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PubMed1999

Population pharmacokinetics of gentamicin in preterm neonates: evaluation of a once-daily dosage regimen.

Population pharmacokinetic parameters of gentamicin in preterm neonates on a once-daily dosage regimen of 3.0 mg/kg given intravenously every 24 hours were established prospectively. In 34 preterm neonates with a mean gestational age of 32 +/- 4 (SD), 182 serum gentamicin levels (91 peak/trough pairs) were determined. Individual adjustments of dose or dosage interval were calculated by computer-aided Bayesian forecasting. The parameters Vd, ke, and CL for each patient were obtained by the nonparametric estimation of maximization method. The predictive power of the model was calculated and the pharmacokinetic estimates were statistically analyzed with SPSS/PC. Cluster analysis showed a division into 2 subpopulations (designated 1 and 2) on the basis of postnatal age. The mean +/- SD postnatal age of subpopulation 1 (n = 29) was 6 +/- 2 days (range 1-7) and of subpopulation 2 (n = 5) 15 +/- 4 days (range 12-24). The mean +/- SD gentamicin relative clearances of subpopulation 1 and subpopulation 2 were 0.0515 +/- 0.0128 and 0.1026 +/- 0.0102 L kg(-1) hr(-1), respectively (p < 0.05). The mean +/- SD values for Vd (Lkg(-1)) in both populations 1 and 2 were 0.6916 +/- 0.1670 and 0.7509 +/- 0.1961, respectively (not significantly different). For ke these data were 0.0744 +/- 0.0200 and 0.1366 +/- 0.0522 (p < 0.05). Statistics showed that the data for Vd and ke of subpopulation 1 were normally distributed (Vd and ke skewness 1.61 and 1.46; kurtosis 3.09 and 3.10 respectively). The model yielded a bias of -0.11 mg/L and a precision of 0.36 mg/L. It is recommended that gentamicin be started in a dosage of 3.5 mg/kg intravenously once-daily under close monitoring.

Age Factors↗
PubMed1992

Bayesian methods and optimal experimental design for gene mapping by radiation hybrids.

Radiation hybrid mapping is a somatic cell technique for ordering human loci along a chromosome and estimating the physical distance between adjacent loci. The present paper considers a realistic model of fragment generation and retention. This model assumes that fragments are generated in the ancestral cell of a clone according to a Poisson breakage process along the chromosome. Once generated, fragments are independently retained in the clone with a common retention probability. Based on this and less restrictive models, statistical criteria such as minimum obligate breaks, maximum likelihood, and Bayesian posterior probabilities can be used to decide order. Distances can be estimated by either maximum likelihood or Bayesian posterior means. The model also permits rational design of radiation dose for optimal statistical precision. A brief examination of some real data illustrates our criteria and computational algorithms.

Algorithms↗
PubMedDate not supplied

Bayes factors for detection of quantitative trait loci.

A fundamental issue in quantitative trait locus (QTL) mapping is to determine the plausibility of the presence of a QTL at a given genome location. Bayesian analysis offers an attractive way of testing alternative models (here, QTL vs. no-QTL) via the Bayes factor. There have been several numerical approaches to computing the Bayes factor, mostly based on Markov Chain Monte Carlo (MCMC), but these strategies are subject to numerical or stability problems. We propose a simple and stable approach to calculating the Bayes factor between nested models. The procedure is based on a reparameterization of a variance component model in terms of intra-class correlation. The Bayes factor can then be easily calculated from the output of a MCMC scheme by averaging conditional densities at the null intra-class correlation. We studied the performance of the method using simulation. We applied this approach to QTL analysis in an outbred population. We also compared it with the Likelihood Ratio Test and we analyzed its stability. Simulation results were very similar to the simulated parameters. The posterior probability of the QTL model increases as the QTL effect does. The location of the QTL was also correctly obtained. The use of meta-analysis is suggested from the properties of the Bayes factor.

Algorithms↗
PubMed2006

Evolution of intrahost HIV-1 genetic diversity during chronic infection.

HIV-1 is one of the fastest evolving entities known. Given that census population sizes of HIV-1 within individuals are much greater than the inverse mutation rate, every possible single point mutation in the viral genome occurs each generation. This enormous capability to generate genetic variation allows for escape from immune surveillance and antiviral therapy. However, compared to this potential, populations of HIV-1 within individuals exhibit little genetic variation. This discrepancy between the known mutation rate of HIV-1 and the average level of genetic variation in the env gene observed in vivo is reflected in comparisons of the actual numbers of productively infected cells, estimated as 10(7), and the effective population size, estimated as 10(3). Using approximate Bayesian computation, we evaluated several hypotheses based on a variety of selective and demographic processes to explain the low effective population size of HIV-1. Of the models we examined, the metapopulation model, in which HIV-1 evolves within an individual as a large collection of small subpopulations subject to frequent migration, extinction, and recolonization, was most consistent with the observed levels of genetic variation and the average frequencies of those variants. The metapopulation model links previous studies of viral dynamics and population genetics.

Bayes Theorem↗
PubMed2002

Bayesian analysis of population PK/PD models: general concepts and software.

Markov chain Monte Carlo (MCMC) techniques have revolutionized the field of Bayesian statistics by enabling posterior inference for arbitrarily complex models. The now widely used WinBUGS software has, over the years, made the methodology accessible to a great many applied scientists, in all fields of research. Despite this, serious application of MCMC methods within the field of population PK/PD has been comparatively limited. We appreciate that for many applied pharmacokineticists the prospect of conducting a Bayesian analysis will require numerous alien concepts to be taken on board and it may be difficult to justify investing the time and effort required in order to understand them (especially since the approach is so computer-intensive). For this reason we provide here a thorough (but often informal) discussion of all aspects of Bayesian inference as they apply specifically to population PK/PD. We also acknowledge that while the WinBUGS software is general purpose, model specification for some types of problem, population PK/PD being a prime example, can be very difficult, to the extent that a specialized interface for describing the problem at hand is often a practical necessity. In the latter part of this paper we describe such an interface, namely PKBugs. A principal aim of the paper is to offer sufficient technical background, in an easy to follow format, that the reader may develop both the confidence and know-how to make appropriate use of the PKBugs/WinBUGS framework (or similar software) for their own data analysis needs, should they choose to adopt a Bayesian approach.

Bayes Theorem↗
PubMed2002

Hierarchical statistical modelling of influenza epidemic dynamics in space and time.

An infectious disease typically spreads via contact between infected and susceptible individuals. Since the small-scale movements and contacts between people are generally not recorded, available data regarding infectious disease are often aggregations in space and time, yielding small-area counts of the number infected during successive, regular time intervals. In this paper, we develop a spatially descriptive, temporally dynamic hierarchical model to be fitted to such data. Disease counts are viewed as a realization from an underlying multivariate autoregressive process, where the relative risk of infection incorporates the space-time dynamic. We take a Bayesian approach, using Markov chain Monte Carlo to compute posterior estimates of all parameters of interest. We apply the methodology to an influenza epidemic in Scotland during the years 1989-1990.

Bayes Theorem↗
PubMed1996

Bayesian reconstruction of PET images: methodology and performance analysis.

We describe a practical statistical methodology for the reconstruction of PET images. Our approach is based on a Bayesian formulation of the imaging problem. The data are modelled as independent Poisson random variables and the image is modelled using a Markov random field smoothing prior. We describe a sequence of calibration procedures which are performed before reconstruction: (i) calculation of accurate attenuation correction factors from re-projected Bayesian reconstructions of the transmission image; (ii) estimation of the mean of the randoms component in the data; and (iii) computation of the scatter component in the data using a Klein-Nishina-based scatter estimation method. The Bayesian estimate of the PET image is then reconstructed using a pre-conditioned conjugate gradient method. We performed a quantitation study with a multi-compartment chest phantom in a Siemens/CTI ECAT931 system. Using 40 1 min frames, we computed the ensemble mean and variance over several regions of interest from images reconstructed using the Bayesian and a standard filtered backprojection (FBP) protocol. The values for the region of interest were compared with well counter data for each compartment. These results show that the Bayesian protocol can produce substantial improvements in relative quantitation over the standard FBP protocol, particularly when short transmission scans are used. An example showing the application of the method to a clinical chest study is also given.

Algorithms↗
PubMed2006

Bayesian restoration using a new nonstationary edge-preserving image prior.

In this paper, we propose a class of image restoration algorithms based on the Bayesian approach and a new hierarchical spatially adaptive image prior. The proposed prior has the following two desirable features. First, it models the local image discontinuities in different directions with a model which is continuous valued. Thus, it preserves edges and generalizes the on/off (binary) line process idea used in previous image priors within the context of Markov random fields (MRFs). Second, it is Gaussian in nature and provides estimates that are easy to compute. Using this new hierarchical prior, two restoration algorithms are derived. The first is based on the maximum a posteriori principle and the second on the Bayesian methodology. Numerical experiments are presented that compare the proposed algorithms among themselves and with previous stationary and non stationary MRF-based with line process algorithms. These experiments demonstrate the advantages of the proposed prior.

Algorithms↗
PubMed2004

CisModule: de novo discovery of cis-regulatory modules by hierarchical mixture modeling.

The regulatory information for a eukaryotic gene is encoded in cis-regulatory modules. The binding sites for a set of interacting transcription factors have the tendency to colocalize to the same modules. Current de novo motif discovery methods do not take advantage of this knowledge. We propose a hierarchical mixture approach to model the cis-regulatory module structure. Based on the model, a new de novo motif-module discovery algorithm, CisModule, is developed for the Bayesian inference of module locations and within-module motif sites. Dynamic programming-like recursions are developed to reduce the computational complexity from exponential to linear in sequence length. By using both simulated and real data sets, we demonstrate that CisModule is not only accurate in predicting modules but also more sensitive in detecting motif patterns and binding sites than standard motif discovery methods are.

Algorithms↗
PubMed1995

Evaluation of partial classification algorithms using ROC curves.

When using computer programs for decision support in clinical routine, an assessment or a comparison of the underlying classification algorithms is essential. In classical (forced) classification, the classification rule always selects exactly one alternative. A number of proven discriminant measures are available here, e.g.sensitivity and error rate. For probabilistic classification, a series of additional measures has been developed [1]. However, for many clinical applications, there are models where an observation is classified into several classes (partial classification), e.g., models from artificial intelligence, decision analysis, or fuzzy set theory. In partial classification, the discriminatory ability (Murphy) can be adjusted a priori to any level, in most practical cases. Here the usual measures do not apply. We investigate the preconditions for assessment and comparison based on medical decision theory. We focus on problems in the medical domain and establish a methodological framework. When using partial classification procedures, a ROC analysis in the classical sense is no longer appropriate. In forced classification for two classes, the problem is to find a cutoff point on the ROC curve; while in partial classification, you have to find two of them. They characterize the elements being classified as coming from both classes. This extends to several classes. We propose measures corresponding to the usual discriminant measures for forced classification (e.g., sensitivity and error rate) and demonstrate the effects using the ROC approach. For this purpose, we extend the existing method for forced classification in a mathematically sound manner. Algorithms for the construction of thresholds can easily be adapted. Two specific measurement models, based on parametric and non-parametric approaches, will be introduced. The basic methodology is suitable for all partial classification problems, whereas the extended ROC analysis assumes a rank order of the selected alternatives. The method is based on the black box principle and makes use only of the results of the compared algorithms and some general intuitive principles. Therefore, algorithms arising from different "philosophical" approaches may also be compared according to their results. For demonstration purposes, a clinical example from cranial computed tomography is presented. Linear discriminant analysis as a reference is compared to a Bayesian and a fuzzy procedure.

Algorithms↗
PubMed2004

Cerebral modeling and dynamic Bayesian networks.

The understanding and the prediction of the clinical outcomes of focal or degenerative cerebral lesions, as well as the assessment of rehabilitation procedures, necessitate knowing the cerebral substratum of cognitive or sensorimotor functions. This is achieved by activation studies, where subjects are asked to perform a specific task while data of their brain functioning are obtained through functional neuroimaging techniques. Such studies, as well as animal experiments, have shown that sensorimotor or cognitive functions are the offspring of the activity of large-scale networks of anatomically connected cerebral regions. However, no one-to-one correspondence between activated networks adn functions can be found. Our research aims at understanding how the activation of large-scale networks derives from cerebral information processing mechanisms, which can only explain apparently conflicting activation data. Our work falls at the crossroads of neuroimaging interpretation techniques and computational neuroscience. Since knowledge in cognitive neuroscience is permanently evolving, our research aims more precisely at defining a new modeling formalism and at building a flexible simulator, allowing a quick implementation of the models, for a better interpretation of cerebral functional images. It also aims at providing plausible models, at eht level of large-scale networks, of cerebral information processing mechanisms in humans. In this paper, we propose a formalism, based on dynamic Bayesian networks (DBNs), that respects the following constraints: an oriented, networks architecture, whose nodes (the cerebral structures) can all be different, the implementation of causality--the activation of the structure is caused by upstream nodes' activation--the explicit representation of different time scales (from 1 ms for the cerebral activity to many seconds for a PET scan image acquisition), the representation of cerebral information at the integrated level of neuronal populations, the imprecision of functional neuroimaging data, the nonlinearity and the uncertainty in cerebral mechanisms, and brain's plasticity (learning, reorganization, modulation). One of the main problems, nonlinearity, has been tackled thanks to new extensions of the Kalman filter. The capabilities of the formalism's current version are illustrated by the modeling of a phoneme categorization process, explaining the different cerebral activations in normal and dyslexic subjects.

Bayes Theorem↗
PubMed2001

Statistical mechanics of learning with soft margin classifiers.

We study the typical learning properties of the recently introduced soft margin classifiers (SMCs), learning realizable and unrealizable tasks, with the tools of statistical mechanics. We derive analytically the behavior of the learning curves in the regime of very large training sets. We obtain exponential and power laws for the decay of the generalization error towards the asymptotic value, depending on the task and on general characteristics of the distribution of stabilities of the patterns to be learned. The optimal learning curves of the SMCs, which give the minimal generalization error, are obtained by tuning the coefficient controlling the trade-off between the error and the regularization terms in the cost function. If the task is realizable by the SMC, the optimal performance is better than that of a hard margin support vector machine and is very close to that of a Bayesian classifier.

Algorithms↗
PubMed2006

Statistical and Bayesian approaches to RNA secondary structure prediction.

Prediction of RNA secondary structure is a fundamental problem in computational structural biology. For several decades, free energy minimization has been the most popular method for prediction from a single sequence. In recent years, the McCaskill algorithm for computation of partition function and base-pair probabilities has become increasingly appreciated. This paradigm-shifting work has inspired the developments of extended partition function algorithms, statistical sampling and clustering, and application of Bayesian statistical inference. The performance of thermodynamics-based methods is limited by thermodynamic rules and parameters. However, further improvements may come from statistical estimates derived from structural databases for thermodynamics parameters with weak or little experimental data. The Bayesian inference approach appears to be promising in this context.

Algorithms↗
PubMed2000

Likelihood analysis of phylogenetic networks using directed graphical models.

A method for computing the likelihood of a set of sequences assuming a phylogenetic network as an evolutionary hypothesis is presented. The approach applies directed graphical models to sequence evolution on networks and is a natural generalization of earlier work by Felsenstein on evolutionary trees, including it as a special case. The likelihood computation involves several steps. First, the phylogenetic network is rooted to form a directed acyclic graph (DAG). Then, applying standard models for nucleotide/amino acid substitution, the DAG is converted into a Bayesian network from which the joint probability distribution involving all nodes of the network can be directly read. The joint probability is explicitly dependent on branch lengths and on recombination parameters (prior probability of a parent sequence). The likelihood of the data assuming no knowledge of hidden nodes is obtained by marginalization, i.e., by summing over all combinations of unknown states. As the number of terms increases exponentially with the number of hidden nodes, a Markov chain Monte Carlo procedure (Gibbs sampling) is used to accurately approximate the likelihood by summing over the most important states only. Investigating a human T-cell lymphotropic virus (HTLV) data set and optimizing both branch lengths and recombination parameters, we find that the likelihood of a corresponding phylogenetic network outperforms a set of competing evolutionary trees. In general, except for the case of a tree, the likelihood of a network will be dependent on the choice of the root, even if a reversible model of substitution is applied. Thus, the method also provides a way in which to root a phylogenetic network by choosing a node that produces a most likely network.

Computer Graphics↗
PubMed2005

Diffuse optical tomography with a priori anatomical information.

Diffuse optical tomography (DOT) poses a typical ill-posed inverse problem with a limited number of measurements and inherently low spatial resolution. In this paper, we propose a hierarchical Bayesian approach to improve spatial resolution and quantitative accuracy by using a priori information provided by a secondary high resolution anatomical imaging modality, such as magnetic resonance (MR) or x-ray. In such a dual imaging approach, while the correlation between optical and anatomical images may be high, it is not perfect. For example, a tumour may be present in the optical image, but may not be discernable in the anatomical image. The proposed hierarchical Bayesian approach allows incorporation of partial a priori knowledge about the noise and unknown optical image models, thereby capturing the function-anatomy correlation effectively. We present a computationally efficient iterative algorithm to simultaneously estimate the optical image and the unknown a priori model parameters. Extensive numerical simulations demonstrate that the proposed method avoids undesirable bias towards anatomical prior information and leads to significantly improved spatial resolution and quantitative accuracy.

Anatomy↗
PubMed1990

Application of a Bayesian method to monitor and adjust vancomycin dosage regimens.

A Bayesian method for monitoring vancomycin concentrations and adjusting regimens in patients with unstable renal function by using a two-compartment population model was evaluated with a personal computer. The population model was derived from data from 12 cardiac outpatients who received single doses of vancomycin. The performance of the method was then tested in 27 acutely ill patients who received multiple doses of vancomycin. Significant renal impairment was observed in 15 patients. Renal function changed in 15 patients. The vancomycin concentrations in the patients with changing renal function were not at steady state during the observation times. Two concentrations in serum (peak and then trough, or trough and then peak) were fitted along with the population model to individualize the parameter values for each patient. All the subsequent concentrations in serum for each patient were then predicted by using the parameter values for each patient. Future concentrations of 118 serum samples were predicted. The mean absolute prediction error was 3.6 +/- 4.5 micrograms/ml, and the mean prediction error was -0.7 +/- 5.3 micrograms/ml. These results confirm that a two-compartment pharmacokinetic model can be sufficiently individualized with the knowledge of just two concentrations of drug in patient serum; it is possible to predict closely subsequent concentrations in serum, and dosing regimens for individual patients can be well adjusted to achieve the chosen therapeutic goals.

Adult↗