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.].

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.

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.

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.

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.].

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.

Differentiated cells are more efficient than adult stem cells for cloning by somatic cell nuclear transfer.

Since the creation of Dolly via somatic cell nuclear transfer (SCNT), more than a dozen species of mammals have been cloned using this technology. One hypothesis for the limited success of cloning via SCNT (1%-5%) is that the clones are likely to be derived from adult stem cells. Support for this hypothesis comes from the findings that the reproductive cloning efficiency for embryonic stem cells is five to ten times higher than that for somatic cells as donors and that cloned pups cannot be produced directly from cloned embryos derived from differentiated B and T cells or neuronal cells. The question remains as to whether SCNT-derived animal clones can be derived from truly differentiated somatic cells. We tested this hypothesis with mouse hematopoietic cells at different differentiation stages: hematopoietic stem cells, progenitor cells and granulocytes. We found that cloning efficiency increases over the differentiation hierarchy, and terminally differentiated postmitotic granulocytes yield cloned pups with the greatest cloning efficiency.

Choosing among partition models in Bayesian phylogenetics.

Bayesian phylogenetic analyses often depend on Bayes factors (BFs) to determine the optimal way to partition the data. The marginal likelihoods used to compute BFs, in turn, are most commonly estimated using the harmonic mean (HM) method, which has been shown to be inaccurate. We describe a new more accurate method for estimating the marginal likelihood of a model and compare it with the HM method on both simulated and empirical data. The new method generalizes our previously described stepping-stone (SS) approach by making use of a reference distribution parameterized using samples from the posterior distribution. This avoids one challenging aspect of the original SS method, namely the need to sample from distributions that are close (in the Kullback-Leibler sense) to the prior. We specifically address the choice of partition models and find that using the HM method can lead to a strong preference for an overpartitioned model. In contrast to the HM method and the original SS method, we show using simulated data that the generalized SS method is strikingly more precise (repeatable BF values of the same data and partition model) and yields BF values that are much more reasonable than those produced by the HM method. Comparisons of HM and generalized SS methods on an empirical data set demonstrate that the generalized SS method tends to choose simpler partition schemes that are more in line with expectation based on inferred patterns of molecular evolution. The generalized SS method shares with thermodynamic integration the need to sample from a series of distributions in addition to the posterior. Such dedicated path-based Markov chain Monte Carlo analyses appear to be a cost of estimating marginal likelihoods accurately.

Improving marginal likelihood estimation for Bayesian phylogenetic model selection.

The marginal likelihood is commonly used for comparing different evolutionary models in Bayesian phylogenetics and is the central quantity used in computing Bayes Factors for comparing model fit. A popular method for estimating marginal likelihoods, the harmonic mean (HM) method, can be easily computed from the output of a Markov chain Monte Carlo analysis but often greatly overestimates the marginal likelihood. The thermodynamic integration (TI) method is much more accurate than the HM method but requires more computation. In this paper, we introduce a new method, steppingstone sampling (SS), which uses importance sampling to estimate each ratio in a series (the "stepping stones") bridging the posterior and prior distributions. We compare the performance of the SS approach to the TI and HM methods in simulation and using real data. We conclude that the greatly increased accuracy of the SS and TI methods argues for their use instead of the HM method, despite the extra computation needed.

Bayesian hierarchical modeling and selection of differentially expressed genes for the EST data.

Expressed sequence tag (EST) sequencing is a one-pass sequencing reading of cloned cDNAs derived from a certain tissue. The frequency of unique tags among different unbiased cDNA libraries is used to infer the relative expression level of each tag. In this article, we propose a hierarchical multinomial model with a nonlinear Dirichlet prior for the EST data with multiple libraries and multiple types of tissues. A novel hierarchical prior is developed and the properties of the proposed prior are examined. An efficient Markov chain Monte Carlo algorithm is developed for carrying out the posterior computation. We also propose a new selection criterion for detecting which genes are differentially expressed between two tissue types. Our new method with the new gene selection criterion is demonstrated via several simulations to have low false negative and false positive rates. A real EST data set is used to motivate and illustrate the proposed method.

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.

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.

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 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.

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.