciation begins when populations become genetically separated through a substantial reduction in gene flow, and it is at this point that a genetically cohesive set of populations attain the sole property of species: the independent evolution of a population-level lineage. The comprehensive delimitation of species within biodiversity hotspots, regardless of their level of divergence, is important for understanding the factors that drive the diversification of biota and for identifying them as targets for conservation. However, delimiting recently diverged species is challenging due to insufficient time for the differential evolution of characters--including morphological differences, reproductive isolation, and gene tree monophyly--that are typically used as evidence for separately evolving lineages. METHODOLOGY: In this study, we assembled multiple lines of evidence from the analysis of mtDNA and nDNA sequence data for the delimitation of a high diversity of cryptically diverged population-level mouse lemur lineages across the island of Madagascar. Our study uses a multi-faceted approach that applies phylogenetic, population genetic, and genealogical analysis for recognizing lineage diversity and presents the most thoroughly sampled species delimitation of mouse lemur ever performed. CONCLUSIONS: The resolution of a large number of geographically defined clades in the mtDNA gene tree provides strong initial evidence for recognizing a high diversity of population-level lineages in mouse lemurs. We find additional support for lineage recognition in the striking concordance between mtDNA clades and patterns of nuclear population structure. Lineages identified using these two sources of evidence also exhibit patterns of population divergence according to genealogical exclusivity estimates. Mouse lemur lineage diversity is reflected in both a geographically fine-scaled pattern of population divergence within established and geographically widespread taxa, as well as newly resolved patterns of micro-endemism revealed through expanded field sampling into previously poorly and well-sampled regions.

The evolutionary origin of Indian Ocean tortoises (Dipsochelys).

Today, the only surviving wild population of giant tortoises in the Indian Ocean occurs on the island of Aldabra. However, giant tortoises once inhabited islands throughout the western Indian Ocean. Madagascar, Africa, and India have all been suggested as possible sources of colonization for these islands. To address the origin of Indian Ocean tortoises (Dipsochelys, formerly Geochelone gigantea), we sequenced the 12S, 16S, and cyt b genes of the mitochondrial DNA. Our phylogenetic analysis shows Dipsochelys to be embedded within the Malagasy lineage, providing evidence that Indian Ocean giant tortoises are derived from a common Malagasy ancestor. This result points to Madagascar as the source of colonization for western Indian Ocean islands by giant tortoises. Tortoises are known to survive long oceanic voyages by floating with ocean currents, and thus, currents flowing northward towards the Aldabra archipelago from the east coast of Madagascar would have provided means for the colonization of western Indian Ocean islands. Additionally, we found an accelerated rate of sequence evolution in the two Malagasy Pyxis species examined. This finding supports previous theories that shorter generation time and smaller body size are related to an increase in mitochondrial DNA substitution rate in vertebrates.

Working at the interface of phylogenetics and population genetics: a biogeographical analysis of Triaenops spp. (Chiroptera: Hipposideridae).

New applications of genetic data to questions of historical biogeography have revolutionized our understanding of how organisms have come to occupy their present distributions. Phylogenetic methods in combination with divergence time estimation can reveal biogeographical centres of origin, differentiate between hypotheses of vicariance and dispersal, and reveal the directionality of dispersal events. Despite their power, however, phylogenetic methods can sometimes yield patterns that are compatible with multiple, equally well-supported biogeographical hypotheses. In such cases, additional approaches must be integrated to differentiate among conflicting dispersal hypotheses. Here, we use a synthetic approach that draws upon the analytical strengths of coalescent and population genetic methods to augment phylogenetic analyses in order to assess the biogeographical history of Madagascar's Triaenops bats (Chiroptera: Hipposideridae). Phylogenetic analyses of mitochondrial DNA sequence data for Malagasy and east African Triaenops reveal a pattern that equally supports two competing hypotheses. While the phylogeny cannot determine whether Africa or Madagascar was the centre of origin for the species investigated, it serves as the essential backbone for the application of coalescent and population genetic methods. From the application of these methods, we conclude that a hypothesis of two independent but unidirectional dispersal events from Africa to Madagascar is best supported by the data.

BAYESIAN MODEL SEARCH AND MULTILEVEL INFERENCE FOR SNP ASSOCIATION STUDIES.

Technological advances in genotyping have given rise to hypothesis-based association studies of increasing scope. As a result, the scientific hypotheses addressed by these studies have become more complex and more difficult to address using existing analytic methodologies. Obstacles to analysis include inference in the face of multiple comparisons, complications arising from correlations among the SNPs (single nucleotide polymorphisms), choice of their genetic parametrization and missing data. In this paper we present an efficient Bayesian model search strategy that searches over the space of genetic markers and their genetic parametrization. The resulting method for Multilevel Inference of SNP Associations, MISA, allows computation of multilevel posterior probabilities and Bayes factors at the global, gene and SNP level, with the prior distribution on SNP inclusion in the model providing an intrinsic multiplicity correction. We use simulated data sets to characterize MISA's statistical power, and show that MISA has higher power to detect association than standard procedures. Using data from the North Carolina Ovarian Cancer Study (NCOCS), MISA identifies variants that were not identified by standard methods and have been externally "validated" in independent studies. We examine sensitivity of the NCOCS results to prior choice and method for imputing missing data. MISA is available in an R package on CRAN.

Association between DNA damage response and repair genes and risk of invasive serous ovarian cancer.

BACKGROUND: We analyzed the association between 53 genes related to DNA repair and p53-mediated damage response and serous ovarian cancer risk using case-control data from the North Carolina Ovarian Cancer Study (NCOCS), a population-based, case-control study. METHODS/PRINCIPAL FINDINGS: The analysis was restricted to 364 invasive serous ovarian cancer cases and 761 controls of white, non-Hispanic race. Statistical analysis was two staged: a screen using marginal Bayes factors (BFs) for 484 SNPs and a modeling stage in which we calculated multivariate adjusted posterior probabilities of association for 77 SNPs that passed the screen. These probabilities were conditional on subject age at diagnosis/interview, batch, a DNA quality metric and genotypes of other SNPs and allowed for uncertainty in the genetic parameterizations of the SNPs and number of associated SNPs. Six SNPs had Bayes factors greater than 10 in favor of an association with invasive serous ovarian cancer. These included rs5762746 (median OR(odds ratio)(per allele) = 0.66; 95% credible interval (CI) = 0.44-1.00) and rs6005835 (median OR(per allele) = 0.69; 95% CI = 0.53-0.91) in CHEK2, rs2078486 (median OR(per allele) = 1.65; 95% CI = 1.21-2.25) and rs12951053 (median OR(per allele) = 1.65; 95% CI = 1.20-2.26) in TP53, rs411697 (median OR (rare homozygote) = 0.53; 95% CI = 0.35 - 0.79) in BACH1 and rs10131 (median OR( rare homozygote) = not estimable) in LIG4. The six most highly associated SNPs are either predicted to be functionally significant or are in LD with such a variant. The variants in TP53 were confirmed to be associated in a large follow-up study. CONCLUSIONS/SIGNIFICANCE: Based on our findings, further follow-up of the DNA repair and response pathways in a larger dataset is warranted to confirm these results.

Bayesian inference of the number of factors in gene-expression analysis: application to human virus challenge studies.

BACKGROUND: Nonparametric Bayesian techniques have been developed recently to extend the sophistication of factor models, allowing one to infer the number of appropriate factors from the observed data. We consider such techniques for sparse factor analysis, with application to gene-expression data from three virus challenge studies. Particular attention is placed on employing the Beta Process (BP), the Indian Buffet Process (IBP), and related sparseness-promoting techniques to infer a proper number of factors. The posterior density function on the model parameters is computed using Gibbs sampling and variational Bayesian (VB) analysis. RESULTS: Time-evolving gene-expression data are considered for respiratory syncytial virus (RSV), Rhino virus, and influenza, using blood samples from healthy human subjects. These data were acquired in three challenge studies, each executed after receiving institutional review board (IRB) approval from Duke University. Comparisons are made between several alternative means of per-forming nonparametric factor analysis on these data, with comparisons as well to sparse-PCA and Penalized Matrix Decomposition (PMD), closely related non-Bayesian approaches. CONCLUSIONS: Applying the Beta Process to the factor scores, or to the singular values of a pseudo-SVD construction, the proposed algorithms infer the number of factors in gene-expression data. For real data the "true" number of factors is unknown; in our simulations we consider a range of noise variances, and the proposed Bayesian models inferred the number of factors accurately relative to other methods in the literature, such as sparse-PCA and PMD. We have also identified a "pan-viral" factor of importance for each of the three viruses considered in this study. We have identified a set of genes associated with this pan-viral factor, of interest for early detection of such viruses based upon the host response, as quantified via gene-expression data.

Lognormal and gamma mixed negative binomial regression

In regression analysis of counts, a lack of simple and efficient algorithms for posterior computation has made Bayesian approaches appear unattractive and thus underdeveloped. We propose a lognormal and gamma mixed negative binomial (NB) regression model for counts, and present efficient closed-form Bayesian inference; unlike conventional Poisson models, the proposed approach has two free parameters to include two different kinds of random effects, and allows the incorporation of prior information, such as sparsity in the regression coefficients. By placing a gamma distribution prior on the NB dispersion parameter r, and connecting a log-normal distribution prior with the logit of the NB probability parameter p, efficient Gibbs sampling and variational Bayes inference are both developed. The closed-form updates are obtained by exploiting conditional conjugacy via both a compound Poisson representation and a Polya-Gamma distribution based data augmentation approach. The proposed Bayesian inference can be implemented routinely, while being easily generalizable to more complex settings involving multivariate dependence structures. The algorithms are illustrated using real examples. Copyright 2012 by the author(s)/owner(s).

Mechanisms of CD8+ T Cell Mediated Virus Inhibition in HIV-1 Virus Controllers

CD8+ T cells are associated with long term control of virus replication to low or undetectable levels in a population of HIV+ therapy-naïve individuals known as virus controllers (VCs; <5000 RNA copies/ml and CD4+ lymphocyte counts >400 cells/µl). These subjects' ability to control viremia in the absence of therapy makes them the gold standard for the type of CD8+ T-cell response that should be induced with a vaccine. Studying the regulation of CD8+ T cells responses in these VCs provides the opportunity to discover mechanisms of durable control of HIV-1. Previous research has shown that the CD8+ T cell population in VCs is heterogeneous in its ability to inhibit virus replication and distinct T cells are responsible for virus inhibition. Further defining both the functional properties and regulation of the specific features of the select CD8+ T cells responsible for potent control of viremia the in VCs would enable better evaluation of T cell-directed vaccine strategies and may inform the design of new therapies.

Here we discuss the progress made in elucidating the features and regulation of CD8+ T cell response in virus controllers. We first detail the development of assays to quantify CD8+ T cells' ability to inhibit virus replication. This includes the use of a multi-clade HIV-1 panel which can subsequently be used as a tool for evaluation of T cell directed vaccines. We used these assays to evaluate the CD8+ response among cohorts of HIV-1 seronegative, HIV-1 acutely infected, and HIV-1 chronically infected (both VC and chronic viremic) patients. Contact and soluble CD8+ T cell virus inhibition assays (VIAs) are able to distinguish these patient groups based on the presence and magnitude of the responses. When employed in conjunction with peptide stimulation, the soluble assay reveals peptide stimulation induces CD8+ T cell responses with a prevalence of Gag p24 and Nef specificity among the virus controllers tested. Given this prevalence, we aimed to determine the gene expression profile of Gag p24-, Nef-, and unstimulated CD8+ T cells. RNA was isolated from CD8+ T-cells from two virus controllers with strong virus inhibition and one seronegative donor after a 5.5 hour stimulation period then analyzed using the Illumina Human BeadChip platform (Duke Center for Human Genome Variation). Analysis revealed that 565 (242 Nef and 323 Gag) genes were differentially expressed in CD8+ T-cells that were able to inhibit virus replication compared to those that could not. We compared the differentially expressed genes to published data sets from other CD8+ T-cell effector function experiments focusing our analysis on the most recurring genes with immunological, gene regulatory, apoptotic or unknown functions. The most commonly identified gene in these studies was TNFRSF9. Using PCR in a larger cohort of virus controllers we confirmed the up-regulation of TNFRSF9 in Gag p24 and Nef-specific CD8+ T cell mediated virus inhibition. We also observed increase in the mRNA encoding antiviral cytokines macrophage inflammatory proteins (MIP-1α, MIP-1αP, MIP-1β), interferon gamma (IFN-γ), granulocyte-macrophage colony-stimulating factor (GM-CSF), and recently identified lymphotactin (XCL1).

Our previous work suggests the CD8+ T-cell response to HIV-1 can be regulated at the level of gene regulation. Because RNA abundance is modulated by transcription of new mRNAs and decay of new and existing RNA we aimed to evaluate the net rate of transcription and mRNA decay for the cytokines we identified as differentially regulated. To estimate rate of mRNA synthesis and decay, we stimulated isolated CD8+ T-cells with Gag p24 and Nef peptides adding 4-thiouridine (4SU) during the final hour of stimulation, allowing for separation of RNA made during the final hour of stimulation. Subsequent PCR of RNA isolated from these cells, allowed us to determine how much mRNA was made for our genes of interest during the final hour which we used to calculate rate of transcription. To assess if stimulation caused a change in RNA stability, we calculated the decay rates of these mRNA over time. In Gag p24 and Nef stimulated T cells , the abundance of the mRNA of many of the cytokines examined was dependent on changes in both transcription and mRNA decay with evidence for potential differences in the regulation of mRNA between Nef and Gag specific CD8+ T cells. The results were highly reproducible in that in one subject that was measured in three independent experiments the results were concordant.

This data suggests that mRNA stability, in addition to transcription, is key in regulating the direct anti-HIV-1 function of antigen-specific memory CD8+ T cells by enabling rapid recall of anti-HIV-1 effector functions, namely the production and increased stability of antiviral cytokines. We have started to uncover the mechanisms employed by CD8+ T cell subsets with antigen-specific anti-HIV-1 activity, in turn, enhancing our ability to inhibit virus replication by informing both cure strategies and HIV-1 vaccine designs that aim to reduce transmission and can aid in blocking HIV-1 acquisition.

The coherence of memories for trauma: evidence from posttraumatic stress disorder.

Participants with posttraumatic stress disorder (PTSD) and participants with a trauma but without PTSD wrote narratives of their trauma and, for comparison, of the most-important and the happiest events that occurred within a year of their trauma. They then rated these three events on coherence. Based on participants' self-ratings and on naïve-observer scorings of the participants' narratives, memories of traumas were not more incoherent than the comparison memories in participants in general or in participants with PTSD. This study comprehensively assesses narrative coherence using a full two (PTSD or not) by two (traumatic event or not) design. The results are counter to most prevalent theoretical views of memory for trauma.

Infection of monkeys by simian-human immunodeficiency viruses with transmitted/founder clade C HIV-1 envelopes.

Simian-human immunodeficiency viruses (SHIVs) that mirror natural transmitted/founder (T/F) viruses in man are needed for evaluation of HIV-1 vaccine candidates in nonhuman primates. Currently available SHIVs contain HIV-1 env genes from chronically-infected individuals and do not reflect the characteristics of biologically relevant HIV-1 strains that mediate human transmission. We chose to develop clade C SHIVs, as clade C is the major infecting subtype of HIV-1 in the world. We constructed 10 clade C SHIVs expressing Env proteins from T/F viruses. Three of these ten clade C SHIVs (SHIV KB9 C3, SHIV KB9 C4 and SHIV KB9 C5) replicated in naïve rhesus monkeys. These three SHIVs are mucosally transmissible and are neutralized by sCD4 and several HIV-1 broadly neutralizing antibodies. However, like natural T/F viruses, they exhibit low Env reactivity and a Tier 2 neutralization sensitivity. Of note, none of the clade C T/F SHIVs elicited detectable autologous neutralizing antibodies in the infected monkeys, even though antibodies that neutralized a heterologous Tier 1 HIV-1 were generated. Challenge with these three new clade C SHIVs will provide biologically relevant tests for vaccine protection in rhesus macaques.

Characterization of B cells in muscle-specific kinase antibody myasthenia gravis.

OBJECTIVE: To characterize B-cell subsets in patients with muscle-specific tyrosine kinase (MuSK) myasthenia gravis (MG). METHODS: In accordance with Human Immunology Project Consortium guidelines, we performed polychromatic flow cytometry and ELISA assays in peripheral blood samples from 18 patients with MuSK MG and 9 healthy controls. To complement a B-cell phenotype assay that evaluated maturational subsets, we measured B10 cell percentages, plasma B cell-activating factor (BAFF) levels, and MuSK antibody titers. Immunologic variables were compared with healthy controls and clinical outcome measures. RESULTS: As expected, patients treated with rituximab had high percentages of transitional B cells and plasmablasts and thus were excluded from subsequent analysis. The remaining patients with MuSK MG and controls had similar percentages of total B cells and naïve, memory, isotype-switched, plasmablast, and transitional B-cell subsets. However, patients with MuSK MG had higher BAFF levels and lower percentages of B10 cells. In addition, we observed an increase in MuSK antibody levels with more severe disease. CONCLUSIONS: We found prominent B-cell pathology in the distinct form of MG with MuSK autoantibodies. Increased BAFF levels have been described in other autoimmune diseases, including acetylcholine receptor antibody-positive MG. This finding suggests a role for BAFF in the survival of B cells in MuSK MG, which has important therapeutic implications. B10 cells, a recently described rare regulatory B-cell subset that potently blocks Th1 and Th17 responses, were reduced, which suggests a potential mechanism for the breakdown in immune tolerance in patients with MuSK MG.