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Results for “Bayesian modelling”

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PubMed1994

Predictive performance of the Bayesian analysis: effects of blood sampling time, population parameters, and pharmacostatistical model.

The present paper reports theoretical equations for the predictive performance of the Bayesian forecasting method. The precision of parameter estimates and predicted concentrations for an individual was described by general equations with the aid of a variance-covariance matrix of parameter estimates that involved the Bayes theorem. The equations were applied to assess the predictive performance of the one-point Bayesian method in association with blood sampling time, the population parameters, and the pharmacostatistical model. The simulation study showed that the prediction error in parameter estimates essentially depended upon the sampling time but the magnitude of dependency was affected by the size of inter- and intraindividual variances. With a smaller value of interindividual variance, the dependency on sampling time was less apparent. Effects of sampling time were further examined using clinical data obtained from 20 patients taking theophylline, and the results were in good agreement with the theoretical consideration. The present general equations are useful to investigate the sampling strategy as well as structural and variance modeling on the predictive performance of the Bayesian method.

Adult↗
PubMed2007

Age, period and cohort effects in Bayesian smoothing of spatial cancer survival with geoadditive models.

Based on the example of data on breast cancer survival in a specific area in France, this paper describes a Bayesian approach to analysing individual continuous-time spatially referenced survival data. Starting from the well-known Cox model we develop a geoadditive survival model with a baseline effect, spatial effects, age, period and cohort effects as well as the effect of the number of metastases at the time of diagnosis. Furthermore, we also investigate temporal and spatial variations in the effect of the number of metastases. Our approach is particularly useful since we find clear hints for a violation of the proportional hazards assumption and the existence of different spatial patterns for patients with no, one and more than one metastasis. The reliability of our approach is attested by comparison with a parametric model and with several simulated data sets with known risk profiles.

Adult↗
PubMed2003

Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network.

We propose a new statistical method for constructing a genetic network from microarray gene expression data by using a Bayesian network. An essential point of Bayesian network construction is the estimation of the conditional distribution of each random variable. We consider fitting nonparametric regression models with heterogeneous error variances to the microarray gene expression data to capture the nonlinear structures between genes. Selecting the optimal graph, which gives the best representation of the system among genes, is still a problem to be solved. We theoretically derive a new graph selection criterion from Bayes approach in general situations. The proposed method includes previous methods based on Bayesian networks. We demonstrate the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae gene expression data newly obtained by disrupting 100 genes.

Bayes Theorem↗
PubMed2006

A Dirichlet process model for detecting positive selection in protein-coding DNA sequences.

Most methods for detecting Darwinian natural selection at the molecular level rely on estimating the rates or numbers of nonsynonymous and synonymous changes in an alignment of protein-coding DNA sequences. In some of these methods, the nonsynonymous rate of substitution is allowed to vary across the sequence, permitting the identification of single amino acid positions that are under positive natural selection. However, it is unclear which probability distribution should be used to describe how the nonsynonymous rate of substitution varies across the sequence. One widely used solution is to model variation in the nonsynonymous rate across the sequence as a mixture of several discrete or continuous probability distributions. Unfortunately, there is little population genetics theory to inform us of the appropriate probability distribution for among-site variation in the nonsynonymous rate of substitution. Here, we describe an approach to modeling variation in the nonsynonymous rate of substitution by using a Dirichlet process mixture model. The Dirichlet process allows there to be a countably infinite number of nonsynonymous rate classes and is very flexible in accommodating different potential distributions for the nonsynonymous rate of substitution. We implemented the model in a fully Bayesian approach, with all parameters of the model considered as random variables.

Animals↗
PubMed2006

A new summarization method for Affymetrix probe level data.

MOTIVATION: We propose a new model-based technique for summarizing high-density oligonucleotide array data at probe level for Affymetrix GeneChips. The new summarization method is based on a factor analysis model for which a Bayesian maximum a posteriori method optimizes the model parameters under the assumption of Gaussian measurement noise. Thereafter, the RNA concentration is estimated from the model. In contrast to previous methods our new method called 'Factor Analysis for Robust Microarray Summarization (FARMS)' supplies both P-values indicating interesting information and signal intensity values. RESULTS: We compare FARMS on Affymetrix's spike-in and Gene Logic's dilution data to established algorithms like Affymetrix Microarray Suite (MAS) 5.0, Model Based Expression Index (MBEI), Robust Multi-array Average (RMA). Further, we compared FARMS with 43 other methods via the 'Affycomp II' competition. The experimental results show that FARMS with default parameters outperforms previous methods if both sensitivity and specificity are simultaneously considered by the area under the receiver operating curve (AUC). We measured two quantities through the AUC: correctly detected expression changes versus wrongly detected (fold change) and correctly detected significantly different expressed genes in two sets of arrays versus wrongly detected (P-value). Furthermore FARMS is computationally less expensive then RMA, MAS and MBEI. AVAILABILITY: The FARMS R package is available from http://www.bioinf.jku.at/software/farms/farms.html. SUPPLEMENTARY INFORMATION: http://www.bioinf.jku.at/publications/papers/farms/supplementary.ps

Algorithms↗
PubMed2004

Extension of the isobolographic approach to interactions studies between more than two drugs: illustration with the convulsant interaction between pefloxacin, norfloxacin, and theophylline in rats.

This work proposes a model to characterize the additivity or the nonadditivity of combinations of more than two agents. Using a Bayesian framework, we modeled the variability between experimental subjects, the errors that occurred during data collection, and the relationship between effects and concentrations of agents at the effect site. The model was used to characterize the additivity (or non-additivity) of norfloxacin, pefloxacin, and theophylline in causing maximal seizures in male Sprague Dawley rats. Animals received the drugs separately or in various combinations. Drug infusion was stopped at the onset of maximal seizures, and cerebrospinal fluid samples were collected for determination of drug concentration by high-performance liquid chromatography. The model was fitted to concentration data using Markov Chain Monte Carlo techniques. Results showed that induction of seizures by mixtures of theophylline and pefloxacin were additive. Seizure induction by mixtures of norfloxacin and pefloxacin or norfloxacin and theophylline were not additive and, given the model, these drugs interacted negatively. There was no triple interaction effect between the drugs. This study demonstrates the ease with which mixtures of more than two drugs can be analyzed with the proposed model.

Animals↗
PubMed2006

Bayesian sequential inference for stochastic kinetic biochemical network models.

As postgenomic biology becomes more predictive, the ability to infer rate parameters of genetic and biochemical networks will become increasingly important. In this paper, we explore the Bayesian estimation of stochastic kinetic rate constants governing dynamic models of intracellular processes. The underlying model is replaced by a diffusion approximation where a noise term represents intrinsic stochastic behavior and the model is identified using discrete-time (and often incomplete) data that is subject to measurement error. Sequential MCMC methods are then used to sample the model parameters on-line in several data-poor contexts. The methodology is illustrated by applying it to the estimation of parameters in a simple prokaryotic auto-regulatory gene network.

Kinetics↗
PubMed2004

Population pharmacokinetics and Bayesian estimation of mycophenolic acid concentrations in stable renal transplant patients.

BACKGROUND: Therapeutic drug monitoring of mycophenolic acid (MPA) may minimise the risk of acute rejection after transplantation. Area under the curve (AUC) rather than trough concentration-based monitoring is recommended and models for AUC estimation are needed. OBJECTIVES: To develop a population pharmacokinetic model suitable for Bayesian estimation of individual AUC in stable renal transplant patients. PATIENTS AND METHODS: The population pharmacokinetics of MPA were studied using nonlinear mixed effects modelling (NONMEM) in 60 patients (index group) receiving MPA on a twice-daily basis. Ten blood samples were collected at fixed timepoints from ten patients and four blood samples were collected at sparse timepoints from 50 patients. Bayesian estimation of individual AUC was made on the basis of three blood concentration measurements and covariates. The predictive performances of the Bayesian procedure were evaluated in an independent group of patients (test group) comprising ten subjects in whom ten blood samples were collected at fixed timepoints. RESULTS: A two-compartment model with zero-order absorption best fitted the data. Covariate analysis showed that bodyweight was positively correlated with oral clearance. However, the weak magnitude of the reduction in variability (from 34.8 to 28.2%) indicates that administration on a per kilogram basis would be of limited value in decreasing interindividual variability in MPA exposure. Bayesian estimation of pharmacokinetic parameters using samples drawn at 20 minutes and 1 and 3 hours enabled estimation of individual AUC with satisfactory accuracy (bias 7.7%, range of prediction errors 0.43-15.1%) and precision (root mean squared error 12.4%) as compared with the reference value obtained using the trapezoidal method. CONCLUSION: This paper reports for the first time population pharmacokinetic data for MPA in stable renal transplant patients, and shows that Bayesian estimation can allow accurate prediction of AUC with only three samples. This method provides a tool for therapeutic drug monitoring of MPA or for concentration-effect studies. Its application to MPA monitoring in the early period post-transplantation needs to be evaluated.

Adolescent↗
PubMed2003

Tuberculosis epidemics driven by HIV: is prevention better than cure?

OBJECTIVE: To compare the benefits of tuberculosis (TB) treatment with TB and HIV prevention for the control of TB in regions with high HIV prevalence. DESIGN AND METHODS: A compartmental difference equation model of TB and HIV has been developed and fitted to time series and other published data using Bayesian methods. The model is used to compare the effectiveness of TB chemotherapy with three strategies for prevention: highly active antiretroviral therapy (HAART), the treatment of latent TB infection (TLTI) and the reduction of HIV transmission. RESULTS: Even where the prevalence of HIV infection is high, finding and curing active TB is the most effective way to minimize the number of TB cases and deaths over the next 10 years. HAART can be as effective, but only with very high levels of coverage and compliance. TLTI is comparatively ineffective over all time scales. Reducing HIV incidence is relatively ineffective in preventing TB and TB deaths over 10 years but is much more effective over 20 years. CONCLUSIONS: In countries where the spread of HIV has led to a substantial increase in the incidence of TB, TB control programmes should maintain a strong emphasis on the treatment of active TB. To ensure effective control of TB in the longer term, methods of TB prevention should be carried out in addition to, but not as a substitute for, treating active cases.

AIDS-Related Opportunistic Infections↗
PubMed2003

A Bayesian approach to the accuracy of clinical observations.

The accuracy of clinical observations was estimated using Bayesian latent-class models with two or more independent tests. Four veterinarians carried out systematic independent clinical examinations on 155 pigs in three herds. Based on the results of binary recordings of clinical observations on dullness, poor body condition (PBC), skin lesions, lameness, respiratory disease, and diarrhea, a latent disease state for each clinical disease was estimated using Gibbs sampling. The accuracy of the clinical observations differed for the four observers and for different clinical signs. Population parameters were estimated from a Bayesian hierarchical model, and the accuracy of a random observer was calculated. We concluded that the accuracy of the veterinarians in this study substantiated the need to pursue more-precise definitions of the clinical findings and that larger sample sizes would be needed to provide reasonable variance estimates. Finally, we concluded that the uncertainty in the clinical decision-making process (starting with the clinical examination) needs to be represented fully.

Animals↗
PubMed2002

Estimating disease prevalence in the absence of a gold standard.

When estimating disease prevalence, it is not uncommon to have data from conditionally dependent diagnostic tests. In such a situation, the estimation of prevalence is difficult if none of the tests is considered to be a gold standard. In this paper we develop a Bayesian approach to estimating disease prevalence based on the results of two diagnostic tests, allowing for the possibility that the tests are conditionally dependent, but not conditioning on any particular dependence structure. This involves the construction of four models with various forms of conditional dependence and uses Bayesian model averaging, enabled by reversible jump MCMC, to obtain an overall estimate of the prevalence. This methodology is demonstrated using a study on the prevalence of Strongyloides infection.

Animals↗
PubMed2006

Using complexity for the estimation of Bayesian networks.

Statistical inference of graphical models has become an important tool in the reconstruction of biological networks of the type which model, for example, gene regulatory interactions. In particular, the construction of a score-based Bayesian posterior density over the space of models provides an intuitive and computationally feasible method of assessing model uncertainty and of assigning statistical confidence to structural features. One problem which frequently occurs with this approach is the tendency to overestimate the degree of model complexity. Spurious graphical features obtained in this way may affect the inference in unpredictable ways, even when using scoring techniques, such as the Bayesian Information Criterion (BIC), that are specifically designed to compensate for overfitting. In this article we propose a simple adjustment to a BIC-based scoring procedure. The method proceeds in two steps. In the first step we derive an independent estimate of the parametric complexity of the model. In the second we modify the BIC score so that the mean parametric complexity of the posterior density is equal to the estimated value. The method is applied to a set of test networks, and to a collection of genes from the yeast genome known to possess regulatory relationships. A Bayesian network model with binary responses is employed. In the examples considered, we find that the number of spurious graph edges inferred is reduced, while the effect on the identification of true edges is minimal.

Algorithms↗
PubMed2006

Brain mechanism of reward prediction under predictable and unpredictable environmental dynamics.

In learning goal-directed behaviors, an agent has to consider not only the reward given at each state but also the consequences of dynamic state transitions associated with action selection. To understand brain mechanisms for action learning under predictable and unpredictable environmental dynamics, we measured brain activities by functional magnetic resonance imaging (fMRI) during a Markov decision task with predictable and unpredictable state transitions. Whereas the striatum and orbitofrontal cortex (OFC) were significantly activated both under predictable and unpredictable state transition rules, the dorsolateral prefrontal cortex (DLPFC) was more strongly activated under predictable than under unpredictable state transition rules. We then modelled subjects' choice behaviours using a reinforcement learning model and a Bayesian estimation framework and found that the subjects took larger temporal discount factors under predictable state transition rules. Model-based analysis of fMRI data revealed different engagement of striatum in reward prediction under different state transition dynamics. The ventral striatum was involved in reward prediction under both unpredictable and predictable state transition rules, although the dorsal striatum was dominantly involved in reward prediction under predictable rules. These results suggest different learning systems in the cortico-striatum loops depending on the dynamics of the environment: the OFC-ventral striatum loop is involved in action learning based on the present state, while the DLPFC-dorsal striatum loop is involved in action learning based on predictable future states.

Brain↗
PubMed2006

Bayesian analysis of physiologically based toxicokinetic and toxicodynamic models.

Physiologically based toxicokinetic (PBTK) and toxicodynamic (TD) models of bromate in animals and humans would improve our ability to accurately estimate the toxic doses in humans based on available animal studies. These mathematical models are often highly parameterized and must be calibrated in order for the model predictions of internal dose to adequately fit the experimentally measured doses. Highly parameterized models are difficult to calibrate and it is difficult to obtain accurate estimates of uncertainty or variability in model parameters with commonly used frequentist calibration methods, such as maximum likelihood estimation (MLE) or least squared error approaches. The Bayesian approach called Markov chain Monte Carlo (MCMC) analysis can be used to successfully calibrate these complex models. Prior knowledge about the biological system and associated model parameters is easily incorporated in this approach in the form of prior parameter distributions, and the distributions are refined or updated using experimental data to generate posterior distributions of parameter estimates. The goal of this paper is to give the non-mathematician a brief description of the Bayesian approach and Markov chain Monte Carlo analysis, how this technique is used in risk assessment, and the issues associated with this approach.

Animals↗
PubMed2005

A comparison of three modelling approaches for quantitative risk assessment using the case study of Salmonella spp. in poultry meat.

A comprehensive review of both the scientific literature and industry practices was undertaken to identify and quantify all sources of contamination throughout the entire poultry meat production chain by Salmonella spp. This information was used to develop a quantitative risk assessment (QRA) model for Salmonella in the production chain from the breeder farm to the chilled carcass. This was subsequently used as the basis on which to compare the merits of three approaches to QRA modelling in such systems. The original model used a Bayesian Network (BN). The second method was a Markov chain Monte Carlo (MCMC) approach, a numerical Bayesian technique which retained a similar network structure but allowed further development, such as the separation of variability and uncertainty. The third method was a more detailed simulation model. The BN responds immediately to changes, such as entering evidence, because it does not use simulation and can propagate information from any point in the network to all others by Bayesian inference. However, it requires all the variables to be discrete, which introduces errors if continuous variables have to be discretized. These errors can accumulate. The MCMC approach does not require discrete variables while retaining some of the properties of the BN model, such as the ability to draw inferences from evidence. Finally, the simulation offers greater flexibility, such as consideration of the individual carcass, but may be more complex to implement as a result and sacrifices the ability to propagate evidence.

Animals↗
PubMed2005

Linear and nonlinear modeling of antifungal activity of some heterocyclic ring derivatives using multiple linear regression and Bayesian-regularized neural networks.

Antifungal activity was modeled for a set of 96 heterocyclic ring derivatives (2,5,6-trisubstituted benzoxazoles, 2,5-disubstituted benzimidazoles, 2-substituted benzothiazoles and 2-substituted oxazolo(4,5-b)pyridines) using multiple linear regression (MLR) and Bayesian-regularized artificial neural network (BRANN) techniques. Inhibitory activity against Candida albicans (log(1/C)) was correlated with 3D descriptors encoding the chemical structures of the heterocyclic compounds. Training and test sets were chosen by means of k-Means Clustering. The most appropriate variables for linear and nonlinear modeling were selected using a genetic algorithm (GA) approach. In addition to the MLR equation (MLR-GA), two nonlinear models were built, model BRANN employing the linear variable subset and an optimum model BRANN-GA obtained by a hybrid method that combined BRANN and GA approaches (BRANN-GA). The linear model fit the training set (n = 80) with r2 = 0.746, while BRANN and BRANN-GA gave higher values of r2 = 0.889 and r2 = 0.937, respectively. Beyond the improvement of training set fitting, the BRANN-GA model was superior to the others by being able to describe 87% of test set (n = 16) variance in comparison with 78 and 81% the MLR-GA and BRANN models, respectively. Our quantitative structure-activity relationship study suggests that the distributions of atomic mass, volume and polarizability have relevant relationships with the antifungal potency of the compounds studied. Furthermore, the ability of the six variables selected nonlinearly to differentiate the data was demonstrated when the total data set was well distributed in a Kohonen self-organizing neural network (KNN).

Antifungal Agents↗
PubMed2004

A hierarchical modeling approach for estimating national distributions of chemicals in public drinking water systems.

Water quality studies often include the analytical challenge of incorporating censored data and quantifying error of estimation. Many analytical methods exist for estimating distribution parameters when censored data are present. This paper presents a Bayesian-based hierarchical model for estimating the national distribution of the mean concentrations of chemicals occurring in U.S. public drinking water systems using fluoride and thallium as examples. The data used are Safe Drinking Water Act compliance monitoring data (with a significant proportion of left-censored data). The model, which assumes log-normality, was evaluated using simulated data sets generated from a series of Weibull distributions to illustrate the robustness of the model. The hierarchical model is easily implemented using the Markov chain Monte Carlo simulation method. In addition, the Bayesian method is able to quantify the uncertainty in the estimated cumulative density function. The estimated fluoride and thallium national distributions are presented. Results from this study can be used to develop prior distributions for future U.S. drinking water regulatory studies of contaminant occurrence.

Bayes Theorem↗
PubMed2002

Hierarchical modeling of sequential behavioral data: an empirical Bayesian approach.

The authors review the common methods for measuring strength of contingency between 2 behaviors in a behavioral sequence, the binomial z score and the adjusted cell residual, and point out a number of limitations of these approaches. They present a new approach using log odds ratios and empirical Bayes estimation in the context of hierarchical modeling, an approach not constrained by these limitations. A series of hierarchical models is presented to test the stationarity of behavioral sequences, the homogeneity of sequences across a sample of episodes, and whether covariates can account for variation in sequences across the sample. These models are applied to observational data taken from a study of the behavioral interactions of 254 couples to illustrate their use.

Bayes Theorem↗