LoRaD: Marginal likelihood estimation with haste (but no waste).

The Lowest Radial Distance (LoRaD) method is a modification of the recently introduced Partition-Weighted Kernel method for estimating the marginal likelihood of a model, a quantity important for Bayesian model selection. For analyses involving a fixed tree topology, LoRaD improves upon the Steppingstone or Thermodynamic Integration (Path Sampling) approaches now in common use in phylogenetics because it requires sampling only from the posterior distribution, avoiding the need to sample from a series of ad hoc power posterior distributions, and yet is more accurate than other fast methods such as the Generalized Harmonic Mean (GHM) method. We show that the method performs well in comparison to the Generalized Steppingstone method on an empirical fixed-topology example from molecular phylogenetics involving 180 parameters. The LoRaD method can also be used to obtain the marginal likelihood in the variable-topology case if at least one tree topology occurs with sufficient frequency in the posterior sample to allow accurate estimation of the marginal likelihood conditional on that topology. [Bayesian; marginal likelihood; phylogenetics.].

Bayesian variable selection for the Cox regression model with spatially varying coefficients with applications to Louisiana respiratory cancer data.

The Cox regression model is a commonly used model in survival analysis. In public health studies, clinical data are often collected from medical service providers of different locations. There are large geographical variations in the covariate effects on survival rates from particular diseases. In this paper, we focus on the variable selection issue for the Cox regression model with spatially varying coefficients. We propose a Bayesian hierarchical model which incorporates a horseshoe prior for sparsity and a point mass mixture prior to determine whether a regression coefficient is spatially varying. An efficient two-stage computational method is used for posterior inference and variable selection. It essentially applies the existing method for maximizing the partial likelihood for the Cox model by site independently first and then applying an Markov chain Monte Carlo algorithm for variable selection based on results of the first stage. Extensive simulation studies are carried out to examine the empirical performance of the proposed method. Finally, we apply the proposed methodology to analyzing a real dataset on respiratory cancer in Louisiana from the Surveillance, Epidemiology, and End Results (SEER) program.

New partition based measures for data compatibility and information gain.

It is of great practical importance to compare and combine data from different studies in order to carry out appropriate and more powerful statistical inference. We propose a partition based measure to quantify the compatibility of two datasets using their respective posterior distributions. We further propose an information gain measure to quantify the information increase (or decrease) in combining two datasets. These measures are well calibrated and efficient computational algorithms are provided for their calculations. We use examples in a benchmark dose toxicology study, a six cities pollution data and a melanoma clinical trial to illustrate how these two measures are useful in combining current data with historical data and missing data.

The Free and Cued Selective Reminding Test Predicts Braak Stage.

BACKGROUND: The ultimate validation of a clinical marker for Alzheimer's disease (AD) is its association with AD neuropathology. OBJECTIVE: To identify clinical measures that predict pathology, we evaluated the relationships of the picture version of the Free and Cued Selective Reminding Test (pFCSRT + IR), the Mini-Mental State Exam (MMSE), and the Clinical Dementia Rating scale Sum of Boxes (CDR-SB) to Braak stage. METHODS: 315 cases from the clinicopathologic series at the Knight Alzheimer's Disease Research Center were classified according to Braak stage. Boxplots of each predictor were compared to identify the earliest stage at which decline was observed and ordinal logistic regression was used to predict Braak stage. RESULTS: Looking at the assessment closest to death, free recall scores were lower in individuals at Braak stage III versus Braak stages 0 and I (combined) while MMSE and CDR scores for individuals did not differ from Braak stages 0/I until Braak stage IV. The sum of free recall and total recall scores independently predicted Braak stage and had higher predictive validity than MMSE and CDR-SB in models including all three. CONCLUSION: pFCSRT + IR scores may be more sensitive to early pathological changes than either the CDR-SB or the MMSE.

Stages of Objective Memory Impairment Predict Alzheimer's Disease Neuropathology: Comparison with the Clinical Dementia Rating Scale-Sum of Boxes.

BACKGROUND: The ultimate validation of a clinical marker for Alzheimer's disease (AD) is its association with AD neuropathology. OBJECTIVE: To examine how well the Stages of Objective Memory Impairment (SOMI) system predicts intermediate/high AD neuropathologic change and extent of neurofibrillary tangle (NFT) pathology defined by Braak stage, in comparison to the Clinical Dementia Rating (CDR) Scale sum of boxes (CDR-SB). METHODS: 251 well-characterized participants from the Knight ADRC clinicopathologic series were classified into SOMI stage at their last assessment prior to death using the free recall and total recall scores from the picture version of the Free and Cued Selective Reminding Test with Immediate Recall (pFCSRT + IR). Logistic regression models assessed the predictive validity of SOMI and CDR-SB for intermediate/high AD neuropathologic change. Receiver operating characteristics (ROC) analysis evaluated the discriminative validity of SOMI and CDR-SB for AD pathology. Ordinal logistic regression was used to predict Braak stage using SOMI and CDR-SB in separate and joint models. RESULTS: The diagnostic accuracy of SOMI for AD diagnosis was similar to that of the CDR-SB (AUC: 85%versus 83%). In separate models, both SOMI and CDR-SB predicted Braak stage. In a joint model SOMI remained a significant predictor of Braak stage but CDR-SB did not. CONCLUSION: SOMI provides a neuropathologically validated staging system for episodic memory impairment in the AD continuum and should be useful in predicting tau positivity based on its association with Braak stage.

Inflated Density Ratio and Its Variation and Generalization for Computing Marginal Likelihoods.

In the Bayesian framework, the marginal likelihood plays an important role in variable selection and model comparison. The marginal likelihood is the marginal density of the data after integrating out the parameters over the parameter space. However, this quantity is often analytically intractable due to the complexity of the model. In this paper, we first examine the properties of the inflated density ratio (IDR) method, which is a Monte Carlo method for computing the marginal likelihood using a single MC or Markov chain Monte Carlo (MCMC) sample. We then develop a variation of the IDR estimator, called the dimension reduced inflated density ratio (Dr.IDR) estimator. We further propose a more general identity and then obtain a general dimension reduced (GDr) estimator. Simulation studies are conducted to examine empirical performance of the IDR estimator as well as the Dr.IDR and GDr estimators. We further demonstrate the usefulness of the GDr estimator for computing the normalizing constants in a case study on the inequality-constrained analysis of variance.

Partition Weighted Approach for Estimating the Marginal Posterior Density with Applications.

The computation of marginal posterior density in Bayesian analysis is essential in that it can provide complete information about parameters of interest. Furthermore, the marginal posterior density can be used for computing Bayes factors, posterior model probabilities, and diagnostic measures. The conditional marginal density estimator (CMDE) is theoretically the best for marginal density estimation but requires the closed-form expression of the conditional posterior density, which is often not available in many applications. We develop the partition weighted marginal density estimator (PWMDE) to realize the CMDE. This unbiased estimator requires only a single MCMC output from the joint posterior distribution and the known unnormalized posterior density. The theoretical properties and various applications of the We carry out simulation studies to investigate the empirical performance of the PWMDE and further demonstrate the desirable features of the proposed method with two real data sets from a study of dissociative identity disorder patients and a prostate cancer study, respectively.

Assessing Combinability of Phylogenomic Data Using Bayes Factors.

With the rapid reduction in sequencing costs of high-throughput genomic data, it has become commonplace to use hundreds of genes to infer phylogeny of any study system. While sampling a large number of genes has given us a tremendous opportunity to uncover previously unknown relationships and improve phylogenetic resolution, it also presents us with new challenges when the phylogenetic signal is confused by differences in the evolutionary histories of sampled genes. Given the incorporation of accurate marginal likelihood estimation methods into popular Bayesian software programs, it is natural to consider using the Bayes Factor (BF) to compare different partition models in which genes within any given partition subset share both tree topology and edge lengths. We explore using marginal likelihood to assess data subset combinability when data subsets have varying levels of phylogenetic discordance due to deep coalescence events among genes (simulated within a species tree), and compare the results with our recently described phylogenetic informational dissonance index (D) estimated for each data set. BF effectively detects phylogenetic incongruence and provides a way to assess the statistical significance of D values. We use BFs to assess data combinability using an empirical data set comprising 56 plastid genes from the green algal order Volvocales. We also discuss the potential need for calibrating BFs and demonstrate that BFs used in this study are correctly calibrated.

Dosage Compensation of the X Chromosomes in Bovine Germline, Early Embryos, and Somatic Tissues.

Dosage compensation of the mammalian X chromosome (X) was proposed by Susumu Ohno as a mechanism wherein the inactivation of one X in females would lead to doubling the expression of the other. This would resolve the dosage imbalance between eutherian females (XX) versus male (XY) and between a single active X versus autosome pairs (A). Expression ratio of X- and A-linked genes has been relatively well studied in humans and mice, despite controversial results over the existence of upregulation of X-linked genes. Here we report the first comprehensive test of Ohno's hypothesis in bovine preattachment embryos, germline, and somatic tissues. Overall an incomplete dosage compensation (0.5 < X:A < 1) of expressed genes and an excess X dosage compensation (X:A > 1) of ubiquitously expressed "dosage-sensitive" genes were seen. No significant differences in X:A ratios were observed between bovine female and male somatic tissues, further supporting Ohno's hypothesis. Interestingly, preimplantation embryos manifested a unique pattern of X dosage compensation dynamics. Specifically, X dosage decreased after fertilization, indicating that the sperm brings in an inactive X to the matured oocyte. Subsequently, the activation of the bovine embryonic genome enhanced expression of X-linked genes and increased the X dosage. As a result, an excess compensation was exhibited from the 8-cell stage to the compact morula stage. The X dosage peaked at the 16-cell stage and stabilized after the blastocyst stage. Together, our findings confirm Ohno's hypothesis of X dosage compensation in the bovine and extend it by showing incomplete and over-compensation for expressed and "dosage-sensitive" genes, respectively.

A Tailored Multivariate Mixture Model for Detecting Proteins of Concordant Change Among Virulent Strains of Clostridium Perfringens.

Necrotic enteritis (NE) is a serious disease of poultry caused by the bacterium C. perfringens. To identify proteins of C. perfringens that confer virulence with respect to NE, the protein secretions of four NE disease-producing strains and one baseline non-disease-producing strain of C. perfringens were examined. The problem then becomes a clustering task, for the identification of two extreme groups of proteins that were produced at either concordantly higher or concordantly lower levels across all four disease-producing strains compared to the baseline, when most of the proteins do not exhibit significant change across all strains. However, the existence of some nuisance proteins of discordant change may severely distort any biologically meaningful cluster pattern. We develop a tailored multivariate clustering approach to robustly identify the proteins of concordant change. Using a three-component normal mixture model as the skeleton, our approach incorporates several constraints to account for biological expectations and data characteristics. More importantly, we adopt a sparse mean-shift parameterization in the reference distribution, coupled with a regularized estimation approach, to flexibly accommodate proteins of discordant change. We explore the connections and differences between our approach and other robust clustering methods, and resolve the issue of unbounded likelihood under an eigenvalue-ratio condition. Simulation studies demonstrate the superior performance of our method compared with a number of alternative approaches. Our protein analysis along with further biological investigations may shed light on the discovery of the complete set of virulence factors in NE.

An Improved Enzyme-Linked Immunoassay for the Detection of Leptospira-Specific Antibodies.

Leptospirosis is a neglected zoonotic disease with worldwide endemicity and continues to be a significant public health burden on resource-limited populations. Previously, we produced three highly purified recombinant antigens (rLipL32, rLipL41, and rLigA-Rep) and evaluated their performance of detecting Leptospira-specific antibodies in enzyme-linked immunosorbent assay (ELISA) as compared with the microscopic agglutination test (MAT). The overall sensitivity of this assay approached 90%. Recently, another recombinant antigen (rLigB-Rep) was prepared. We tested each individual antigen and a 1:1:1:1 mixture of these four antigens for the detection of Leptospira-specific antibodies in ELISA. The performance of these recombinant antigens was evaluated with a much larger febrile patient panel (337 MAT-confirmed positive sera and 92 MAT-negative sera from febrile patients). Combining the detection results of immunoglobulin M and immunoglobulin G from these four individual antigens, the overall sensitivity was close to 90% but the specificity was only 66%, based on the MAT reference method. The overall sensitivity and specificity of the four-antigen mixture were 82% and 86%, respectively. The mixture of four antigens also exhibited a broader reactivity with MAT-positive samples of 18 serovars from six major pathogenic Leptospira species. Given the limitations of MAT, the data were further analyzed by Bayesian latent class model, showing that ELISA using a 1:1:1:1 mixture still maintained high sensitivity (79%) and specificity (88%) as compared with the sensitivity (90%) and specificity (83%) of MAT. Therefore, ELISA using a mixture of these four antigens could be a very useful test for seroprevalence studies.

A New Monte Carlo Method for Estimating Marginal Likelihoods.

Evaluating the marginal likelihood in Bayesian analysis is essential for model selection. Estimators based on a single Markov chain Monte Carlo sample from the posterior distribution include the harmonic mean estimator and the inflated density ratio estimator. We propose a new class of Monte Carlo estimators based on this single Markov chain Monte Carlo sample. This class can be thought of as a generalization of the harmonic mean and inflated density ratio estimators using a partition weighted kernel (likelihood times prior). We show that our estimator is consistent and has better theoretical properties than the harmonic mean and inflated density ratio estimators. In addition, we provide guidelines on choosing optimal weights. Simulation studies were conducted to examine the empirical performance of the proposed estimator. We further demonstrate the desirable features of the proposed estimator with two real data sets: one is from a prostate cancer study using an ordinal probit regression model with latent variables; the other is for the power prior construction from two Eastern Cooperative Oncology Group phase III clinical trials using the cure rate survival model with similar objectives.

Risk analysis of use of different classes of antidepressants on subsequent dementia: A nationwide cohort study in Taiwan.

Depression and dementia are common mental health problems and are associated in several ways. Early-life depression is associated with increased risk of later life dementia, and depression can present as a preclinical symptom or consequence of dementia. Despite the plausible relationship between these two clinical entities, the potential association between antidepressant medication and dementia has rarely been investigated. We conducted a 9-year retrospective analysis of Taiwan's National Health Insurance Research Database (NHIRD), enrolling 5819 cases who had received prescriptions of antidepressants between 2003 and 2006, and 23,276 (with ratio of 1:4) age, sex, and index date-matched controls. The hazard ratio (HR) of dementia among antidepressant users with depression was 2.42 (95% confidence interval (CI): 1.15-5.10), for those without depression was 4.05 (95% CI: 3.19-5.15), compared to antidepressant non-users respectively. Among the 6 classes of common antidepressants used in Taiwan, the adjusted HRs were 3.66 (95% CI: 2.62-5.09) for SSRIs, 4.73 (95% CI: 2.54-8.80) for SNRI, 3.26 (95% CI: 2.30-4.63) for TCAs, 6.62 (95% CI: 3.34-13.13) for TeCA, 4.94 (95% CI: 2.17-11.24) for MAOI, and 4.48 (95% CI: 3.13-6.40) for SARI. Furthermore, the multivariate analysis result showed that the adjusted HRs of cumulative defined daily doses (cDDDs) were 3.74 (95% CI: 2.91-4.82), 3.73 (95% CI: 2.39-5.80) and 5.22 (95% CI: 3.35-8.14) for those who had cDDDs of <90, 90-180 and >180 compared to those who had taken no antidepressant medication. This is a retrospective study based on secondary data, hence, we could not claim causality between antidepressant medication and dementia. However, a potential association between antidepressant and occurrence of dementia after controlling for the status of depression was observed. Lack of patients' data about smoking status and body mass index in NHIRD, which are considered related to dementia, was also a limitation in this study. In this study, we concluded that antidepressant medication is a potential risk factor for dementia, independent from any effect of depression itself.

Estimating Bayesian Phylogenetic Information Content.

Measuring the phylogenetic information content of data has a long history in systematics. Here we explore a Bayesian approach to information content estimation. The entropy of the posterior distribution compared with the entropy of the prior distribution provides a natural way to measure information content. If the data have no information relevant to ranking tree topologies beyond the information supplied by the prior, the posterior and prior will be identical. Information in data discourages consideration of some hypotheses allowed by the prior, resulting in a posterior distribution that is more concentrated (has lower entropy) than the prior. We focus on measuring information about tree topology using marginal posterior distributions of tree topologies. We show that both the accuracy and the computational efficiency of topological information content estimation improve with use of the conditional clade distribution, which also allows topological information content to be partitioned by clade. We explore two important applications of our method: providing a compelling definition of saturation and detecting conflict among data partitions that can negatively affect analyses of concatenated data. [Bayesian; concatenation; conditional clade distribution; entropy; information; phylogenetics; saturation.].

Effects of High Hydrostatic Pressure on Expression Profiles of In Vitro Produced Vitrified Bovine Blastocysts.

High hydrostatic pressure (HHP) has been used to pre-condition embryos before essential, yet potentially detrimental procedures such as cryopreservation. However, the mechanisms for HHP are poorly understood. We treated bovine blastocysts with three different HHP (40, 60 and 80 MPa) in combination with three recovery periods (0, 1 h, 2 h post HHP). Re-expansion rates were significantly higher at 40 and 60 but lower at 80 MPa after vitrification-warming in the treated groups than controls. Microarray analysis revealed 399 differentially expressed transcripts, representing 254 unique genes, among different groups. Gene ontology analysis indicated that HHP at 40 and 60 MPa promoted embryo competence through down-regulation of genes in cell death and apoptosis, and up-regulation of genes in RNA processing, cellular growth and proliferation. In contrast, 80 MPa up-regulated genes in apoptosis, and down-regulated protein folding and cell cycle-related genes. Moreover, gene expression was also influenced by the length of the recovery time after HHP. The significantly over-represented categories were apoptosis and cell death in the 1 h group, and protein folding, response to unfolded protein and cell cycle in the 2 h group compared to 0 h. Taken together, HHP promotes competence of vitrified bovine blastocysts through modest transcriptional changes.

Increasing radiation dose improves immunotherapy outcome and prolongation of tumor dormancy in a subgroup of mice treated for advanced intracerebral melanoma.

Previously, we developed a clinically relevant therapy model for advanced intracerebral B16 melanomas in syngeneic mice combining radiation and immunotherapies. Here, 7 days after B16-F10-luc2 melanoma cells were implanted intracerebrally (D7), syngeneic mice with bioluminescent tumors that had formed (1E10(5) to 7E10(6) photons per minute (>1E10(6), large; <1E10(6), small) were segregated into large-/small-balanced subgroups. Then, mice received either radiation therapy alone (RT) or radiation therapy plus immunotherapy (RT plus IT) (single injection of mAbPC61 to deplete regulatory T cells followed by multiple injections of irradiated granulocyte macrophage colony stimulating factor transfected B16-F10 cells) (RT plus IT). Radiation dose was varied (15, 18.75 or 22.5 Gy, given on D8), while immunotherapy was provided similarly to all mice. The data support the hypothesis that increasing radiation dose improves the outcome of immunotherapy in a subgroup of mice. The tumors that were greatly delayed in beginning their progressive growth were bioluminescent in vivo-some for many months, indicating prolonged tumor "dormancy," in some cases presaging long-term cures. Mice bearing such tumors had far more likely received radiation plus immunotherapy, rather than RT alone. Radiotherapy is a very important adjunct to immunotherapy; the greater the tumor debulking by RT, the greater should be the benefit to tumor immunotherapy.

Confident difference criterion: a new Bayesian differentially expressed gene selection algorithm with applications.

BACKGROUND: Recently, the Bayesian method becomes more popular for analyzing high dimensional gene expression data as it allows us to borrow information across different genes and provides powerful estimators for evaluating gene expression levels. It is crucial to develop a simple but efficient gene selection algorithm for detecting differentially expressed (DE) genes based on the Bayesian estimators. RESULTS: In this paper, by extending the two-criterion idea of Chen et al. (Chen M-H, Ibrahim JG, Chi Y-Y. A new class of mixture models for differential gene expression in DNA microarray data. J Stat Plan Inference. 2008;138:387-404), we propose two new gene selection algorithms for general Bayesian models and name these new methods as the confident difference criterion methods. One is based on the standardized differences between two mean expression values among genes; the other adds the differences between two variances to it. The proposed confident difference criterion methods first evaluate the posterior probability of a gene having different gene expressions between competitive samples and then declare a gene to be DE if the posterior probability is large. The theoretical connection between the proposed first method based on the means and the Bayes factor approach proposed by Yu et al. (Yu F, Chen M-H, Kuo L. Detecting differentially expressed genes using alibrated Bayes factors. Statistica Sinica. 2008;18:783-802) is established under the normal-normal-model with equal variances between two samples. The empirical performance of the proposed methods is examined and compared to those of several existing methods via several simulations. The results from these simulation studies show that the proposed confident difference criterion methods outperform the existing methods when comparing gene expressions across different conditions for both microarray studies and sequence-based high-throughput studies. A real dataset is used to further demonstrate the proposed methodology. In the real data application, the confident difference criterion methods successfully identified more clinically important DE genes than the other methods. CONCLUSION: The confident difference criterion method proposed in this paper provides a new efficient approach for both microarray studies and sequence-based high-throughput studies to identify differentially expressed genes.

Posterior predictive Bayesian phylogenetic model selection.

We present two distinctly different posterior predictive approaches to Bayesian phylogenetic model selection and illustrate these methods using examples from green algal protein-coding cpDNA sequences and flowering plant rDNA sequences. The Gelfand-Ghosh (GG) approach allows dissection of an overall measure of model fit into components due to posterior predictive variance (GGp) and goodness-of-fit (GGg), which distinguishes this method from the posterior predictive P-value approach. The conditional predictive ordinate (CPO) method provides a site-specific measure of model fit useful for exploratory analyses and can be combined over sites yielding the log pseudomarginal likelihood (LPML) which is useful as an overall measure of model fit. CPO provides a useful cross-validation approach that is computationally efficient, requiring only a sample from the posterior distribution (no additional simulation is required). Both GG and CPO add new perspectives to Bayesian phylogenetic model selection based on the predictive abilities of models and complement the perspective provided by the marginal likelihood (including Bayes Factor comparisons) based solely on the fit of competing models to observed data.

A Bayesian Approach to Pathway Analysis by Integrating Gene-Gene Functional Directions and Microarray Data.

Many statistical methods have been developed to screen for differentially expressed genes associated with specific phenotypes in the microarray data. However, it remains a major challenge to synthesize the observed expression patterns with abundant biological knowledge for more complete understanding of the biological functions among genes. Various methods including clustering analysis on genes, neural network, Bayesian network and pathway analysis have been developed toward this goal. In most of these procedures, the activation and inhibition relationships among genes have hardly been utilized in the modeling steps. We propose two novel Bayesian models to integrate the microarray data with the putative pathway structures obtained from the KEGG database and the directional gene-gene interactions in the medical literature. We define the symmetric Kullback-Leibler divergence of a pathway, and use it to identify the pathway(s) most supported by the microarray data. Monte Carlo Markov Chain sampling algorithm is given for posterior computation in the hierarchical model. The proposed method is shown to select the most supported pathway in an illustrative example. Finally, we apply the methodology to a real microarray data set to understand the gene expression profile of osteoblast lineage at defined stages of differentiation. We observe that our method correctly identifies the pathways that are reported to play essential roles in modulating bone mass.

Multi-stage transitional models with random effects and their application to the Einstein aging study.

Longitudinal studies of aging often gather repeated observations of cognitive status to describe the development of dementia and to assess the influence of risk factors. Clinical progression to dementia is often conceptualized by a multi-stage model of several transitions that synthesizes time-varying effects. In this study, we assess the influence of risk factors on the transitions among three cognitive status: cognitive stability (normal cognition for age), memory impairment, and clinical dementia. We have developed a shared random effects model that not only links the propensity of transitions and to the probability of informative missingness due to death, but also incorporates heterogeneous transition between subjects. We evaluate four approaches using generalized logit and four using proportional odds models to the first-order Markov transition probabilities as a function of covariates. Random effects were incorporated into these models to account for within-subject correlations. Data from the Einstein Aging Study are used to evaluate the goodness-of-fit of these models using the Akaike information criterion. The best fitting model for each type (generalized logit and proportional odds) is recommended and their results are discussed in more details.