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PubMed2000

Statistical analysis of Fisher et al. PBPK model of trichloroethylene kinetics.

Two physiologically based pharmacokinetic models for trichloroethylene (TCE) in mice and humans were calibrated with new toxicokinetic data sets. Calibration is an important step in model development, essential to a legitimate use of models for research or regulatory purposes. A Bayesian statistical framework was used to combine prior information about the model parameters with the data likelihood to yield posterior parameter distributions. For mice, these distributions represent uncertainty. For humans, the use of a population statistical model yielded estimates of both variability and uncertainty in human toxicokinetics of TCE. After adjustment of the models by Markov chain Monte Carlo sampling, the mouse model agreed with a large part of the data. Yet, some data on secondary metabolites were not fit well. The posterior parameter distributions obtained for mice were quite narrow (coefficient of variation [CV] of about 10 or 20%), but these CVs might be underestimated because of the incomplete fit of the model. The data fit, for humans, was better than for mice. Yet, some improvement of the model is needed to correctly describe trichloroethanol concentrations over long time periods. Posterior uncertainties about the population means corresponded to 10-20% CV. In terms of human population variability, volumes and flows varied across subject by approximately 20% CV. The variability was somewhat higher for partition coefficients (between 30 and 40%) and much higher for the metabolic parameters (standard deviations representing about a factor of 2). Finally, the analysis points to differences between human males and females in the toxicokinetics of TCE. The significance of these differences in terms of risk remains to be investigated.

Animals↗

PubMed2002

Coping with missing data in clinical trials: a model-based approach applied to asthma trials.

In most clinical trials, some patients do not complete their intended follow-up according to protocol, for a variety of reasons, and are often described as having 'dropped out' before the conclusion of the trial. Their subsequent measurements are missing, and this makes the analysis of the trial's repeated measures data more difficult. In this paper we briefly review the reasons for patient drop-out, and their implications for some commonly used methods of analysis. We then propose a class of models for modelling both the response to treatment and the drop-out process. Such models are readily fitted in a Bayesian framework using non-informative priors with the software BUGS. The results from such models are then compared with the results of standard methods for dealing with missing data in clinical trials, such as last observation carried forward. We further propose the use of a time transformation to linearize an asymptotic pattern of repeated measures over time and therefore simplify the modelling. All these ideas are illustrated using data from a five-arm asthma clinical trial.

Asthma↗

PubMed2006

Mixed models and empirical bayes estimation for retrospective exposure assessment of dust exposures in Canadian sawmills.

OBJECTIVES: Data on job histories is commonly available from study subjects and worksites, therefore jobs are often used for assigning exposures in historical epidemiological studies. Exposure estimates are often derived by offering jobs as fixed effects in statistical models. An alternative approach would be to offer job as a random effect to obtain empirical Bayes estimates of exposure. This approach is more efficient since it weights exposure estimates according to the within-job and between-job variability and the number of measurements for each job. We assess three models for predicting historical dust exposures of sawmill workers. METHODS: Models were developed using 407 inhalable dust measurements collected from 58 jobs in four sawmills. The first model incorporated all variables as fixed effects; the second added a random term to account for correlation within workers; and the third offered random terms for worker, job and mill (hierarchical model). Empirical Bayes estimates were used to calculate job-specific exposures from the hierarchical model. RESULTS: The fixed effects and random worker mixed models performed nearly identically because there was low within-worker correlation (r = 0.26). The Bayesian exposure predictions from the hierarchical model were slightly more correlated with the observed mill-job arithmetic means than those from the models where jobs were fixed effects (0.74 versus 0.70). CONCLUSIONS: While we observed no large differences in exposure estimates by treating job as a fixed or random effect, treating job as a random effect allowed for job-specific coefficients to be estimated for every job while borrowing strength in the presence of sparse data by assuming that the job means are normally distributed around the group mean. In addition, empirical Bayes job estimates can be used for a posteriori job grouping. The use of this method for retrospective exposure assessment should continue to be examined.

Air Pollutants, Occupational↗

PubMed2005

Evaluation of decay times in coupled spaces: reliability analysis of Bayeisan decay time estimation.

This paper discusses quantitative tools to evaluate the reliability of "decay time estimates" and inter-relationships between multiple decay times for estimates made within a Bayesian framework. Previous works [Xiang and Goggans, J. Acoust. Soc. Am. 110, 1415-1424 (2001); 113, 2685-2697 (2003)] have applied Bayesian framework to cope with the demanding tasks in estimating multiple decay times from Schroeder decay functions measured in acoustically coupled spaces. A parametric model of Schroeder decay function [Xiang, J. Acoust. Soc. Am. 98, 2112-2121 (1995)] has been used for the Bayesian model-based analysis. The relevance of this work is that architectural acousticians need to know how well determined are the estimated decay times calculated within Bayesian framework using Schroeder decay function data. This paper will first address the estimation of global variance of the residual errors between the Schroeder function data and its model. Moreover, this paper discusses how the "landscape" shape of the posterior probability density function over the decay parameter space influences the individual decay time estimates, their associated variances, and their inter-relationships. This paper uses experimental results from measured room impulse responses in real halls to describe a model-based sampling method for an efficient estimation of decay times, and their individual variances. These parameters along with decay times are relevant decay parameters for evaluation and understanding of acoustically coupled spaces.

Journal Article↗

PubMed2003

Inferring gene networks from time series microarray data using dynamic Bayesian networks.

Dynamic Bayesian networks (DBNs) are considered as a promising model for inferring gene networks from time series microarray data. DBNs have overtaken Bayesian networks (BNs) as DBNs can construct cyclic regulations using time delay information. In this paper, a general framework for DBN modelling is outlined. Both discrete and continuous DBN models are constructed systematically and criteria for learning network structures are introduced from a Bayesian statistical viewpoint. This paper reviews the applications of DBNs over the past years. Real data applications for Saccharomyces cerevisiae time series gene expression data are also shown.

Algorithms↗

PubMed2003

Time scale of eutherian evolution estimated without assuming a constant rate of molecular evolution.

Controversies over the molecular clock hypothesis were reviewed. Since it is evident that the molecular clock does not hold in an exact sense, accounting for evolution of the rate of molecular evolution is a prerequisite when estimating divergence times with molecular sequences. Recently proposed statistical methods that account for this rate variation are overviewed and one of these procedures is applied to the mitochondrial protein sequences and to the nuclear gene sequences from many mammalian species in order to estimate the time scale of eutherian evolution. This Bayesian method not only takes account of the variation of molecular evolutionary rate among lineages and among genes, but it also incorporates fossil evidence via constraints on node times. With denser taxonomic sampling and a more realistic model of molecular evolution, this Bayesian approach is expected to increase the accuracy of divergence time estimates.

Animals↗

PubMed1999

Population modelling in drug development.

In this paper we discuss the vital role that population (hierarchical) modelling can play within the drug development process. Specifically, population pharmacokinetic/pharmacodynamic models can provide reliable predictions of an individualized dose-exposure-response relationship. A predictive model of this kind can be used to simulate and hence design clinical trials, find initial dosage regimens satisfying an optimality criterion on the population distribution of responses, and individualized regimens satisfying such a criterion conditional on individual features, such as sex, age, etc. Throughout we emphasize prediction and advocate mechanistic as opposed to empirical modelling, and argue that the Bayesian approach is particularly natural in this setting.

Bayes Theorem↗

PubMed2003

Assessing brain activity through spatial Bayesian variable selection.

Statistical parametric mapping (SPM), relying on the general linear model and classical hypothesis testing, is a benchmark tool for assessing human brain activity using data from fMRI experiments. Friston et al. discuss some limitations of this frequentist approach and point out promising Bayesian perspectives. In particular, a Bayesian formulation allows explicit modeling and estimation of activation probabilities. In this study, we directly address this issue and develop a new regression based approach using spatial Bayesian variable selection. Our method has several advantages. First, spatial correlation is directly modeled for activation probabilities and indirectly for activation amplitudes. As a consequence, there is no need for spatial adjustment in a postprocessing step. Second, anatomical prior information, such as the distribution of grey matter or expert knowledge, can be included as part of the model. Third, the method has superior edge-preservation properties as well as being fast to compute. When applied to data from a simple visual experiment, the results demonstrate improved sensitivity for detecting activated cortical areas and for better preserving details of activated structures.

Adult↗

PubMed2005

Bayesian predictions of final outcomes: regulatory approval of a spinal implant.

We describe a randomized controlled trial of an investigational spinal implant. The investigational device has an obvious benefit in comparison with control in that it precludes the need for harvesting bone graft and the pain and morbidity associated with it. Therefore, the principal comparison is one of noninferiority. The primary endpoint is overall success at two years. The "noninferiority margin" is 10%. Waiting for two years after the last patient's surgery may not be necessary depending on earlier measurements of success. We model the relationship between one- and two-year results. Our Bayesian analysis considers all available information, including some patients who have both one- and two-year results and some patients who have only one-year results. Our study provides an example in which Bayesian predictive modeling provided earlier information than otherwise and therefore it shortened the time line of the development of a therapeutic strategy.

Bayes Theorem↗

PubMed2026

HiCPotts: An R/Bioconductor package to identify significant interactions in chromosome conformation capture data and model sources of bias.

MOTIVATION: Chromosome Conformation Capture methods, including Hi-C, micro-C or Capture-C, are used to map chromatin interactions genome-wide. Most of the existing computational methods do not account for sources of bias (such as DNA accessibility, GC content or TE content) in the data. RESULTS: We previously developed ZipHiC, a Bayesian method based on the hidden Markov random field (HMRF) model and the Approximate Bayesian Computation (ABC), that uses zero-inflated Poisson distribution to model the noise, signal and false signal of the data and showed that this approach was able to detect bias from DNA accessibility, GC content and TE content in both Hi-C and micro-C data. Here, we present HiCPotts, another Bayesian method based on the HMRF model and the ABC that uses a zero-inflated Negative Binomial distribution instead to model the noise and signal of the data. We systematically show that HiCPotts reduces false positives and increases recovery of true interactions compared to ZipHiC, but also compared to other methods such as FastHiC, Juicer and HiCExplorer. Most importantly, we provide an R/Bioconductor package that allows modelling the noise, signal and false signal using various distributions such as the zero-inflated Negative Binomial (ZINB) and the zero-inflated Poisson distribution (ZIP). AVAILABILITY AND IMPLEMENTATION: https://bioconductor.org/packages/HiCPotts/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Approximate Bayesian Computation↗

PubMed2005

A rapid computational filter for cytochrome P450 1A2 inhibition potential of compound libraries.

QSAR models for a diverse set of compounds for cytochrome P450 1A2 inhibition have been produced using 4 statistical approaches; partial least squares (PLS), multiple linear regression (MLR), classification and regression trees (CART), and bayesian neural networks (BNN). The models complement one another and have identified the following descriptors as important features for CYP1A2 inhibition; lipophilicity, aromaticity, charge, and the HOMO/LUMO energies. Furthermore all models are global and have been used to predict a diverse independent set of compounds. For the first time in the field of QSAR, the kappa index of agreement has comprehensively been used to assess the overall accuracy of the model's predictive power. The models are statistically significant and can be used as a rapid computational filter for cytochrome P450 1A2 inhibition potential of compound libraries.

Bayes Theorem↗

PubMed2006

Bayesian perspectives for epidemiological research: I. Foundations and basic methods.

One misconception (of many) about Bayesian analyses is that prior distributions introduce assumptions that are more questionable than assumptions made by frequentist methods; yet the assumptions in priors can be more reasonable than the assumptions implicit in standard frequentist models. Another misconception is that Bayesian methods are computationally difficult and require special software. But perfectly adequate Bayesian analyses can be carried out with common software for frequentist analysis. Under a wide range of priors, the accuracy of these approximations is just as good as the frequentist accuracy of the software--and more than adequate for the inaccurate observational studies found in health and social sciences. An easy way to do Bayesian analyses is via inverse-variance (information) weighted averaging of the prior with the frequentist estimate. A more general method expresses the prior distributions in the form of prior data or 'data equivalents', which are then entered in the analysis as a new data stratum. That form reveals the strength of the prior judgements being introduced and may lead to tempering of those judgements. It is argued that a criterion for scientific acceptability of a prior distribution is that it be expressible as prior data, so that the strength of prior assumptions can be gauged by how much data they represent.

Bayes Theorem↗

PubMed2007

Sequential updating of a new dynamic pharmacokinetic model for caffeine in premature neonates.

BACKGROUND AND OBJECTIVE: Caffeine treatment is widely used in nursing care to reduce the risk of apnoea in premature neonates. To check the therapeutic efficacy of the treatment against apnoea, caffeine concentration in blood is an important indicator. The present study was aimed at building a pharmacokinetic model as a basis for a medical decision support tool. METHODS: In the proposed model, time dependence of physiological parameters is introduced to describe rapid growth of neonates. To take into account the large variability in the population, the pharmacokinetic model is embedded in a population structure. The whole model is inferred within a Bayesian framework. To update caffeine concentration predictions as data of an incoming patient are collected, we propose a fast method that can be used in a medical context. This involves the sequential updating of model parameters (at individual and population levels) via a stochastic particle algorithm. RESULTS: Our model provides better predictions than the ones obtained with models previously published. We show, through an example, that sequential updating improves predictions of caffeine concentration in blood (reduce bias and length of credibility intervals). The update of the pharmacokinetic model using body mass and caffeine concentration data is studied. It shows how informative caffeine concentration data are in contrast to body mass data. CONCLUSION: This study provides the methodological basis to predict caffeine concentration in blood, after a given treatment if data are collected on the treated neonate.

Bayes Theorem↗

PubMed1999

Modeling excessive nutrient loading in the environment.

Models addressing excessive nutrient loading in the environment originated over 50 years ago with the simple nutrient concentration thresholds proposed by Sawyer (1947. Fertilization of lakes by agricultural and urban drainage. New Engl. Water Works Assoc. 61, 109-127). Since then, models have improved due to progress in modeling techniques and technology as well as enhancements in scientific knowledge. Several of these advances are examined here. Among the recent approaches in modeling techniques we review are error propagation, model confirmation, generalized sensitivity analysis, and Bayesian analysis. In the scientific arena and process characterization, we focus on advances in surface water modeling, discussing enhanced modeling of organic carbon, improved hydrodynamics, and refined characterization of sediment diagenesis. We conclude with some observations on future needs and anticipated developments.

Journal Article↗

PubMed2005

Bayesian eggs and Bayesian omelettes: reply to Stern (2005).

In this response to Stern's (2005) discussion of Klugkist, Laudy, and Hoijtink (2005), model inference based on posterior probabilities on the parameter space is discussed. Furthermore, the authors respond to Stern's example in which all possible orderings are included via a short discussion of exploratory versus theory-based modeling. Finally, the authors show that the Bayesian approach is flexible and can deal with many types of constraints. This is illustrated using a model with constraints on the differences between means.

Bayes Theorem↗

PubMed2006

Bayesian spatio-temporal approach for EEG source reconstruction: conciliating ECD and distributed models.

Characterizing the cortical activity sources of electroencephalography (EEG)/magnetoencephalography data is a critical issue since it requires solving an ill-posed inverse problem that does not admit a unique solution. Two main different and complementary source models have emerged: equivalent current dipoles (ECD) and distributed linear (DL) models. While ECD models remain highly popular since they provide an easy way to interpret the solutions, DL models (also referred to as imaging techniques) are known to be more realistic and flexible. In this paper, we show how those two representations of the brain electromagnetic activity can be cast into a common general framework yielding an optimal description and estimation of the EEG sources. From this extended source mixing model, we derive a hybrid approach whose key aspect is the separation between temporal and spatial characteristics of brain activity, which allows to dramatically reduce the number of DL model parameters. Furthermore, the spatial profile of the sources, as a temporal invariant map, is estimated using the entire time window data, allowing to significantly enhance the information available about the spatial aspect of the EEG inverse problem. A Bayesian framework is introduced to incorporate distinct temporal and spatial constraints on the solution and to estimate both parameters and hyperparameters of the model. Using simulated EEG data, the proposed inverse approach is evaluated and compared with standard distributed methods using both classical criteria and ROC curves.

Algorithms↗

PubMed2001

Bayesian optimal designs for estimating a set of symmetrical quantiles.

We propose multiple-objective Bayesian optimal designs for the logit model. As an example, we consider the design problem for estimating several percentiles with possibly unequal interest in each of the percentiles. Characteristics of these designs are studied and illustrated for the case when the interest lies in estimating the three quartiles. We compare these optimal designs with the sequential designs generated via a generalized Pólya urn model and found the latter to be highly efficient. In addition, comparisons are made between locally optimal designs and Bayesian optimal designs.

Adult↗

PubMed2005

Use of multiple data streams to conduct Bayesian biologic surveillance.

INTRODUCTION: Emergency department (ED) records and over-the-counter (OTC) sales data are two of the most commonly used sources of data for syndromic surveillance. The majority of detection algorithms monitor these data sources separately and either do not combine them or combine them in an ad hoc fashion. This report outlines a new causal model that combines the two data sources coherently to perform outbreak detection. OBJECTIVES: This report describes the extension of the Population-wide Anomaly Detection and Assessment (PANDA) Bayesian biologic surveillance algorithm to combine information from multiple data streams. It also outlines the assumptions and techniques used to make this approach scalable for real-time surveillance of a large population. METHODS: A causal Bayesian network model used previously was extended to incorporate evidence from daily OTC sales data. At the level of individual persons, the actions that result in the purchase of OTC products and in admission to an ED were modeled. RESULTS: Preliminary results indicate that this model has a tractable running time consisting of 209 seconds for initialization and approximately 4 seconds for every hour's worth of ED data, as measured on a Pentium-4 three-Gigahertz machine with two Gigabytes of RAM. CONCLUSION: Preliminary results for surveillance using a new Bayesian algorithm that models the interaction between ED and OTC data are positive regarding the run time of the algorithm.

Algorithms↗