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Results for “Bayesian analysis”

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PubMed1999

Significance testing of clinical data using virus dynamics models with a Markov chain Monte Carlo method: application to emergence of lamivudine-resistant hepatitis B virus.

Bayesian analysis using a virus dynamics model is demonstrated to facilitate hypothesis testing of patterns in clinical time-series. Our Markov chain Monte Carlo implementation demonstrates that the viraemia time-series observed in two sets of hepatitis B patients on antiviral (lamivudine) therapy, chronic carriers and liver transplant patients, are significantly different, overcoming clinical trial design differences that question the validity of non-parametric tests. We show that lamivudine-resistant mutants grow faster in transplant patients than in chronic carriers, which probably explains the differences in emergence times and failure rates between these two sets of patients. Incorporation of dynamic models into Bayesian parameter analysis is of general applicability in medical statistics.

Antiviral Agents↗

PubMed2006

A Bayesian meta-analysis of prophylactic granulocyte colony-stimulating factor and granulocyte-macrophage colony-stimulating factor in children with cancer.

The purpose of this analysis was to examine the efficacy of prophylactic hematopoietic colony-stimulating factors (CSFs) in pediatric cancer and to describe how a Bayesian meta-analysis can be conducted and then modified to incorporate information not readily included in a frequentist meta-analysis. Three Bayesian models were developed. The simplest model used the same data as a published frequentist meta-analysis. The second model included data that could not easily be incorporated into the frequentist meta-analysis, including data from different courses of chemotherapy and continuous outcomes that did not report variance estimates. The third model examined the effect of CSF type (granulocyte CSF vs. granulocyte-macrophage CSF). Compared with the frequentist model, the Bayesian model with the most data suggested a greater benefit of CSFs, with a 3.2-day reduction in duration of parenteral antibiotics (95% credible interval: -7.1, 0.7) in the expanded Bayesian model compared with a 0.8-day (95% confidence interval: -2.3, 0.7) reduction in the frequentist model. Bayesian meta-analysis also suggested that, compared with granulocyte-macrophage CSF, granulocyte CSF was associated with a 4.8-day decrease in the duration of parenteral antibiotics. Bayesian meta-analysis can readily include information not easily incorporated in a frequentist meta-analysis. Some treatment effect estimates were larger by a clinically important amount when additional data contributed to the pooled estimate.

Bayes Theorem↗

PubMed2005

Spatiotemporal Bayesian inference dipole analysis for MEG neuroimaging data.

Recently, we described a Bayesian inference approach to the MEG/EEG inverse problem that used numerical techniques to estimate the full posterior probability distributions of likely solutions upon which all inferences were based [Schmidt, D.M., George, J.S., Wood, C.C., 1999. Bayesian inference applied to the electromagnetic inverse problem. Human Brain Mapping 7, 195; Schmidt, D.M., George, J.S., Ranken, D.M., Wood, C.C., 2001. Spatial-temporal bayesian inference for MEG/EEG. In: Nenonen, J., Ilmoniemi, R. J., Katila, T. (Eds.), Biomag 2000: 12th International Conference on Biomagnetism. Espoo, Norway, p. 671]. Schmidt et al. (1999) focused on the analysis of data at a single point in time employing an extended region source model. They subsequently extended their work to a spatiotemporal Bayesian inference analysis of the full spatiotemporal MEG/EEG data set. Here, we formulate spatiotemporal Bayesian inference analysis using a multi-dipole model of neural activity. This approach is faster than the extended region model, does not require use of the subject's anatomical information, does not require prior determination of the number of dipoles, and yields quantitative probabilistic inferences. In addition, we have incorporated the ability to handle much more complex and realistic estimates of the background noise, which may be represented as a sum of Kronecker products of temporal and spatial noise covariance components. This reduces the effects of undermodeling noise. In order to reduce the rigidity of the multi-dipole formulation which commonly causes problems due to multiple local minima, we treat the given covariance of the background as uncertain and marginalize over it in the analysis. Markov Chain Monte Carlo (MCMC) was used to sample the many possible likely solutions. The spatiotemporal Bayesian dipole analysis is demonstrated using simulated and empirical whole-head MEG data.

Algorithms↗

PubMed2002

Combined nuclear and mitochondrial DNA sequences resolve generic relationships within the Cracidae (Galliformes, Aves).

The Cracidae is one of the most endangered and distinctive bird families in the Neotropics, yet the higher relationships among taxa remain uncertain. The molecular phylogeny of its 11 genera was inferred using 10,678 analyzable sites (5,412 from seven different mitochondrial segments and 5,266 sites from four nuclear genes). We performed combinability tests to check conflicts in phylogenetic signals of separate genes and genomes. Phylogenetic analysis showed that the unrooted tree of ((curassows, horned guan) (guans, chachalacas)) was favored by most data partitions and that different data partitions provided support for different parts of the tree. In particular, the concatenated mitochondrial DNA (mtDNA) genes resolved shallower nodes, whereas the combined nuclear sequences resolved the basal connections among the major clades of curassows, horned guan, chachalacas, and guans. Therefore, we decided that for the Cracidae all data should be combined for phylogenetic analysis. Maximum parsimony (MP), maximum likelihood (ML), and Bayesian analyses of this large data set produced similar trees. The MP tree indicated that guans are the sister group to (horned guan, (curassows, chachalacas)), whereas the ML and Bayesian analysis recovered a tree where the horned guan is a sister clade to curassows, and these two clades had the chachalacas as a sister group. Parametric bootstrapping showed that alternative trees previously proposed for the cracid genera are significantly less likely than our estimate of their relationships. A likelihood ratio test of the hypothesis of a molecular clock for cracid mtDNA sequences using the optimal ML topology did not reject rate constancy of substitutions through time. We estimated cracids to have originated between 64 and 90 million years ago (MYA), with a mean estimate of 76 MYA. Diversification of the genera occurred approximately 41-3 MYA, corresponding with periods of global climate change and other Earth history events that likely promoted divergences of higher level taxa.

Animals↗

PubMedDate not supplied

Longitudinal random effects models for genetic analysis of binary data with application to mastitis in dairy cattle.

A Bayesian analysis of longitudinal mastitis records obtained in the course of lactation was undertaken. Data were 3341 test-day binary records from 329 first lactation Holstein cows scored for mastitis at 14 and 30 days of lactation and every 30 days thereafter. First, the conditional probability of a sequence for a given cow was the product of the probabilities at each test-day. The probability of infection at time t for a cow was a normal integral, with its argument being a function of "fixed" and "random" effects and of time. Models for the latent normal variable included effects of: (1) year-month of test + a five-parameter linear regression function ("fixed", within age-season of calving) + genetic value of the cow + environmental effect peculiar to all records of the same cow + residual. (2) As in (1), but with five parameter random genetic regressions for each cow. (3) A hierarchical structure, where each of three parameters of the regression function for each cow followed a mixed effects linear model. Model 1 posterior mean of heritability was 0.05. Model 2 heritabilities were: 0.27, 0.05, 0.03 and 0.07 at days 14, 60, 120 and 305, respectively. Model 3 heritabilities were 0.57, 0.16, 0.06 and 0.18 at days 14, 60, 120 and 305, respectively. Bayes factors were: 0.011 (Model 1/Model 2), 0.017 (Model 1/Model 3) and 1.535 (Model 2/Model 3). The probability of mastitis for an "average" cow, using Model 2, was: 0.06, 0.05, 0.06 and 0.07 at days 14, 60, 120 and 305, respectively. Relaxing the conditional independence assumption via an autoregressive process (Model 2) improved the results slightly.

Animals↗

PubMed1991

[Bayesian and RFLP linkage analysis on a DMD family].

Three methods were applied to estimate the carrier risk of the daughter of an obligate carrier of the Duchenne gene in a pedigree of Duchenne muscular dystrophy (DMD). According to Mendel's law of segregation, the daughter (III-3) of the obligate carrier (II-2) has a 50% chance of being a carrier. III-3 is also found to have a normal value in a carrier test, creatine phosphate kinase (CPK), and so the Bayesian analysis in risk estimation shows that the posterior probability that she is a carrier (25%). The restriction fragment length polymorphism (RFLP) linkage analysis indicates that the probability that III-3 is a carrier less than 5%. This result can be included in the Bayesian analysis to give an even lower risk of less than 2%. Our study demonstrates that the best result of carrier risk estimation can be obtained by a simultaneous application of Mendel's law, RFLP linkage analysis and the Bayesian analysis.

Bayes Theorem↗

PubMed2004

A Bayesian approach for the analysis of panel-count data with dependent termination.

We consider modeling and Bayesian analysis for panel-count data when the termination time for each subject may depend on its history of the recurrent events. We propose a fully specified semiparametric model for the joint distribution of the recurrent events and the termination time. For this model, we provide a natural motivation, derive several novel properties, and develop a Bayesian analysis based on a Markov chain Monte Carlo algorithm. Comparisons are made to other existing models and methods for panel-count data. We demonstrate the usefulness of our new models and methodologies through the reanalysis of a data set from a clinical trial.

Algorithms↗

PubMed1996

Uremic autonomic neuropathy: recovery following bicarbonate hemodialysis.

Autonomic function was followed in 8 chronic uremic patients on periodic hemodialysis over a period of almost eight years. The cardiovascular autonomic testing included R-R interval variation test, deep breathing, Valsalva manoeuvre, heart rate and blood pressure responses to standing, sustained handgrip. The patients were investigated on entry into the study and after 18, 56, and 92 months. Six months after the study at time 56 months, they switched from acetate to bicarbonate dialysis. The response to deep breathing test was significantly reduced at time 18 months versus baseline (P = 0.014), but significantly increased at time 92 months versus 56 months (P = 0.042). A significant decrease was found in the systolic blood pressure response to standing between baseline and 18 months (P = 0.014) and in the response to handgrip test between 18 and 56 months (P = 0.014). Multivariate analysis of the autonomic tests by a pattern recognition method (Bayesian analysis) showed that, at the time of entry into the study, two out of eight patients had autonomic damage. At 18 and 56 months, 6/8 patients had autonomic dysfunction. At the last time of investigation, 30 months after the onset of bicarbonate dialysis, all the patients showed a reversal of autonomic damage. Age and duration of dialysis on entry did not affect autonomic function. The present study is the first demonstration that autonomic neuropathy can recover after long-term dialysis. Since chronic hypoxemia is a cause of polyneuropathy, we postulate that: 1) hypoxemia in dialysis patients may have a role in the pathogenesis of uremic polyneuropathy, and particularly of autonomic dysfunction; 2) in patients on bicarbonate dialysis, a greater hemodynamic stability with less hypoxemia may lead to a recovery of autonomic function.

Acetates↗

PubMed2003

Phylogeny estimation: traditional and Bayesian approaches.

The construction of evolutionary trees is now a standard part of exploratory sequence analysis. Bayesian methods for estimating trees have recently been proposed as a faster method of incorporating the power of complex statistical models into the process. Researchers who rely on comparative analyses need to understand the theoretical and practical motivations that underlie these new techniques, and how they differ from previous methods. The ability of the new approaches to address previously intractable questions is making phylogenetic analysis an essential tool in an increasing number of areas of genetic research.

Bayes Theorem↗

PubMed2002

Molecular and morphological phylogenetics of weevils (coleoptera, curculionoidea): do niche shifts accompany diversification?

The main goals of this study were to provide a robust phylogeny for the families of the superfamily Curculionoidea, to discover relationships and major natural groups within the family Curculionidae, and to clarify the evolution of larval habits and host-plant associations in weevils to analyze their role in weevil diversification. Phylogenetic relationships among the weevils (Curculionoidea) were inferred from analysis of nucleotide sequences of 18S ribosomal DNA (rDNA; approximately 2,000 bases) and 115 morphological characters of larval and adult stages. A worldwide sample of 100 species was compiled to maximize representation of weevil morphological and ecological diversity. All families and the main subfamilies of Curculionoidea were represented. The family Curculionidae sensu lato was represented by about 80 species in 30 "subfamilies" of traditional classifications. Phylogenetic reconstruction was accomplished by parsimony analysis of separate and combined molecular and morphological data matrices and Bayesian analysis of the molecular data; tree topology support was evaluated. Results of the combined analysis of 18S rDNA and morphological data indicate that monophyly of and relationships among each of the weevil families are well supported with the topology ((Nemonychidae, Anthribidae) (Belidae (Attelabidae (Caridae (Brentidae, Curculionidae))))). Within the clade Curculionidae sensu lato, the basal positions are occupied by mostly monocot-associated taxa with the primitive type of male genitalia followed by the Curculionidae sensu stricto, which is made up of groups with the derived type of male genitalia. High support values were found for the monophyly of some distinct curculionid groups such as Dryophthorinae (several tribes represented) and Platypodinae (Tesserocerini plus Platypodini), among others. However, the subfamilial relationships in Curculionidae are unresolved or weakly supported. The phylogeny estimate based on combined 18S rDNA and morphological data suggests that diversification in weevils was accompanied by niche shifts in host-plant associations and larval habits. Pronounced conservatism is evident in larval feeding habits, particularly in the host tissue consumed. Multiple shifts to use of angiosperms in Curculionoidea were identified, each time associated with increases in weevil diversity and subsequent shifts back to gymnosperms, particularly in the Curculionidae.

Animals↗

PubMed2001

Bayesian methods for quantitative trait loci mapping based on model selection: approximate analysis using the Bayesian information criterion.

We describe an approximate method for the analysis of quantitative trait loci (QTL) based on model selection from multiple regression models with trait values regressed on marker genotypes, using a modification of the easily calculated Bayesian information criterion to estimate the posterior probability of models with various subsets of markers as variables. The BIC-delta criterion, with the parameter delta increasing the penalty for additional variables in a model, is further modified to incorporate prior information, and missing values are handled by multiple imputation. Marginal probabilities for model sizes are calculated, and the posterior probability of nonzero model size is interpreted as the posterior probability of existence of a QTL linked to one or more markers. The method is demonstrated on analysis of associations between wood density and markers on two linkage groups in Pinus radiata. Selection bias, which is the bias that results from using the same data to both select the variables in a model and estimate the coefficients, is shown to be a problem for commonly used non-Bayesian methods for QTL mapping, which do not average over alternative possible models that are consistent with the data.

Alleles↗

PubMed2006

Bayesian multivariate hierarchical transformation models for ROC analysis.

A Bayesian multivariate hierarchical transformation model (BMHTM) is developed for receiver operating characteristic (ROC) curve analysis based on clustered continuous diagnostic outcome data with covariates. Two special features of this model are that it incorporates non-linear monotone transformations of the outcomes and that multiple correlated outcomes may be analysed. The mean, variance, and transformation components are all modelled parametrically, enabling a wide range of inferences. The general framework is illustrated by focusing on two problems: (1) analysis of the diagnostic accuracy of a covariate-dependent univariate test outcome requiring a Box-Cox transformation within each cluster to map the test outcomes to a common family of distributions; (2) development of an optimal composite diagnostic test using multivariate clustered outcome data. In the second problem, the composite test is estimated using discriminant function analysis and compared to the test derived from logistic regression analysis where the gold standard is a binary outcome. The proposed methodology is illustrated on prostate cancer biopsy data from a multi-centre clinical trial.

Bayes Theorem↗

PubMed1986

Evaluation of a Bayesian regression-analysis computer program for predicting phenytoin concentration.

A microcomputer program using Bayesian regression analysis to predict serum phenytoin concentrations was evaluated. Phenytoin concentration-time data from nine healthy male volunteers and one male patient were obtained from published studies. For two different dosage regimens that each subject received, the last available predose concentration on the sixth day of the regimen was predicted using observed predose concentrations on both the morning of the third day and on each of the first three days of phenytoin administration. In nine subjects who received at least 10 days of phenytoin therapy, observed concentrations after more than 10 days of therapy were predicted using both one and three observed serum concentrations. Also, in six subjects, the observed predose concentrations for the first three days of an initial phenytoin regimen were used to predict the last predose concentration observed during each subject's second regimen. Predictive performance of the program was evaluated using mean error (m.e.) as a measure of bias, mean absolute error (m.a.e.) as a measure of precision, and root mean square error (r.m.s.e.) as a composite measure of bias and precision. The majority of the predicted serum concentrations were accurate. Predictions of serum concentrations after six days and after more than 10 days of phenytoin therapy were somewhat more accurate when three serum concentrations were used than when only one concentration was used. In the six subjects for whom concentrations from an initial regimen were used to predict those in a second regimen, the largest prediction error was 5 mg/L (m.e. 0.88, m.a.e. 1.9, and r.m.s.e. 2.4).(ABSTRACT TRUNCATED AT 250 WORDS)

Bayes Theorem↗

PubMed1991

Nuclear grading of breast carcinoma by image analysis. Classification by multivariate and neural network analysis.

The use of nuclear grade as a prognostic indicator for breast carcinoma has been limited by interobserver variability. Advances in image analysis and automated cell classification offer one approach to this problem. The authors used the CAS-100 (Cell Analysis System. Elmhurst, IL) system to measure and analyze nuclear morphometric and texture features of cytologic preparations from 35 breast carcinomas (well, moderate, and poorly differentiated) as well as benign lesions. Morphometric and Markovian texture feature data from breast cancer nuclei of various grades comprised a training set, which was then used to establish classification criteria by multivariate (Bayesian) analysis and to train a neural network system. Both systems were tested for the ability to classify the nuclear grade of individual nuclei. There was good agreement between computer classification and the grade assigned by human observer to individual nuclei using either Bayesian or neural network analysis. Thirty-one unknown cases, which were assigned an overall grade by an observer, were then analyzed by computer, and an overall grade assigned based on the grade of nucleus most frequently present. Using this method, both classification systems were able to assign a "correct" grade to low-grade lesions (approximately 70% correct) more often than to high-grade tumors (approximately 20%). Difficulty in computer assignment of high-grade tumors was explained by nuclear heterogeneity in these tumors (i.e., although the percentage of high-grade nuclei was increased compared with that of low-grade tumors, high-grade nuclei frequently did not predominate). The authors present this study to demonstrate the feasibility of using image analysis as an objective means of nuclear grading. Further studies will be needed to establish criteria for assigning overall nuclear grade based on computer analysis of imaging data.

Artificial Intelligence↗

PubMedDate not supplied

Continuous trees and NEVADA simulation: a quadrature approach to modeling continuous random variables in decision analysis.

This paper introduces an improved technique for modeling risk and decision problems that have continuous random variables and probabilistic dependence. Variables are modeled with mixtures of four-parameter random variables, called "continuous trees." Functions of random variables are calculated using gaussian quadrature in a manner called "Nevada simulation" (NumErical Integration of Variance And probabilistic Dependence Analyzer). This technique is compared with traditional decision-tree modeling in terms of analytic technique, solution-time complexity, and accuracy. Nevada simulation takes advantage of the probabilistic independence in a decision problem while allowing for probabilistic dependence to achieve polynomial computational-time complexity for many decision problems. It improves on the accuracy of traditional decision trees by employing larger approximations than traditional decision analysis. It improves on traditional decision analysis by modeling continuous variables with continuous, rather than discrete, distributions. A Bayesian analysis using a mixed discrete-continuous probability distribution for cigarette smoking rate is presented.

Algorithms↗

PubMed1981

The role of modeling methods in medical diagnosis.

Modeling methods in medical diagnosis are concerned with medical information processing as it pertains to utilizing biological modeling methods to facilitate patient care. Major considerations in this particular area are (1) the classification problem related to the establishment of disease entities-the taxonomy problem, and (2) the diagnosis of diseases. Available are properties, criteria, signs, symptoms, and manifestations of diseases that have been cumulated and categorized by clinicians and researchers. The problem is to optimally utilize the information content of a sign or set of signs in the practice of patient care as pertaining to the medical diagnosis problem. Some mathematical approaches implemented to facilitate such analyses include cluster analysis, discriminant analysis, Bayesian methods, computer approaches, game theory, information theory, stochastic representations, stepwise procedures, decision analysis, and pattern recognition techniques. Each of these has been studied in depth by numerous researchers advocating computer applications in medicine. Here we discuss the scope and limitations of utilizing modeling methods as a viable approach to interpreting vast amounts of biological data collected on a single patient during an encounter. We consider the following: (1) limitations associated with modeling methodologies; (2) levels of responsibilities, ranging over logging, summarizing, reporting, monitoring, and therapy selection; and (3) operational strategies and considerations as they affect hardware logistics, the actual algorithm utilized, and implementation of these sophisticated analysis systems.

Decision Theory↗

PubMed2004

Simultaneous analysis of five molecular markers provides a well-supported phylogenetic hypothesis for the living bony-tongue fishes (Osteoglossomorpha: Teleostei).

Fishes of the Superorder Osteoglossomorpha (the "bonytongues") constitute a morphologically heterogeneous group of basal teleosts, including highly derived subgroups such as African electric fishes, the African butterfly fish, and Old World knifefishes. Lack of consensus among hypotheses of osteoglossomorph relationships advanced during the past 30 years may be due in part to the difficulty of identifying shared derived characters among the morphologically differentiated extant families of this group. In this study, we present a novel phylogenetic hypothesis for this group, based on the analysis of more than 4000 characters from five molecular markers (the mitochondrial cytochrome b, 12S and 16S rRNA genes, and the nuclear genes RAG2 and MLL). Our taxonomic sampling includes one representative of each extant non-mormyrid osteoglossomorph genus, one representative for the monophyletic family Mormyridae, and four outgroup taxa within the basal Teleostei. Maximum parsimony analysis of combined and equally weighted characters from the five molecular markers and Bayesian analysis provide a single, well-supported, hypothesis of osteoglossomorph interrelationships and show the group to be monophyletic. The tree topology is the following: (Hiodon alosoides, (Pantodon buchholzi, (((Osteoglossum bicirrhosum, Scleropages sp.), (Arapaima gigas, Heterotis niloticus)), ((Gymnarchus niloticus, Ivindomyrus opdenboschi), ((Notopterus notopterus, Chitala ornata), (Xenomystus nigri, Papyrocranus afer)))))). We compare our results with previously published phylogenetic hypotheses based on morpho-anatomical data. Additionally, we explore the consequences of the long terminal branch length for the taxon Pantodon buchholzi in our phylogenetic reconstruction and we use the obtained phylogenetic tree to reconstruct the evolutionary history of electroreception in the Notopteroidei.

Animals↗

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↗