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PubMed2005

Direct reconstruction of kinetic parameter images from dynamic PET data.

Our goal in this paper is the estimation of kinetic model parameters for each voxel corresponding to a dense three-dimensional (3-D) positron emission tomography (PET) image. Typically, the activity images are first reconstructed from PET sinogram frames at each measurement time, and then the kinetic parameters are estimated by fitting a model to the reconstructed time-activity response of each voxel. However, this "indirect" approach to kinetic parameter estimation tends to reduce signal-to-noise ratio (SNR) because of the requirement that the sinogram data be divided into individual time frames. In 1985, Carson and Lange proposed, but did not implement, a method based on the expectation-maximization (EM) algorithm for direct parametric reconstruction. The approach is "direct" because it estimates the optimal kinetic parameters directly from the sinogram data, without an intermediate reconstruction step. However, direct voxel-wise parametric reconstruction remained a challenge due to the unsolved complexities of inversion and spatial regularization. In this paper, we demonstrate and evaluate a new and efficient method for direct voxel-wise reconstruction of kinetic parameter images using all frames of the PET data. The direct parametric image reconstruction is formulated in a Bayesian framework, and uses the parametric iterative coordinate descent (PICD) algorithm to solve the resulting optimization problem. The PICD algorithm is computationally efficient and is implemented with spatial regularization in the domain of the physiologically relevant parameters. Our experimental simulations of a rat head imaged in a working small animal scanner indicate that direct parametric reconstruction can substantially reduce root-mean-squared error (RMSE) in the estimation of kinetic parameters, as compared to indirect methods, without appreciably increasing computation.

Algorithms↗
PubMed2004

Bayesian mixture model based clustering of replicated microarray data.

MOTIVATION: Identifying patterns of co-expression in microarray data by cluster analysis has been a productive approach to uncovering molecular mechanisms underlying biological processes under investigation. Using experimental replicates can generally improve the precision of the cluster analysis by reducing the experimental variability of measurements. In such situations, Bayesian mixtures allow for an efficient use of information by precisely modeling between-replicates variability. RESULTS: We developed different variants of Bayesian mixture based clustering procedures for clustering gene expression data with experimental replicates. In this approach, the statistical distribution of microarray data is described by a Bayesian mixture model. Clusters of co-expressed genes are created from the posterior distribution of clusterings, which is estimated by a Gibbs sampler. We define infinite and finite Bayesian mixture models with different between-replicates variance structures and investigate their utility by analyzing synthetic and the real-world datasets. Results of our analyses demonstrate that (1) improvements in precision achieved by performing only two experimental replicates can be dramatic when the between-replicates variability is high, (2) precise modeling of intra-gene variability is important for accurate identification of co-expressed genes and (3) the infinite mixture model with the 'elliptical' between-replicates variance structure performed overall better than any other method tested. We also introduce a heuristic modification to the Gibbs sampler based on the 'reverse annealing' principle. This modification effectively overcomes the tendency of the Gibbs sampler to converge to different modes of the posterior distribution when started from different initial positions. Finally, we demonstrate that the Bayesian infinite mixture model with 'elliptical' variance structure is capable of identifying the underlying structure of the data without knowing the 'correct' number of clusters. AVAILABILITY: The MS Windows based program named Gaussian Infinite Mixture Modeling (GIMM) implementing the Gibbs sampler and corresponding C++ code are available at http://homepages.uc.edu/~medvedm/GIMM.htm SUPPLEMENTAL INFORMATION: http://expression.microslu.washington.edu/expression/kayee/medvedovic2003/medvedovic_bioinf2003.html

Algorithms↗
PubMed1999

Autoregressive models for describing non-linear changes in biological parameters fitted using BUGS.

Many biological processes give outcome data which show a curvilinear association with time which tends to an asymptote. We show how autoregressive models can be used to describe this association within individual subjects. We also present a Bayesian approach implemented using statistical software, BUGS, to fit these models in a multi-level (hierarchical) setting that describes variation in the association between subjects. Peak expiratory flow data from a clinical trial involving subjects with asthma are used to illustrate the methods.

Anti-Inflammatory Agents↗
PubMed2006

Bayesian semi-parametric ROC analysis.

This paper describes a semi-parametric Bayesian approach for estimating receiver operating characteristic (ROC) curves based on mixtures of Dirichlet process priors (MDP). We address difficulties in modelling the underlying distribution of screening scores due to non-normality that may lead to incorrect choices of diagnostic cut-offs and unreliable estimates of prevalence of the disease. MDP is a robust tool for modelling non-standard diagnostic distributions associated with imperfect classification of an underlying diseased population, for example, when a diagnostic test is not a gold standard. For posterior computations, we propose an efficient Gibbs sampling framework based on a finite-dimensional approximation to MDP. We show, using both simulated and real data sets, that MDP modelling for ROC curve estimation closely parallels the frequentist kernel density estimation (KDE) approach.

Adolescent↗
PubMed2005

Dual multiple change-point model leads to more accurate recombination detection.

MOTIVATION: We introduce a dual multiple change-point (MCP) model for recombination detection among aligned nucleotide sequences. The dual MCP model is an extension of the model introduced previously by Suchard and co-workers. In the original single MCP model, one change-point process is used to model spatial phylogenetic variation. Here, we show that using two change-point processes, one for spatial variation of tree topologies and the other for spatial variation of substitution process parameters, increases recombination detection accuracy. Statistical analysis is done in a Bayesian framework using reversible jump Markov chain Monte Carlo sampling to approximate the joint posterior distribution of all model parameters. RESULTS: We use primate mitochondrial DNA data with simulated recombination break-points at specific locations to compare the two models. We also analyze two real HIV sequences to identify recombination break-points using the dual MCP model.

Algorithms↗
PubMed1999

Software for population pharmacokinetics and pharmacodynamics.

Pharmacokinetic-pharmacodynamic modelling is being used increasingly as a tool in drug development because often in phase III clinical trials only sparse data are available for analysis and so a nonlinear mixed effects modelling approach has to be adopted. Specialist data analytical techniques and software are required to analyse such data. This article reviews some of the software currently available for performing nonlinear mixed effects modelling. A questionnaire was devised and sent to a number of software producers and the findings are presented and discussed in this paper. The programs could be grouped into 3 main categories: parametric and nonparametric maximum likelihood and Bayesian. It was apparent from the questionnaire that software development for population data analysis is a very active area of investigation. The implementation of methodologies varied widely between the packages: some were self-contained programs, whereas others were written within another application, usually a statistical package. They also varied with respect to their ease of use and level of support offered by the software producers. Although robustness and reliability are important concerns, they were not addressed in the present review. Most of the programs surveyed are in continual development.

Animals↗
PubMed2006

Bayesian analysis of quasi-life tables.

Quasi-life tables, in which the data arise from many concurrent, independent, discrete-time renewal processes, were defined by Baxter (1994, Biometrika 81:567-577), who outlined some methods for estimation. The processes are not observed individually; only the total numbers of renewals at each time point are observed. Crowder and Stephens (2003, Lifetime Data Anal 9:345-355) implemented a formal estimating-equation approach that invokes large-sample theory. However, these asymptotic methods fail to yield sensible estimates for smaller samples. In this paper, we implement a Bayesian analysis based on MCMC computation that works equally well for large and small sample sizes. We give three simulated examples, studying the Bayesian results, the impact of changing prior specification, and empirical properties of the Bayesian estimators of the lifetime distribution parameters. We also study the Baxter (1994, Biometrika 81:567-577) data, and uncover structure that has not been commented upon previously.

Bayes Theorem↗
PubMed2003

Random effects selection in linear mixed models.

We address the important practical problem of how to select the random effects component in a linear mixed model. A hierarchical Bayesian model is used to identify any random effect with zero variance. The proposed approach reparameterizes the mixed model so that functions of the covariance parameters of the random effects distribution are incorporated as regression coefficients on standard normal latent variables. We allow random effects to effectively drop out of the model by choosing mixture priors with point mass at zero for the random effects variances. Due to the reparameterization, the model enjoys a conditionally linear structure that facilitates the use of normal conjugate priors. We demonstrate that posterior computation can proceed via a simple and efficient Markov chain Monte Carlo algorithm. The methods are illustrated using simulated data and real data from a study relating prenatal exposure to polychlorinated biphenyls and psychomotor development of children.

Algorithms↗
PubMed1999

Robust QSAR models using Bayesian regularized neural networks.

We describe the use of Bayesian regularized artificial neural networks (BRANNs) in the development of QSAR models. These networks have the potential to solve a number of problems which arise in QSAR modeling such as: choice of model; robustness of model; choice of validation set; size of validation effort; and optimization of network architecture. The application of the methods to QSAR of compounds active at the benzodiazepine and muscarinic receptors is illustrated.

Drug Design↗
PubMed2002

A Bayesian method for classification of images from electron micrographs.

Particle classification is an important component of multivariate statistical analysis methods that has been used extensively to extract information from electron micrographs of single particles. Here we describe a new Bayesian Gibbs sampling algorithm for the classification of such images. This algorithm, which is applied after dimension reduction by correspondence analysis or by principal components analysis, dynamically learns the parameters of the multivariate Gaussian distributions that characterize each class. These distributions describe tilted ellipsoidal clusters that adaptively adjust shape to capture differences in the variances of factors and the correlations of factors within classes. A novel Bayesian procedure to objectively select factors for inclusion in the classification models is a component of this procedure. A comparison of this algorithm with hierarchical ascendant classification of simulated data sets shows improved classification over a broad range of signal-to-noise ratios.

Algorithms↗
PubMed2007

Population pharmacokinetic model for gatifloxacin in pediatric patients.

The broad spectrum of antimicrobial activity, oral bioavailability, extensive tissue distribution, and once-daily intravenous or oral dosing of gatifloxacin, an expanded-spectrum 8-methoxy fluoroquinolone, make it a potentially useful agent for the treatment of pediatric infections. A population pharmacokinetic model was developed to describe the pharmacokinetics of gatifloxacin in children. Data for analysis were obtained from a single-dose safety/pharmacokinetic study utilizing intensive blood sampling in patients aged 6 months to 16 years. Each subject received a single oral dose of gatifloxacin as a suspension, at doses of 5, 10, or 15 mg/kg of body weight. A total of 845 samples were obtained from 82 patients. A one-compartment model with first-order absorption and elimination was the most appropriate to describe the gatifloxacin concentrations. Covariate analysis using forward selection and backward elimination found that apparent clearance was related to body surface area, and apparent volume of distribution was related to body weight. No effect of age on drug clearance could be identified once clearance was corrected for body surface area. Based on pharmacokinetic simulations, the 10-mg/kg (maximum, 400 mg) once-daily dose of gatifloxacin is expected to provide drug exposure similar to that in healthy adults. The population pharmacokinetic model described herein will be used for Bayesian analyses of sparse pharmacokinetic sampling in phase II/III clinical trials and for Monte Carlo simulation experiments. The success of this strategy provides a model for future pediatric drug development programs.

Administration, Oral↗
PubMed1999

Evaluating variable selection methods for diagnosis of myocardial infarction.

This paper evaluates the variable selection performed by several machine-learning techniques on a myocardial infarction data set. The focus of this work is to determine which of 43 input variables are considered relevant for prediction of myocardial infarction. The algorithms investigated were logistic regression (with stepwise, forward, and backward selection), backpropagation for multilayer perceptrons (input relevance determination), Bayesian neural networks (automatic relevance determination), and rough sets. An independent method (self-organizing maps) was then used to evaluate and visualize the different subsets of predictor variables. Results show good agreement on some predictors, but also variability among different methods; only one variable was selected by all models.

Algorithms↗
PubMed2003

Statistical inversion for medical x-ray tomography with few radiographs: II. Application to dental radiology.

Diagnostic and operational tasks in dental radiology often require three-dimensional information that is difficult or impossible to see in a projection image. A CT-scan provides the dentist with comprehensive three-dimensional data. However, often CT-scan is impractical and, instead, only a few projection radiographs with sparsely distributed projection directions are available. Statistical (Bayesian) inversion is well-suited approach for reconstruction from such incomplete data. In statistical inversion, a priori information is used to compensate for the incomplete information of the data. The inverse problem is recast in the form of statistical inference from the posterior probability distribution that is based on statistical models of the projection data and the a priori information of the tissue. In this paper, a statistical model for three-dimensional imaging of dentomaxillofacial structures is proposed. Optimization and MCMC algorithms are implemented for the computation of posterior statistics. Results are given with in vitro projection data that were taken with a commercial intraoral x-ray sensor. Examples include limited-angle tomography and full-angle tomography with sparse projection data. Reconstructions with traditional tomographic reconstruction methods are given as reference for the assessment of the estimates that are based on the statistical model.

Algorithms↗
PubMed2004

Neural network uncertainty assessment using Bayesian statistics: a remote sensing application.

Neural network (NN) techniques have proved successful for many regression problems, in particular for remote sensing; however, uncertainty estimates are rarely provided. In this article, a Bayesian technique to evaluate uncertainties of the NN parameters (i.e., synaptic weights) is first presented. In contrast to more traditional approaches based on point estimation of the NN weights, we assess uncertainties on such estimates to monitor the robustness of the NN model. These theoretical developments are illustrated by applying them to the problem of retrieving surface skin temperature, microwave surface emissivities, and integrated water vapor content from a combined analysis of satellite microwave and infrared observations over land. The weight uncertainty estimates are then used to compute analytically the uncertainties in the network outputs (i.e., error bars and correlation structure of these errors). Such quantities are very important for evaluating any application of an NN model. The uncertainties on the NN Jacobians are then considered in the third part of this article. Used for regression fitting, NN models can be used effectively to represent highly nonlinear, multivariate functions. In this situation, most emphasis is put on estimating the output errors, but almost no attention has been given to errors associated with the internal structure of the regression model. The complex structure of dependency inside the NN is the essence of the model, and assessing its quality, coherency, and physical character makes all the difference between a blackbox model with small output errors and a reliable, robust, and physically coherent model. Such dependency structures are described to the first order by the NN Jacobians: they indicate the sensitivity of one output with respect to the inputs of the model for given input data. We use a Monte Carlo integration procedure to estimate the robustness of the NN Jacobians. A regularization strategy based on principal component analysis is proposed to suppress the multicollinearities in order to make these Jacobians robust and physically meaningful.

Algorithms↗
PubMed2004

MITOM: a new unfolding code based on a spectra model method applied to neutron spectrometry.

The MITOM code was developed at UAB (Universitat Autònoma de Barcelona) for unfolding neutron spectrometric measurements with a Bonner spheres system (BSS). One of the main characteristics of this code is that an initial parameterisation of the neutron energy components (thermal, intermediate and fast) is needed. This code uses the Monte Carlo method and the Bayesian theorem to obtain a set of solutions achieving different criteria and conditions between calculated and measured count rates. The final solution is an average of the acceptable solutions. The MITOM code was tested for ISO sources and a good agreement was observed between the reference values and the unfolded ones for global magnitudes. The code was applied recently to characterise both thermal SIGMA and CANEL/T400 sources of the IRSN facilities. The results of these applications were very satisfactory as well.

Algorithms↗
PubMed2005

Uncertainty in white matter fiber tractography.

In this work we address the uncertainty associated with fiber paths obtained in white matter fiber tractography. This uncertainty, which arises for example from noise and partial volume effects, is quantified using a Bayesian modeling framework. The theory for estimating the probability of a connection between two areas in the brain is presented, and a new model of the local water diffusion profile is introduced. We also provide a theorem that facilitates the estimation of the parameters in this diffusion model, making the presented method simple to implement.

Algorithms↗
PubMed1997

Generative models for discovering sparse distributed representations.

We describe a hierarchical, generative model that can be viewed as a nonlinear generalization of factor analysis and can be implemented in a neural network. The model uses bottom-up, top-down and lateral connections to perform Bayesian perceptual inference correctly. Once perceptual inference has been performed the connection strengths can be updated using a very simple learning rule that only requires locally available information. We demonstrate that the network learns to extract sparse, distributed, hierarchical representations.

Algorithms↗
PubMed2006

[An approach to adaptive stereo brain image's segmentation].

This paper presents a new method for automatically segmenting brain parenchyma and cerebrospinal fluid in routine single-echo MR images. This method is based on the coupled Markov models. They can model intensity measurement at each voxel site to implement piecewise smoothness constraint, and at the same time, model discontinuities to control the interaction between each pair of the neighboring voxel. The method is to derive the maximum a posteriori estimate of the regions and the boundaries by using Bayesian inference and neighborhood constraints based on Markov random fields (MRFs) models. This method has the following desirable properties: (1) the brain image can be well classified into white matter, grey matter and cerebrospinal fluid (CSF), and (2) it has a better robustness to noise and intensity inhomogeneity.

Algorithms↗