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Results for “Bayesian modelling”

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PubMed2005

Inferring genetic regulatory logic from expression data.

MOTIVATION: High-throughput molecular genetics methods allow the collection of data about the expression of genes at different time points and under different conditions. The challenge is to infer gene regulatory interactions from these data and to get an insight into the mechanisms of genetic regulation. RESULTS: We propose a model for genetic regulatory interactions, which has a biologically motivated Boolean logic semantics, but is of a probabilistic nature, and is hence able to confront noisy biological processes and data. We propose a method for learning the model from data based on the Bayesian approach and utilizing Gibbs sampling. We tested our method with previously published data of the Saccharomyces cerevisiae cell cycle and found relations between genes consistent with biological knowledge.

Bayes Theorem↗
PubMed1989

Prospective use of optimal sampling theory: steady-state ciprofloxacin pharmacokinetics in critically ill trauma patients.

We examined the use of optimal sampling theory to determine a sparse sampling design to estimate pharmacokinetic parameters of ciprofloxacin in patients who had sustained trauma. Two serum sampling strategies, consisting of six sampling times each, were derived on the basis of the patient's renal function (patients with creatinine clearance greater than or equal to 6 L/hr/1.73 m2 and patients with creatinine clearances less than 6 L/hr/1.73 m2). Two additional serum samples were obtained for other aspects to the study. A timed urine collection was also obtained. Pharmacokinetic parameter estimates were determined by comodeling the serum and urine data with a three-compartment open model (parameterized as microconstants) with a bayesian algorithm and by noncompartmental analysis. Bayesian-derived parameter estimates were total body clearance of drug from plasma, 29.8 L/hr/1.73 m2; renal clearance, 17.0 L/hr/1.73 m2; and nonrenal clearance, 12.7 L/hr/1.73 m2 and were not significantly different from noncompartmentally derived parameters (p = 0.80, p = 0.65 and p = 0.333, respectively). The study demonstrates the use of optimal sampling theory to determine an informative yet relatively sparse sampling strategy for a drug with a complex pharmacokinetic model.

Adult↗
PubMedDate not supplied

Multivariate Bayesian analysis of Gaussian, right censored Gaussian, ordered categorical and binary traits using Gibbs sampling.

A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed.

Bayes Theorem↗
PubMed2000

Baseline risk as predictor of treatment benefit: three clinical meta-re-analyses.

A relationship between baseline risk and treatment effect is increasingly investigated as a possible explanation of between-study heterogeneity in clinical trial meta-analysis. An approach that is still often applied in the medical literature is to plot the estimated treatment effects against the estimated measures of risk in the control groups (as a measure of baseline risk), and to compute the ordinary weighted least squares regression line. However, it has been pointed out by several authors that this approach can be seriously flawed. The main problem is that the observed treatment effect and baseline risk measures should be viewed as estimates rather than the true values. In recent years several methods have been proposed in the statistical literature to potentially deal with the measurement errors in the estimates. In this article we propose a vague priors Bayesian solution to the problem which can be carried out using the 'Bayesian inference using Gibbs sampling' (BUGS) implementation of Markov chain Monte Carlo numerical integration techniques. Different from other proposed methods, it uses the exact rather than an approximate likelihood, while it can handle many different treatment effect measures and baseline risk measures. The method differs from a recently proposed Bayesian method in that it explicitly models the distribution of the underlying baseline risks. We apply the method to three meta-analyses published in the medical literature and compare the results with the outcomes of the other recently proposed methods. In particular we compare our approach to McIntosh's method, for which we show how it can be carried out using standard statistical software. We conclude that our proposed method offers a very general and flexible solution to the problem, which can be carried out relatively easily with existing Bayesian analysis software. A confidence band for the underlying relationship between true effect measure and baseline risk and a confidence interval for the value of the baseline risk measure for which there is no treatment effect are easily obtained by-products of our approach.

Bayes Theorem↗
PubMed2003

Genetic analysis of somatic cell score in Norwegian cattle using random regression test-day models.

The dataset used in this analysis contained a total of 341,736 test-day observations of somatic cell scores from 77,110 primiparous daughters of 1965 Norwegian Cattle sires. Initial analyses, using simple random regression models without genetic effects, indicated that use of homogeneous residual variance was appropriate. Further analyses were carried out by use of a repeatability model and 12 random regression sire models. Legendre polynomials of varying order were used to model both permanent environmental and sire effects, as did the Wilmink function, the Lidauer-Mäntysaari function, and the Ali-Schaeffer function. For all these models, heritability estimates were lowest at the beginning (0.05 to 0.07) and higher at the end (0.09 to 0.12) of lactation. Genetic correlations between somatic cell scores early and late in lactation were moderate to high (0.38 to 0.71), whereas genetic correlations for adjacent DIM were near unity. Models were compared based on likelihood ratio tests, Bayesian information criterion, Akaike information criterion, residual variance, and predictive ability. Based on prediction of randomly excluded observations, models with 4 coefficients for permanent environmental effect were preferred over simpler models. More highly parameterized models did not substantially increase predictive ability. Evaluation of the different model selection criteria indicated that a reduced order of fit for sire effects was desireable. Models with zeroth- or first-order of fit for sire effects and higher order of fit for permanent environmental effects probably underestimated sire variance. The chosen model had Legendre polynomials with 3 coefficients for sire, and 4 coefficients for permanent environmental effects. For this model, trajectories of sire variance and heritability were similar assuming either homogeneous or heterogeneous residual variance structure.

Animals↗
PubMed2001

Bayesian technique for investigating linearity in event-related BOLD fMRI.

Event-related BOLD fMRI data is modeled as a linear time-invariant system. Together with Bayesian inference techniques, a statistical test is developed for rigorously detecting linearity/nonlinearity in the BOLD response system. The test is applied to data collected from eight subjects using an event-related paradigm with a switching checkerboard as the visual stimulus. Analyzed as a group, the results clearly find the response to be nonlinear. When each subject is analyzed individually, however, the results are predominantly nonlinear, but there is some evidence to suggest that there may be a crossover from a linear to a nonlinear regime and vice versa. This could be important when estimating physiological parameters for individuals. Additionally, estimates of the hemodynamic response function and corresponding response were obtained, but there was no consistent appearance of a poststimulus undershoot in the event-related BOLD response.

Adult↗
PubMed1997

Modeling of trough plasma bismuth concentrations.

Disposition pharmacokinetics of bismuth following oral dosing of ranitidine bismuth citrate are complicated and variable. An analysis of data from healthy volunteers suggests a model with three disposition compartments and first-order absorption. Patient data are pooled from 10 separate studies and consist of 1140 trough concentrations measured in 802 patients following dosing of 2 to 12 weeks duration. There are therefore insufficient data to obtain reliable parameter estimates for the full model and we use instead a much reduced model and an informative prior based on the volunteer data. Individual parameter estimates from this model can then be used to establish covariate relationships. Trough concentrations were influenced by the coadministration of clarithromycin and by creatinine clearance. A simulation study was carried out to check the validity of the estimates obtained from the reduced model. We carry out analysis via Bayesian sampling-based techniques. Throughout, we use predictive distributions for both diagnostic and inference purposes. In particular, we determine predicted distributions for the Cmax, Cmin and AUC characteristics of new individuals.

Bayes Theorem↗
PubMed2004

Modeling T-cell activation using gene expression profiling and state-space models.

MOTIVATION: We have used state-space models to reverse engineer transcriptional networks from highly replicated gene expression profiling time series data obtained from a well-established model of T-cell activation. State space models are a class of dynamic Bayesian networks that assume that the observed measurements depend on some hidden state variables that evolve according to Markovian dynamics. These hidden variables can capture effects that cannot be measured in a gene expression profiling experiment, e.g. genes that have not been included in the microarray, levels of regulatory proteins, the effects of messenger RNA and protein degradation, etc. RESULTS: Bootstrap confidence intervals are developed for parameters representing 'gene-gene' interactions over time. Our models represent the dynamics of T-cell activation and provide a methodology for the development of rational and experimentally testable hypotheses. AVAILABILITY: Supplementary data and Matlab computer source code will be made available on the web at the URL given below. SUPPLEMENTARY INFORMATION: http://public.kgi.edu/~wild/LDS/index.htm

Computer Simulation↗
PubMed2006

Hidden Markov models for wavelet-based blind source separation.

In this paper, we consider the problem of blind source separation in the wavelet domain. We propose a Bayesian estimation framework for the problem where different models of the wavelet coefficients are considered: the independent Gaussian mixture model, the hidden Markov tree model, and the contextual hidden Markov field model. For each of the three models, we give expressions of the posterior laws and propose appropriate Markov chain Monte Carlo algorithms in order to perform unsupervised joint blind separation of the sources and estimation of the mixing matrix and hyper parameters of the problem. Indeed, in order to achieve an efficient joint separation and denoising procedures in the case of high noise level in the data, a slight modification of the exposed models is presented: the Bernoulli-Gaussian mixture model, which is equivalent to a hard thresholding rule in denoising problems. A number of simulations are presented in order to highlight the performances of the aforementioned approach: 1) in both high and low signal-to-noise ratios and 2) comparing the results with respect to the choice of the wavelet basis decomposition.

Algorithms↗
PubMedDate not supplied

Review of the development, validation, and application of predictive instruments in interventional cardiology.

Within the last few years, risk assessment has become an integral part of clinical practice, particularly for thoracic surgery and interventional procedures. Risk assessment statistical models are being used in medical decision making, quality improvement tools, and as aids to patient counseling. This literature review was conducted to evaluate the types of predictive models and outcomes measures that have been examined, and methods used in development, validation, and application of these models. A Medline search performed to identify articles (limited to human studies) published in English from 1980 to 1999 resulted in 89 articles, of which 71 were evaluable. Populations studied for model development included patients undergoing coronary artery bypass graft (CABG), percutaneous transluminal coronary revascularization (PTCR), cardiac catheterization, or stenting procedures and patients with angina or stroke. The models were equally developed from a single center versus multicenter and from retrospective databases versus prospective studies. In terms of model perspectives, only three of the models measured cost or cost-effectiveness as the outcome; the remainder considered only clinical outcomes. The most commonly reported types of predictive models were developed using logistic regression and Bayesian techniques, followed by neural networks, rule-based artificial intelligence, simultaneous equation system, and multiple linear regression. Factors to consider when developing or evaluating a predictive model include uniformity of definitions of outcomes, uniformity of definitions of variables, completeness of data, number and frequency of variables, timeliness and source of data, development population characteristics, development and testing (validation) cohorts, and calibration and discrimination. Application of these models to an individual patient can spur quality improvement efforts that can lead to dramatic, system-wide improvements in outcomes.

Cardiovascular Diseases↗
PubMed2005

Bayesian tests of extra-Binomial variability.

A simple model for extra-Binomial variability is the Beta-Binomial. A complication in testing the Binomial against the Beta-Binomial alternative is that the Binomial lies on the boundary of the Beta-Binomial, which forces modifications to the usual asymptotic arguments. In this paper, we propose a Bayesian test using a pair of approximate Bayes factors, one for the case in which the maximum likelihood estimator (MLE) of the extra-Binomial variability is zero and one for the case in which it is positive. These approximate Bayes factors are easy to compute. We evaluate the operating characteristics of the Bayes factors and find them to be more powerful than the likelihood ratio test. We then apply the method to three data sets, including one in which the issue is whether a logistic regression intercept should be considered a random effect. In each case, our approximate Bayes factors are close to the exact Bayes factors, which may also be computed with additional effort.

Amputation, Surgical↗
PubMed1992

Adaptive control with feedback strategies for suramin dosing.

Suramin, a drug used in the treatment of parasitic diseases, is currently being evaluated in clinical trials as an antineoplastic agent. The use of therapeutic drug monitoring and adaptive control with feedback in clinical trials of suramin was initially motivated by an association between acute neurologic toxicity and plasma suramin concentrations in excess of 350 micrograms/ml. We have prospectively examined the performance of both two- and three-compartment population pharmacokinetic models in controlling plasma suramin concentrations and have found that a three-compartment model best describes this drug. No correlation was found between the clearance of suramin and creatinine clearance, as had been previously hypothesized. The low systemic clearance of suramin and the number of parameters required to describe the three-compartment model suggest the need for a bayesian approach to the estimation of individual pharmacokinetics.

Adrenal Gland Neoplasms↗
PubMed1998

Acute middle ear infection in small children: a Bayesian analysis using multiple time scales.

The study is based on a sample of 965 children living in Oulu region (Finland), who were monitored for acute middle ear infections from birth to the age of two years. We introduce a nonparametrically defined intensity model for ear infections, which involves both fixed and time dependent covariates, such as calendar time, current age, length of breast-feeding time until present, or current type of day care. Unmeasured heterogeneity, which manifests itself in frequent infections in some children and rare in others and which cannot be explained in terms of the known covariates, is modelled by using individual frailty parameters. A Bayesian approach is proposed to solve the inferential problem. The numerical work is carried out by Monte Carlo integration (Metropolis-Hastings algorithm).

Acute Disease↗
PubMed2001

Developing a Bayesian belief network for the management of geriatric hospital care.

Resource management is an essential feature of hospital management. This is especially true for geriatric services, as older people often have complex medical and social needs. Hospital management should benefit from an explanatory model that provides predictions of duration of stay and destination on discharge. We describe how a Bayesian belief network models the behaviour of geriatric patients using predictive variables: personal details, admission reasons and dependency levels. This approach is illustrated using data on 4,722 patients admitted to geriatric medicine at St. George's Hospital, London; distributions of the patient outcome given typical values of the predictive variables are provided.

Aged↗
PubMed2001

Selecting the best-fit model of nucleotide substitution.

Despite the relevant role of models of nucleotide substitution in phylogenetics, choosing among different models remains a problem. Several statistical methods for selecting the model that best fits the data at hand have been proposed, but their absolute and relative performance has not yet been characterized. In this study, we compare under various conditions the performance of different hierarchical and dynamic likelihood ratio tests, and of Akaike and Bayesian information methods, for selecting best-fit models of nucleotide substitution. We specifically examine the role of the topology used to estimate the likelihood of the different models and the importance of the order in which hypotheses are tested. We do this by simulating DNA sequences under a known model of nucleotide substitution and recording how often this true model is recovered by the different methods. Our results suggest that model selection is reasonably accurate and indicate that some likelihood ratio test methods perform overall better than the Akaike or Bayesian information criteria. The tree used to estimate the likelihood scores does not influence model selection unless it is a randomly chosen tree. The order in which hypotheses are tested, and the complexity of the initial model in the sequence of tests, influence model selection in some cases. Model fitting in phylogenetics has been suggested for many years, yet many authors still arbitrarily choose their models, often using the default models implemented in standard computer programs for phylogenetic estimation. We show here that a best-fit model can be readily identified. Consequently, given the relevance of models, model fitting should be routine in any phylogenetic analysis that uses models of evolution.

Algorithms↗
PubMed2004

Probabilistic methods of identifying genes in prokaryotic genomes: connections to the HMM theory.

In this paper, we review developments in probabilistic methods of gene recognition in prokaryotic genomes with the emphasis on connections to the general theory of hidden Markov models (HMM). We show that the Bayesian method implemented in GeneMark, a frequently used gene-finding tool, can be augmented and reintroduced as a rigorous forward-backward (FB) algorithm for local posterior decoding described in the HMM theory. Another earlier developed method, prokaryotic GeneMark.hmm, uses a modification of the Viterbi algorithm for HMM with duration to identify the most likely global path through hidden functional states given the DNA sequence. GeneMark and GeneMark.hmm programs are worth using in concert for analysing prokaryotic DNA sequences that arguably do not follow any exact mathematical model. The new extension of GeneMark using the FB algorithm was implemented in the software program GeneMark.fba. Given the DNA sequence, this program determines an a posteriori probability for each nucleotide to belong to coding or non-coding region. Also, for any open reading frame (ORF), it assigns a score defined as a probabilistic measure of all paths through hidden states that traverse the ORF as a coding region. The prediction accuracy of GeneMark.fba determined in our tests was compared favourably to the accuracy of the initial (standard) GeneMark program. Comparison to the prokaryotic GeneMark.hmm has also demonstrated a certain, yet species-specific, degree of improvement in raw gene detection, ie detection of correct reading frame (and stop codon). The accuracy of exact gene prediction, which is concerned about precise prediction of gene start (which in a prokaryotic genome unambiguously defines the reading frame and stop codon, thus, the whole protein product), still remains more accurate in GeneMarkS, which uses more elaborate HMM to specifically address this task.

Algorithms↗
PubMedDate not supplied

Modeling the diagnosis of stroke at two hospitals.

A comparison of five major categories of stroke in 651 patients revealed significant differences in the frequencies of diagnoses at the Beth Israel and Massachusetts General hospitals in Boston, Mass. (P less than 0.001 by chi-square test). To analyze these differences, we modeled the diagnostic process at each hospital with a Bayesian procedure and performed a crossover study in which each patient was rediagnosed by the model from the opposite hospital. The results indicate that the differences in the frequency of lacune and subarachnoid hemorrhage were associated with the patient population, whereas the differences in the frequency of embolism and atherothrombosis were associated with the diagnostic process. There was a marked difference in the use of arteriograms on the two stroke services, but no difference in morbidity or mortality. The modeling procedure described can be used to compare clinical processes when the allocation of patients is thought to be biased.

Bayes Theorem↗