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PubMed2005

Proceedings of the SMBE Tri-National Young Investigators' Workshop 2005. Improved consensus network techniques for genome-scale phylogeny.

Although recent studies indicate that estimating phylogenies from alignments of concatenated genes greatly reduces the stochastic error, the potential for systematic error still remains, heightening the need for reliable methods to analyze multigene data sets. Consensus methods provide an alternative, more inclusive, approach for analyzing collections of trees arising from multiple genes. We extend a previously described consensus network method for genome-scale phylogeny (Holland, B. R., K. T. Huber, V. Moulton, and P. J. Lockhart. 2004. Using consensus networks to visualize contradictory evidence for species phylogeny. Mol. Biol. Evol. 21:1459-1461) to incorporate additional information. This additional information could come from bootstrap analysis, Bayesian analysis, or various methods to find confidence sets of trees. The new methods can be extended to include edge weights representing genetic distance. We use three data sets to illustrate the approach: 61 genes from 14 angiosperm taxa and one gymnosperm, 106 genes from eight yeast taxa, and 46 members of a gene family from 15 vertebrate taxa.

Animals↗

PubMed1993

Predicting the probability of helper T cell immunodominant sites through discriminant analysis.

Bayesian discriminant analysis is used to predict whether or not a given protein segment will activate helper T cells. The predictor variables are drawn from the products of frequencies of amino acid residues. The model's predictive validity compares favourably with that of alternative modelling strategies, suggesting that this approach merits further investigation.

Amino Acid Sequence↗

PubMed2006

[Bayesian statistics-based method for genetic linkage analysis].

Bayesian School as one of the important statistical schools is different from the Classical Statistics, and the Bayesian methods have been widely used in many fields of modern sciences. In the present paper, we discussed the application of Bayesian method in linkage analysis, including the Bayesian estimation of recombination fraction, linkage testing based on the Bayes Factor and the Bayesian approach for genetic linkage map construction via Markov chain Monte Carlo algorithm. Simulation study and real data analysis were performed using SAS/IML software, and the validity and practicability of Bayesian method in genetic linkage analysis were thus verified.

Bayes Theorem↗

PubMed1991

Meta-analysis for combining Bayesian probabilities.

Bayesian analysis is a method by which the reliability of diagnostic tests can be determined. It produces a probability of a patient having the disease given a positive test result (posterior probability). If more than one study of a given test's diagnostic accuracy is done, then how can we determine which of these studies has produced the most reliable posterior probability? Meta-analysis is a method whereby data from different studies can be combined. This paper proposes that meta-analysis more accurately estimates the true Bayesian posterior probability than other methods of data pooling.

Bayes Theorem↗

PubMed2001

Using Bayesian inference to perform meta-analysis.

Bayesian modeling offers an elegant approach to meta-analysis that efficiently incorporates all sources of variability and relevant quantifiable external information. It provides a more informative summary of the likely value of parameters after observing the data than do non-Bayesian approaches. This leads to direct probabilistic inference about model parameters such as the average treatment effect, the between-study variance, and individual study treatment effects. The latter are weighted averages of the common mean and individual study means with weights reflecting the amount of information provided by each study relative to the others. Homogeneity among these posterior study estimates indicates that pooling these studies is appropriate; heterogeneity suggests that some cause of between-study variation should be explored. The author describes the construction of such models and shows how to use them to estimate a common mean and regression slopes. Two examples illustrate the additional inferences available with the Bayesian methodology.

Angiotensin-Converting Enzyme Inhibitors↗

PubMed1990

Analysing clinical decision analyses.

We present a critical review of aspects of clinical decision analysis which uses an application to screening for familial intracranial aneurysms. The analysis is reported together with methods for assessing decision trees. These methods appear to be powerful checks on the usually rather intuitive way in which decision trees are built. The problem of assessing the uncertainty in the results of a decision analysis is discussed in detail. In practice, sensitivity analysis covers nearly every calculation apart from the standard evaluation of the decision tree. Different forms of sensitivity analysis are distinguished and given appropriate names: influence analysis, threshold analysis, full Bayesian analysis, Bayesian influence analysis, attribute analysis, generalization analysis and scenario analysis. The biostatistical community may well contribute to the much needed methodological improvement in decision analysis and its different forms of sensitivity analysis, especially if prepared to look beyond the standard statistical techniques.

Adult↗

PubMed2007

Bayesian sensitivity analysis for unmeasured confounding in observational studies.

We consider Bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure, binary response, measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models. A model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder. Simulation from the posterior distribution is accomplished using Markov chain Monte Carlo. Because the model for unmeasured confounding is not identifiable, standard large-sample theory for Bayesian analysis is not applicable. Consequently, the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown. Using simulations, we investigate the coverage probability when averaged with respect to various distributions over the parameter space. The results indicate that credible intervals will have approximately nominal coverage probability, on average, when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies. We motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure.

Adrenergic beta-Antagonists↗

PubMed1989

31P NMR Bayesian spectral analysis of rat brain in vivo.

Bayesian spectrum analysis for parameter estimation is a rigorous statistical (non-Fourier-based) method. Herein the Bayesian quadrature NMR model is introduced and applied to analysis of 31P NMR time domain data from in vivo rat brain. Immunity to both the brain spectrum "baseline hump" and the phase twist is demonstrated.

Animals↗

PubMed2001

Sensitivity analysis, Monte Carlo risk analysis, and Bayesian uncertainty assessment.

Standard statistical methods understate the uncertainty one should attach to effect estimates obtained from observational data. Among the methods used to address this problem are sensitivity analysis, Monte Carlo risk analysis (MCRA), and Bayesian uncertainty assessment. Estimates from MCRAs have been presented as if they were valid frequentist or Bayesian results, but examples show that they need not be either in actual applications. It is concluded that both sensitivity analyses and MCRA should begin with the same type of prior specification effort as Bayesian analysis.

Bayes Theorem↗

PubMed1997

Bayesian statistical analysis of protein side-chain rotamer preferences.

We present a Bayesian statistical analysis of the conformations of side chains in proteins from the Protein Data Bank. This is an extension of the backbone-dependent rotamer library, and includes rotamer populations and average chi angles for a full range of phi, psi values. The Bayesian analysis used here provides a rigorous statistical method for taking account of varying amounts of data. Bayesian statistics requires the assumption of a prior distribution for parameters over their range of possible values. This prior distribution can be derived from previous data or from pooling some of the present data. The prior distribution is combined with the data to form the posterior distribution, which is a compromise between the prior distribution and the data. For the chi 2, chi 3, and chi 4 rotamer prior distributions, we assume that the probability of each rotamer type is dependent only on the previous chi rotamer in the chain. For the backbone-dependence of the chi 1 rotamers, we derive prior distributions from the product of the phi-dependent and psi-dependent probabilities. Molecular mechanics calculations with the CHARMM22 potential show a strong similarity with the experimental distributions, indicating that proteins attain their lowest energy rotamers with respect to local backbone-side-chain interactions. The new library is suitable for use in homology modeling, protein folding simulations, and the refinement of X-ray and NMR structures.

Bayes Theorem↗

PubMedDate not supplied

Selected topics in statistical analysis of clinical research.

Statistical analysis usually is employed in the evaluation of clinical research studies. This paper reviews and makes recommendations in three areas frequently overlooked in the conduct of clinical research: power analysis, specification of a priori research hypotheses, and Bayesian analysis. Power analysis determines the number of subjects required to conduct a meaningful study and should be performed during the planning phase. Research and null hypotheses are essential elements of research design and should be specified prior to statistical analysis. Bayesian analysis can be used both to evaluate diagnostic tests and as an alternative to traditional statistical approaches for testing multiple hypotheses. Application of these methods is described and clinical examples are provided. The discussion is nontechnical and is directed toward the clinical researcher.

Aged↗

PubMed1988

Reliability of Bayesian probability analysis for predicting coronary artery disease in a veterans hospital.

To assess the accuracy of Bayesian probability analysis for the prediction of coronary artery disease, post-test probabilities were generated by the application of three Bayesian algorithms to the clinical and noninvasive test results of 199 patients undergoing angiography in a veterans' hospital. All assumed conditional independence but each used different pre-test and conditional probabilities. Two statistical approaches were employed: (1) Sorting of patients in ascending deciles of probability and comparing expected and observed probabilities in each decile. (2) Calculation of normally distributed reliability statistics which do not depend on probability subsets and the comparison of resulting probability distributions using these statistics. Both statistical approaches revealed that the Bayesian algorithms overestimated disease probability when it was high and underestimated it when low. Though all three algorithms were frequently incorrect, they differed significantly in their accuracies, suggesting that errors in Bayesian analysis are caused by factors other than the assumption of independence. The errors may be due to differences in sensitivity and specificity of tests applied in different institutions.

Adult↗

PubMed2001

Bayesian semiparametric analysis of developmental toxicology data.

Modeling of developmental toxicity studies often requires simple parametric analyses of the dose-response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure. This article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations. We approach our analysis using a Bayesian semiparametric model that we tailored specifically to developmental toxicology studies. It combines parametric dose-response relationships with a flexible nonparametric specification of the distribution of the response, obtained via a product of Dirichlet process mixtures approach (PDPM). Our formulation achieves three goals: (1) the distribution of the response is modeled in a general way, (2) the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data, and (3) the marginal posterior distribution of the parameters of interest is available in closed form. The logistic regression model, as well as many of its extensions such as the beta-binomial model and finite mixture models, are special cases. In the context of the two motivating examples and a simulated example, we provide model comparisons, illustrate overdispersion diagnostics that can assist model specification, show how to derive posterior distributions of the effective dose parameters and predictive distributions of response, and discuss the sensitivity of the results to the choice of the prior distribution.

2,4,5-Trichlorophenoxyacetic Acid↗

PubMed2006

On the association between statin and fracture: a Bayesian consideration.

BACKGROUND: The association between statin use and fracture risk is controversial, due to conflicting findings from previous studies. This study utilized the Bayesian approach to combine existing evidence and update the association with consideration of potential bias. METHODS: Data on the association between statin use and fracture incidence from 11 observational studies and 4 RCTs were synthesized by both empirical Bayesian analysis and fully Bayesian random-effects meta-analysis models. RESULTS: Empirical Bayesian analysis showed that statin use was associated with a reduction in hip fracture risk (OR=0.57, 95% credible interval (CrI): 0.46-0.71) and for non-vertebral (OR=0.69, 95% CrI, 0.63-0.74). These results were comparable with results from the fully Bayesian random-effects meta-analysis only for hip fracture (OR 0.56, 95% CrI, 0.42-0.73), but not for non-vertebral fracture (OR 0.77, 95% CrI, 0.58-1.03). The probability that statin use reduces fracture risk by at least 20% was 0.995 for hip fracture and 0.61 for non-vertebral fracture. Under the assumption that bias over-estimates the true OR by 20%, there is still a probability of 0.97 that statin use reduces hip fracture risk by at least 20%; however, the effect on non-vertebral fracture was much less robust with a probability of 0.27. CONCLUSIONS: Results of this Bayesian consideration are highly consistent with the hypothesis that statin use reduces hip fracture, but the association between statin use and non-vertebral fracture remains uncertain. The Bayesian approach presented here has the ability to help updating existing evidence as new data becomes available.

Bayes Theorem↗

PubMed2006

High frequency edges (but not contrast) predict where we fixate: A Bayesian system identification analysis.

A Bayesian system identification technique was used to determine which image characteristics predict where people fixate when viewing natural images. More specifically an estimate was derived for the mapping between image characteristics at a given location and the probability that this location was fixated. Using a large database of eye fixations to natural images, we determined the most probable (a posteriori) model of this mapping. From a set of candidate feature maps consisting of edge, contrast and luminance maps (at two different spatial scales), fixation probability was dominated by high spatial frequency edge information. The best model applied compressive non-linearity to the high frequency edge detecting filters (approximately a square root). Both low spatial frequency edges and contrast had weaker, but inhibitory, effects. The contributions of the other maps were so small as to be behaviourally irrelevant. This Bayesian method identifies not only the relevant weighting of the different maps, but how this weighting varies as a function of distance from the point of fixation. It was found that rather than centre surround inhibition, the weightings simply averaged over an area of about 2 degrees.

Bayes Theorem↗

PubMed2003

Approaches to mapping genetically correlated complex traits.

Our Markov chain Monte Carlo (MCMC) methods were used in linkage analyses of the Framingham Heart Study data using all available pedigrees. Our goal was to detect and map loci associated with covariate-adjusted traits log triglyceride (lnTG) and high-density lipoprotein cholesterol (HDL) using multipoint LOD score analysis, Bayesian oligogenic linkage analysis and identity-by-descent (IBD) scoring methods. Each method used all marker data for all markers on a chromosome. Bayesian linkage analysis detected a linkage signal on chromosome 7 for lnTG and HDL, corroborating previously published results. However, these results were not replicated in a classical linkage analysis of the data or by using IBD scoring methods.We conclude that Bayesian linkage analysis provides a powerful paradigm for mapping trait loci but interpretation of the Bayesian linkage signals is subjective. In the absence of a LOD score method accommodating genetically complex traits and linkage heterogeneity, validation of these signals remains elusive.

Cholesterol, HDL↗

PubMed2004

Bayesian phylogenetic analysis of combined data.

The recent development of Bayesian phylogenetic inference using Markov chain Monte Carlo (MCMC) techniques has facilitated the exploration of parameter-rich evolutionary models. At the same time, stochastic models have become more realistic (and complex) and have been extended to new types of data, such as morphology. Based on this foundation, we developed a Bayesian MCMC approach to the analysis of combined data sets and explored its utility in inferring relationships among gall wasps based on data from morphology and four genes (nuclear and mitochondrial, ribosomal and protein coding). Examined models range in complexity from those recognizing only a morphological and a molecular partition to those having complex substitution models with independent parameters for each gene. Bayesian MCMC analysis deals efficiently with complex models: convergence occurs faster and more predictably for complex models, mixing is adequate for all parameters even under very complex models, and the parameter update cycle is virtually unaffected by model partitioning across sites. Morphology contributed only 5% of the characters in the data set but nevertheless influenced the combined-data tree, supporting the utility of morphological data in multigene analyses. We used Bayesian criteria (Bayes factors) to show that process heterogeneity across data partitions is a significant model component, although not as important as among-site rate variation. More complex evolutionary models are associated with more topological uncertainty and less conflict between morphology and molecules. Bayes factors sometimes favor simpler models over considerably more parameter-rich models, but the best model overall is also the most complex and Bayes factors do not support exclusion of apparently weak parameters from this model. Thus, Bayes factors appear to be useful for selecting among complex models, but it is still unclear whether their use strikes a reasonable balance between model complexity and error in parameter estimates.

Animals↗

PubMed2006

A Bayesian heterogeneous analysis of variance approach to inferring recent selective sweeps.

The distribution of microsatellite allele sizes in populations aids in understanding the genetic diversity of species and the evolutionary history of recent selective sweeps. We propose a heterogeneous Bayesian analysis of variance model for inferring loci involved in recent selective sweeps by analyzing the distribution of allele sizes at multiple loci in multiple populations. Our model is shown to be consistent with a multilocus test statistic, ln RV, proposed for identifying microsatellite loci involved in recent selective sweeps. Our methodology differs in that it accepts original allele size data rather than summary statistics and allows the incorporation of prior knowledge about allele frequencies using a hierarchical prior distribution consisting of log normal and gamma probability distributions. Interesting features of the model are its ability to simultaneously analyze allele size data for any number of populations and to cope with the presence of any number of selected loci. The utility of the method is illustrated by application to two sets of microsatellite allele size data for a group of West African Anopheles gambiae populations. The results are consistent with the suppressed-recombination model of speciation, and additional candidate loci on chromosomes 2 (079 and 175) and 3 (088) are discovered that escaped former analysis.

Alleles↗