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At least 73 records · Page 4Linked to original sources
PubMed2000

Bayesian accelerated failure time analysis with application to veterinary epidemiology.

Standard methods for analysing survival data with covariates rely on asymptotic inferences. Bayesian methods can be performed using simple computations and are applicable for any sample size. We propose a practical method for making prior specifications and discuss a complete Bayesian analysis for parametric accelerated failure time regression models. We emphasize inferences for the survival curve rather than regression coefficients. A key feature of the Bayesian framework is that model comparisons for various choices of baseline distribution are easily handled by the calculation of Bayes factors. Such comparisons between non-nested models are difficult in the frequentist setting. We illustrate diagnostic tools and examine the sensitivity of the Bayesian methods.

Abortion, Veterinary↗
PubMed2005

A Bayesian approach to modeling dynamic effective connectivity with fMRI data.

A state-space modeling approach for examining dynamic relationship between multiple brain regions was proposed in Ho, Ombao and Shumway (Ho, M.R., Ombao, H., Shumway, R., 2005. A State-Space Approach to Modelling Brain Dynamics to Appear in Statistica Sinica). Their approach assumed that the quantity representing the influence of one neuronal system over another, or effective connectivity, is time-invariant. However, more and more empirical evidence suggests that the connectivity between brain areas may be dynamic which calls for temporal modeling of effective connectivity. A Bayesian approach is proposed to solve this problem in this paper. Our approach first decomposes the observed time series into measurement error and the BOLD (blood oxygenation level-dependent) signals. To capture the complexities of the dynamic processes in the brain, region-specific activations are subsequently modeled, as a linear function of the BOLD signals history at other brain regions. The coefficients in these linear functions represent effective connectivity between the regions under consideration. They are further assumed to follow a random walk process so to characterize the dynamic nature of brain connectivity. We also consider the temporal dependence that may be present in the measurement errors. ML-II method (Berger, J.O., 1985. Statistical Decision Theory and Bayesian Analysis (2nd ed.). Springer, New York) was employed to estimate the hyperparameters in the model and Bayes factor was used to compare among competing models. Statistical inference of the effective connectivity coefficients was based on their posterior distributions and the corresponding Bayesian credible regions (Carlin, B.P., Louis, T.A., 2000. Bayes and Empirical Bayes Methods for Data Analysis (2nd ed.). Chapman and Hall, Boca Raton). The proposed method was applied to a functional magnetic resonance imaging data set and results support the theory of attentional control network and demonstrate that this network is dynamic in nature.

Attention↗
PubMedDate not supplied

Bayesian inference on genetic merit under uncertain paternity.

A hierarchical animal model was developed for inference on genetic merit of livestock with uncertain paternity. Fully conditional posterior distributions for fixed and genetic effects, variance components, sire assignments and their probabilities are derived to facilitate a Bayesian inference strategy using MCMC methods. We compared this model to a model based on the Henderson average numerator relationship (ANRM) in a simulation study with 10 replicated datasets generated for each of two traits. Trait 1 had a medium heritability (h2) for each of direct and maternal genetic effects whereas Trait 2 had a high h2 attributable only to direct effects. The average posterior probabilities inferred on the true sire were between 1 and 10% larger than the corresponding priors (the inverse of the number of candidate sires in a mating pasture) for Trait 1 and between 4 and 13% larger than the corresponding priors for Trait 2. The predicted additive and maternal genetic effects were very similar using both models; however, model choice criteria (Pseudo Bayes Factor and Deviance Information Criterion) decisively favored the proposed hierarchical model over the ANRM model.

Animals↗
PubMed2004

Bayesian analysis of two-level nonlinear structural equation models with continuous and polytomous data.

Two-level structural equation models with mixed continuous and polytomous data and nonlinear structural equations at both the between-groups and within-groups levels are important but difficult to deal with. A Bayesian approach is developed for analysing this kind of model. A Markov chain Monte Carlo procedure based on the Gibbs sampler and the Metropolis-Hasting algorithm is proposed for producing joint Bayesian estimates of the thresholds, structural parameters and latent variables at both levels. Standard errors and highest posterior density intervals are also computed. A procedure for computing Bayes factor, based on the key idea of path sampling, is established for model comparison.

Bayes Theorem↗
PubMed2005

Strange bayes indeed: uniform topological priors imply non-uniform clade priors.

While Bayesian analysis has become common in phylogenetics, the effects of topological prior probabilities on tree inference have not been investigated. In Bayesian analyses, the prior probability of topologies is almost always considered equal for all possible trees, and clade support is calculated from the majority rule consensus of the approximated posterior distribution of topologies. These uniform priors on tree topologies imply non-uniform prior probabilities of clades, which are dependent on the number of taxa in a clade as well as the number of taxa in the analysis. As such, uniform topological priors do not model ignorance with respect to clades. Here, we demonstrate that Bayesian clade support, bootstrap support, and jackknife support from 17 empirical studies are significantly and positively correlated with non-uniform clade priors resulting from uniform topological priors. Further, we demonstrate that this effect disappears for bootstrap and jackknife when data sets are free from character conflict, but remains pronounced for Bayesian clade supports, regardless of tree shape. Finally, we propose the use of a Bayes factor to account for the fact that uniform topological priors do not model ignorance with respect to clade probability.

Bayes Theorem↗
PubMed1999

Toward evidence-based medical statistics. 1: The P value fallacy.

An important problem exists in the interpretation of modern medical research data: Biological understanding and previous research play little formal role in the interpretation of quantitative results. This phenomenon is manifest in the discussion sections of research articles and ultimately can affect the reliability of conclusions. The standard statistical approach has created this situation by promoting the illusion that conclusions can be produced with certain "error rates," without consideration of information from outside the experiment. This statistical approach, the key components of which are P values and hypothesis tests, is widely perceived as a mathematically coherent approach to inference. There is little appreciation in the medical community that the methodology is an amalgam of incompatible elements, whose utility for scientific inference has been the subject of intense debate among statisticians for almost 70 years. This article introduces some of the key elements of that debate and traces the appeal and adverse impact of this methodology to the P value fallacy, the mistaken idea that a single number can capture both the long-run outcomes of an experiment and the evidential meaning of a single result. This argument is made as a prelude to the suggestion that another measure of evidence should be used--the Bayes factor, which properly separates issues of long-run behavior from evidential strength and allows the integration of background knowledge with statistical findings.

Bayes Theorem↗
PubMed2001

Bayesian model selection: analysis of a survival model with a surviving fraction.

We describe a methodology for model comparison in a Bayesian framework as applied to survival with a surviving fraction. This is illustrated using a case study of a randomized and controlled clinical trial investigating time until recurrence of depression. Posterior distributions are simulated using Metropolis-within-Gibbs Markov chain methods. Models reflecting the effects of covariates on the log odds of being in the surviving fraction, the log of the hazard rate, as well as both and neither are compared. Bayes factors for comparing the models are obtained by using the bridge sampling method of calculating normalizing constants.

Algorithms↗
PubMed2000

A Bayesian approach to finite mixture models in bioassay via data augmentation and Gibbs sampling and its application to-insecticide resistance.

After continued treatment with an insecticide, within the population of the susceptible insects, resistant strains will occur. It is important to know whether there are any resistant strains, what the proportions are, and what the median lethal doses are for the insecticide. Lwin and Martin (1989, Biometrics 45, 721-732) propose a probit mixture model and use the EM algorithm to obtain the maximum likelihood estimates for the parameters. This approach has difficulties in estimating the confidence intervals and in testing the number of components. We propose a Bayesian approach to obtaining the credible intervals for the location and scale of the tolerances in each component and for the mixture proportions by using data augmentation and Gibbs sampler. We use Bayes factor for model selection and determining the number of components. We illustrate the method with data published in Lwin and Martin (1989).

Algorithms↗
PubMed2001

Bayesian analysis of liability of clinical mastitis in Norwegian cattle with a threshold model: effects of data sampling method and model specification.

First-lactation records of Norwegian Cattle were used to infer heritability of liability to clinical mastitis with a threshold sire model. Mastitis was defined as a binary response (presence or absence) in a defined period of first lactation (opportunity period). Length of opportunity period (from 30 d before calving up to 120 or 300 d of lactation) had less effect on heritability estimates than data sampling methods (include or exclude records of cows culled before the end of the opportunity period) whereas sire ranking was more affected by the former. Including all cows, whether culled before the end of the opportunity period or not, gave a sharper and more symmetric posterior distribution of heritability of liability to clinical mastitis. When we analyzed data for all cows, model specification had a small effect on heritability estimates, while sire ranking was affected markedly. Posterior means of heritability range from 0.058 to 0.074. A model regressing on the length of the opportunity period for culled cows without mastitis, was shown favorable for the two opportunity periods using Bayes factors and the deviance information criterion for model comparison. This model, in which liability of mastitis depends on time to culling, may allow utilizing information from all first lactations in genetic evaluation, irrespectively of duration and culling outcome.

Animals↗
PubMed2007

Bayesian analysis of latent variable models with non-ignorable missing outcomes from exponential family.

To provide a comprehensive framework for analysing complex non-normal medical and biological data, we propose a Bayesian approach for a non-linear latent variable model with covariates, and non-ignorable missing data, under the exponential family of distributions. The non-ignorable missing mechanism is defined via a logistic regression model. Based on conjugate prior distributions, full conditional distributions for the implementation of Markov chain Monte Carlo methods in simulating observations from the joint posterior distribution are derived. These observations are used in computing the Bayesian estimates, as well as in implementing a path sampling procedure to evaluate the Bayes factor for model comparison. The proposed methods are illustrated using real data from a study on the non-adherence of hypertension patients.

Antihypertensive Agents↗
PubMed2003

Application of models for multivariate mixed outcomes to medical device trials: coronary artery stenting.

The approval process for some medical devices involves a single-arm trial in which the outcomes associated with the new device are compared to the expected outcomes associated with approved devices, the latter denoted the objective performance criterion (OPC). In this paper, models for multivariate mixed outcomes are applied to derive the OPC for a medical device to be used in clinical evaluations of the same type of device. We illustrate the techniques by determining the OPC for coronary artery stents, metal cages used to widen blocked coronary arteries in patients with coronary artery disease, using data from seven randomized trials of stents approved for use in the U.S.A. involving 5806 patients. The OPC is based on two 9-month endpoints: target lesion revascularization, a binary outcome, and proportion diameter stenosis, a continuous outcome. To account for the correlation between mixed outcomes we consider factorization of the likelihood into marginal and conditional components, or adoption of a latent variable model. Because the models have different structural forms, standard methods for model comparison (such as the AIC and BIC) cannot be used. We discuss how model identifiability and valid inference are achieved, and then adapt the deviance information criterion (DIC) and the pseudo-Bayes factor (PSBF) to select the best model. Nine months post-stenting, we find that the average posterior probability (standard deviation) of target lesion revascularization ranges from 0.086 (0.008) for non-diabetics with one diseased vessel to 0.163 (0.022) for diabetics with three diseased vessels. When considering proportion diameter stenosis, the corresponding posterior means are 0.375 (0.020) and 0.427 (0.030). The correlation coefficient of the components of the OPC lies in the range 0.042 to 0.116.

Bayes Theorem↗
PubMed2005

Inequality constrained analysis of variance: a Bayesian approach.

Researchers often have one or more theories or expectations with respect to the outcome of their empirical research. When researchers talk about the expected relations between variables if a certain theory is correct, their statements are often in terms of one or more parameters expected to be larger or smaller than one or more other parameters. Stated otherwise, their statements are often formulated using inequality constraints. In this article, a Bayesian approach to evaluate analysis of variance or analysis of covariance models with inequality constraints on the (adjusted) means is presented. This evaluation contains two issues: estimation of the parameters given the restrictions using the Gibbs sampler and model selection using Bayes factors in the case of competing theories. The article concludes with two illustrations: a one-way analysis of covariance and an analysis of a three-way table of ordered means.

Analysis of Variance↗
PubMed2003

Bayesian inference on order-constrained parameters in generalized linear models.

In biomedical studies, there is often interest in assessing the association between one or more ordered categorical predictors and an outcome variable, adjusting for covariates. For a k-level predictor, one typically uses either a k-1 degree of freedom (df) test or a single df trend test, which requires scores for the different levels of the predictor. In the absence of knowledge of a parametric form for the response function, one can incorporate monotonicity constraints to improve the efficiency of tests of association. This article proposes a general Bayesian approach for inference on order-constrained parameters in generalized linear models. Instead of choosing a prior distribution with support on the constrained space, which can result in major computational difficulties, we propose to map draws from an unconstrained posterior density using an isotonic regression transformation. This approach allows flat regions over which increases in the level of a predictor have no effect. Bayes factors for assessing ordered trends can be computed based on the output from a Gibbs sampling algorithm. Results from a simulation study are presented and the approach is applied to data from a time-to-pregnancy study.

Adult↗
PubMed2002

Effects of models of rate evolution on estimation of divergence dates with special reference to the metazoan 18S ribosomal RNA phylogeny.

The molecular clock, i.e., constancy of the rate of evolution over time, is commonly assumed in estimating divergence dates. However, this assumption is often violated and has drastic effects on date estimation. Recently, a number of attempts have been made to relax the clock assumption. One approach is to use maximum likelihood, which assigns rates to branches and allows the estimation of both rates and times. An alternative is the Bayes approach, which models the change of the rate over time. A number of models of rate change have been proposed. We have extended and evaluated models of rate evolution, i.e., the lognormal and its recent variant, along with the gamma, the exponential, and the Ornstein-Uhlenbeck processes. These models were first applied to a small hominoid data set, where an empirical Bayes approach was used to estimate the hyperparameters that measure the amount of rate variation. Estimation of divergence times was sensitive to these hyperparameters, especially when the assumed model is close to the clock assumption. The rate and date estimates varied little from model to model, although the posterior Bayes factor indicated the Ornstein-Uhlenbeck process outperformed the other models. To demonstrate the importance of allowing for rate change across lineages, this general approach was used to analyze a larger data set consisting of the 18S ribosomal RNA gene of 39 metazoan species. We obtained date estimates consistent with paleontological records, the deepest split within the group being about 560 million years ago. Estimates of the rates were in accordance with the Cambrian explosion hypothesis and suggested some more recent lineage-specific bursts of evolution.

Algorithms↗
PubMed1998

Effect of delayed observations on Bayesian decisions for binary data.

A Bayesian decision rule for early termination of an experimental study of binary responses is presented. This early termination occurs when the predictive probability of reversing the decision when utilizing the delayed observations is small. The proposed approach utilizes Bayesian inferential tools such as Bayes factors and predictive distributions. A simulation study is conducted to evaluate the performance of the proposed approach. Some guidelines are given to determine when the study should be terminated early and when the investigator should wait for delayed observations before making a conclusion.

Bayes Theorem↗
PubMed2003

How Bayes tests of molecular phylogenies compare with frequentist approaches.

MOTIVATION: The desire to compare molecular phylogenies has stimulated the design of numerous tests. Most of these tests are formulated in a frequentist framework, and it is not known how they compare with Bayes procedures. I propose here two new Bayes tests that either compare pairs of trees (Bayes hypothesis test, BHT), or test each tree against an average of the trees included in the analysis (Bayes significance test, BST). RESULTS: The algorithm, based on a standard Metropolis-Hastings sampler, integrates nuisance parameters out and estimates the probability of the data under each topology. These quantities are used to estimate Bayes factors for composite vs. composite hypotheses. Based on two data sets, the BHT and BST are shown to construct similar confidence sets to the bootstrap and the Shimodaira Hasegawa test, respectively. This suggests that the known difference among previous tests is mainly due to the null hypothesis considered.

Algorithms↗
PubMedDate not supplied

Bayesian extensions of the Tobit model for analyzing measures of health status.

Self-reported health status is often measured using utility indices that provide a score intended to summarize an individual's health. Measurements of health status can be subject to a ceiling effect. Frequently, researchers want to examine relationships between determinants of health and measures of health status. In this article, Bayesian extensions of the classical Tobit model are used to study the relationship between health status and predictors of health. The author examined models where the conditional distribution of health status was either normal or lognormal, and allowed for both homoscedasticity and heteroscedasticity. Bayes factors were then used to compare the evidence for a given model against that for a competing model. The author found very strong evidence that the distribution of the Health Utilities Index, conditional on age, gender, income adequacy, and number of chronic conditions, was normal with nonuniform variance, compared to the competing models.

Bayes Theorem↗
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↗