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PubMed2006

Hypothesis testing and Bayesian estimation using a sigmoid Emax model applied to sparse dose-response designs.

Application of a sigmoid Emax model is described for the assessment of dose-response with designs containing a small number of doses (typically, three to six). The expanded model is a common Emax model with a power (Hill) parameter applied to dose and the ED50 parameter. The model will be evaluated following a strategy proposed by Bretz et al. (2005). The sigmoid Emax model is used to create several contrasts that have high power to detect an increasing trend from placebo. Alpha level for the hypothesis of no dose-response is controlled using multiple comparison methods applied to the p-values obtained from the contrasts. Subsequent to establishing drug activity, Bayesian methods are used to estimate the dose-response curve from the sparse dosing design. Bayesian estimation applied to the sigmoid model represents uncertainty in model selection that is missed when a single simpler model is selected from a collection of non-nested models. The goal is to base model selection on substantive knowledge and broad experience with dose-response relationships rather than criteria selected to ensure convergence of estimators. Bayesian estimation also addresses deficiencies in confidence intervals and tests derived from asymptotic-based maximum likelihood estimation when some parameters are poorly determined, which is typical for data from common dose-response designs.

Algorithms↗
PubMed2003

Are you my mother? Bayesian phylogenetic inference of recombination among putative parental strains.

Reconstructing evolutionary relationships using Bayesian inference has become increasingly popular due to the ability of Bayesian inference to handle complex models of evolution. In this review we concentrate on inference of recombination events between strains of viruses when these events are sporadic, ie rare relative to point mutations. Bayesian inference is especially attractive in the detection of recombination events because it allows for simultaneous inferences about the presence, number and location of crossover points and the identification of parental sequences. Current frequentist recombination identification falls into a sequential testing trap. The most likely parental sequences and crossover points are identified using the data and then the certainty of recombination is assessed conditional on this identification. After briefly outlining basic phylogenetic models, Bayesian inference and Markov chain Monte Carlo (MCMC) computation, we summarise three different approaches to recombination detection and discuss current challenges in applying Bayesian phylogenetic inference of recombination.

Algorithms↗
PubMed2006

Bayesian analysis of the linear reaction norm model with unknown covariates.

The reaction norm model is becoming a popular approach for the analysis of genotype x environment interactions. In a classical reaction norm model, the expression of a genotype in different environments is described as a linear function (a reaction norm) of an environmental gradient or value. An environmental value is typically defined as the mean performance of all genotypes in the environment, which is usually unknown. One approximation is to estimate the mean phenotypic performance in each environment and then treat these estimates as known covariates in the model. However, a more satisfactory alternative is to infer environmental values simultaneously with the other parameters of the model. This study describes a method and its Bayesian Markov Chain Monte Carlo implementation that makes this possible. Frequentist properties of the proposed method are tested in a simulation study. Estimates of parameters of interest agree well with the true values. Further, inferences about genetic parameters from the proposed method are similar to those derived from a reaction norm model using true environmental values. On the other hand, using phenotypic means as proxies for environmental values results in poor inferences.

Bayes Theorem↗
PubMed2001

A comparison of a Bayesian vs. a frequentist method for profiling hospital performance.

The objective of this study was to compare the classification of hospitals as outcomes outliers using a commonly implemented frequentist statistical approach vs. an implementation of Bayesian hierarchical statistical models, using 30-day hospital-level mortality rates for a cohort of acute myocardial infarction patients as a test case. For the frequentist approach, a logistic regression model was constructed to predict mortality. For each hospital, a risk-adj usted mortality rate was computed. Those hospitals whose 95% confidence interval, around the risk-adjusted mortality rate, excludes the mean mortality rate were classified as outliers. With the Bayesian hierarchical models, three factors could vary: the profile of the typical patient (low, medium or high risk), the extent to which the mortality rate for the typical patient departed from average, and the probability that the mortality rate was indeed different by the specified amount. The agreement between the two methods was compared for different patient profiles, threshold differences from the average and probabilities. Only marginal agreement was shown between the Bayesian and frequentist approaches. In only five of the 27 comparisons was the kappa statistic at least 0.40. The remaining 22 comparisons demonstrated only marginal agreement between the two methods. Within the Bayesian framework, hospital classification clearly depended on patient profile, threshold and probability of exceeding the threshold. These inconsistencies raise questions about the validity of current methods for classifying hospital performance, and suggest a need for urgent research into which methods are most meaningful to clinicians, managers and the general public.

Aged↗
PubMed2003

Bayesian two-compartment and classic single-compartment minimal models: comparison on insulin modified IVGTT and effect of experiment reduction.

Models describing plasma glucose and insulin concentration of an intravenous glucose tolerance test (IVGTT) allow a noninvasive cost-effective approach to estimate important indexes characterizing the efficiency of glucose-insulin control system, i.e., glucose effectiveness (S(G)) and insulin sensitivity (S(I)). To overcome some limitations of the classic single compartment minimal model (1CMM) of glucose kinetics , a two-compartment Bayesian minimal model (2CBMM) has been recently proposed for the standard IVGTT. This study aims to assess 2CBMM ability to describe the insulin-modified IVGTT (IM-IVGTT) which is the protocol of choice since it allows to study insulinopenic states. Both a full-length IM-IVGTT (240 min) as well as a reduced version (90 min) of it are studied. Results of the maximum a posteriori identification of IM-IVGTT (240 min) in 13 normals agree with those of standard IVGTT, i.e., a 42% decrease (P < 0.002) of S(G) and a 13% increase (P < 0.006) of S(I) with respect to ICMM. When identified from IM-IVGTT (90 min), 2CBMM not only provides S(G) and S(I) estimates 46% lower (P < 0.002) and 41% higher (P < 0.002) than 1CMM ones respectively, but also seems to overcome some limitations of the 240 min-based identification that probably arise because the minimal model is unable to properly account for the hyperglycemic hormonal response taking place in the second half of IM-IVGTT.

Bayes Theorem↗
PubMed2006

Variational learning for Gaussian mixture models.

This paper proposes a joint maximum likelihood and Bayesian methodology for estimating Gaussian mixture models. In Bayesian inference, the distributions of parameters are modeled, characterized by hyperparameters. In the case of Gaussian mixtures, the distributions of parameters are considered as Gaussian for the mean, Wishart for the covariance, and Dirichlet for the mixing probability. The learning task consists of estimating the hyperparameters characterizing these distributions. The integration in the parameter space is decoupled using an unsupervised variational methodology entitled variational expectation-maximization (VEM). This paper introduces a hyperparameter initialization procedure for the training algorithm. In the first stage, distributions of parameters resulting from successive runs of the expectation-maximization algorithm are formed. Afterward, maximum-likelihood estimators are applied to find appropriate initial values for the hyperparameters. The proposed initialization provides faster convergence, more accurate hyperparameter estimates, and better generalization for the VEM training algorithm. The proposed methodology is applied in blind signal detection and in color image segmentation.

Algorithms↗
PubMedDate not supplied

A general approach to mixed effects modeling of residual variances in generalized linear mixed models.

We propose a general Bayesian approach to heteroskedastic error modeling for generalized linear mixed models (GLMM) in which linked functions of conditional means and residual variances are specified as separate linear combinations of fixed and random effects. We focus on the linear mixed model (LMM) analysis of birth weight (BW) and the cumulative probit mixed model (CPMM) analysis of calving ease (CE). The deviance information criterion (DIC) was demonstrated to be useful in correctly choosing between homoskedastic and heteroskedastic error GLMM for both traits when data was generated according to a mixed model specification for both location parameters and residual variances. Heteroskedastic error LMM and CPMM were fitted, respectively, to BW and CE data on 8847 Italian Piemontese first parity dams in which residual variances were modeled as functions of fixed calf sex and random herd effects. The posterior mean residual variance for male calves was over 40% greater than that for female calves for both traits. Also, the posterior means of the standard deviation of the herd-specific variance ratios (relative to a unitary baseline) were estimated to be 0.60 +/- 0.09 for BW and 0.74 +/- 0.14 for CE. For both traits, the heteroskedastic error LMM and CPMM were chosen over their homoskedastic error counterparts based on DIC values.

Analysis of Variance↗
PubMed2002

Bayesian phylogenetics using an RNA substitution model applied to early mammalian evolution.

We study the phylogeny of the placental mammals using molecular data from all mitochondrial tRNAs and rRNAs of 54 species. We use probabilistic substitution models specific to evolution in base paired regions of RNA. A number of these models have been implemented in a new phylogenetic inference software package for carrying out maximum likelihood and Bayesian phylogenetic inferences. We describe our Bayesian phylogenetic method which uses a Markov chain Monte Carlo algorithm to provide samples from the posterior distribution of tree topologies. Our results show support for four primary mammalian clades, in agreement with recent studies of much larger data sets mainly comprising nuclear DNA. We discuss some issues arising when using Bayesian techniques on RNA sequence data.

Animals↗
PubMed2005

Hierarchical inverse Gaussian models and multiple testing: application to gene expression data.

Detecting differentially expressed genes in microarray experiments is a topic that has been well studied in the literature. Many hypothesis testing methods have been proposed that rely on strong distributional assumptions for the gene intensities. However, the shape of microarray data may vary substantially from one experiment to another, and model assumptions may be seriously violated in many cases. The literature on microarray data is mainly based on two distributions: the log-normal and the gamma distributions, that often appear to be effective when used in a Bayesian hierarchical framework. However, if a model that fits the data well in a global manner seems attractive, two points should be regarded with attention: the ability of the model to fit the tail of the observed distribution, and its robustness to a wrong specification of the model, in terms of error rates for the hypothesis tests. In order to focus on these aspects, we propose to use Bayesian models involving the inverse Gaussian distribution to describe gene expression data. We show that these models can be good competitors to the traditional Bayesian or random effect gamma or log-normal models in some situations. A multiple testing procedure is then proposed, based on an asymptotic property of the posterior probability of the one-sided alternative hypothesis. We show that the asymptotic property is well approximated for inverse Gaussian models, even when the number of observations available for each test is very small.

Journal Article↗
PubMed2003

Genetic analysis of longitudinal trajectory of clinical mastitis in first-lactation Norwegian cattle.

Clinical mastitis records for 36,178 first-lactation daughters of 245 Norwegian Cattle (NRF) sires were analyzed with a Bayesian longitudinal threshold model. For each cow, the period going from 30 d before calving to 300 d after calving was divided into 11 intervals of 30 d length each. Absence or presence of clinical mastitis within each interval was scored as "0" or "1", respectively. A Bayesian threshold model consisting of a set of explanatory variables plus Legendre polynomials on time of order four was used to describe the trajectory of liability to clinical mastitis. Heritability ranged between 0.07 and 0.13 before calving, from 0.04 to 0.15 during the first 270 d after calving, and increased sharply thereafter, as a consequence of the form of the polynomial. Genetic correlations between adjacent days were close to 1, and decreased when days were further apart. Most genetic correlations were moderate to high. A measure of probability of future daughters contracting clinical mastitis during lactation was computed for each sire. A typical curve had a peak near calving followed by a decrease thereafter. The best sires had a low peak around calving and a low expected probability of mastitis among daughters throughout lactation. Expected fraction of days without mastitis was derived from the probability curves and used for ranking of sires. Rank correlations with genetic evaluations of sires obtained from cross-sectional models were high. However, sire selection was affected markedly, especially at high selection intensity. An advantage of the longitudinal model for clinical mastitis is its ability to take multiple treatments and time aspects into account.

Animals↗
PubMed2006

Decision support tool to individualize cyclosporine dose in stable, long-term heart transplant recipients receiving metabolic inhibitors: overcoming limitations of cyclosporine C2 monitoring.

BACKGROUND: Monitoring of the 2-hour post-dose sample (C(2)) for cyclosporine (CsA) has gained favor; however, choosing a single-point surrogate marker of therapeutic effect for a drug with extensive pharmacokinetic variability is problematic and has limitations. METHODS: A Bayesian decision support tool was developed using published pharmacokinetic information implemented using ABBOTTBASE pharmacokinetic software. The model was evaluated in 47 stable heart transplant recipients who received concomitant administration of drugs known to inhibit CsA metabolism: diltiazem; ketoconazole; and a combination of diltiazem and ketoconazole. RESULTS: A 3-point feedback strategy with samples collected at 0, 1 and 2 hours after an oral CsA dose was used to predict area under the concentration-time curve in the first 12 hours post-dose (AUC(0-12)). In Group A, patients who received CsA alone showed a good correlation between observed and model-predicted CsA AUC(0-12) (r(2) = 0.871, p < 0.001, precision of 12%, accuracy of 13%). Furthermore, the Bayesian model provided acceptable predictions in patients who received CsA with metabolic inhibitors: Group B (diltiazem), r(2) = 0.791, p < 0.001, precision of 19%, accuracy of 22%; Group C (ketoconazole), r(2) = 0.761, p < 0.001, precision of 4%, accuracy of 12%; and Group D (diltiazem plus ketoconazole), r(2) = 0.818, p < 0.001, precision of 14%, accuracy of 17%. CONCLUSIONS: A Bayesian decision support tool is described that can predict CsA AUC(0-12) in a cohort of patients with variable CsA absorption who received metabolic inhibitors. Bayesian modeling offers a number of advantages over single point metrics that are used to adjust CsA dose and may provide another refinement to optimize CsA therapy.

Area Under Curve↗
PubMed2005

Bayesian error-in-variable survival model for the analysis of GeneChip arrays.

DNA microarrays in conjunction with statistical models may help gain a deeper understanding of the molecular basis for specific diseases. An intense area of research is concerned with the identification of genes related to particular phenotypes. The technology, however, is subject to various sources of error that may lead to expression readings that are substantially different from the true transcript levels. Few methods for microarray data analysis have accounted for measurement error in a substantial way and that is the purpose of this investigation. We describe a Bayesian error-in-variable model for the analysis of microarray data from a clinical study of patients with acute lymphoblastic leukemia. We focus in particular on the problem of identifying genes whose expression patterns are associated with duration of remission. This is a question of great practical interest since relapse is a major concern in the treatment of this disease. We explore the effects of ignoring the uncertainty in the expression estimates on the selection and ranking of genes.

Bayes Theorem↗
PubMed2006

Economic evaluation of health effects with preference imprecision.

The estimation of economic benefits of health effects through direct methods, such as contingent valuation, presents the problem of preference imprecision. This paper deals with this problem by proposing an elicitation method that allows the subject to state an interval for willingness to pay, without inducing any specific amount as a response. The paper also analyzes the effects of the context where changes in health occur on the associated imprecision level and the estimates, by comparing a situation without context with another in which effects are due to atmospheric pollution. The econometric modelling develops a Bayesian estimation method for censored intervals, which models the existing uncertainty between the lower and upper limits derived from the elicitation process. Results prove that data dispersion is significantly higher for the non-contextual scenario, and increases for the most severe symptoms.

Bayes Theorem↗
PubMed2006

On the association between statin and fracture: a Bayesian consideration.

BACKGROUND: The association between statin use and fracture risk is controversial, due to conflicting findings from previous studies. This study utilized the Bayesian approach to combine existing evidence and update the association with consideration of potential bias. METHODS: Data on the association between statin use and fracture incidence from 11 observational studies and 4 RCTs were synthesized by both empirical Bayesian analysis and fully Bayesian random-effects meta-analysis models. RESULTS: Empirical Bayesian analysis showed that statin use was associated with a reduction in hip fracture risk (OR=0.57, 95% credible interval (CrI): 0.46-0.71) and for non-vertebral (OR=0.69, 95% CrI, 0.63-0.74). These results were comparable with results from the fully Bayesian random-effects meta-analysis only for hip fracture (OR 0.56, 95% CrI, 0.42-0.73), but not for non-vertebral fracture (OR 0.77, 95% CrI, 0.58-1.03). The probability that statin use reduces fracture risk by at least 20% was 0.995 for hip fracture and 0.61 for non-vertebral fracture. Under the assumption that bias over-estimates the true OR by 20%, there is still a probability of 0.97 that statin use reduces hip fracture risk by at least 20%; however, the effect on non-vertebral fracture was much less robust with a probability of 0.27. CONCLUSIONS: Results of this Bayesian consideration are highly consistent with the hypothesis that statin use reduces hip fracture, but the association between statin use and non-vertebral fracture remains uncertain. The Bayesian approach presented here has the ability to help updating existing evidence as new data becomes available.

Bayes Theorem↗
PubMed2005

A Bayesian analysis of mouse infectivity data to evaluate the effectiveness of using ultraviolet light as a drinking water disinfectant.

Modelling disinfectant performance using Bayesian hierarchical methods can overcome problems with traditional methods and lead to improved estimates. Animal and cell-culture assays are used to estimate the degree of inactivation of a microorganism produced by a given disinfectant dose. Assay data traditionally are analyzed with logistic model or most probable number (MPN) method. These methods are limited particularly when assays show all (or no) animals or cells to be infected-estimates are reported as greater than (or less than) a measurement limit (i.e., censored data). The proposed Bayesian approach (1) properly models the propagation of uncertainty through the data analysis/modelling process, resulting in reduced model uncertainty, and (2) uses appropriate probability distribution models for the response variables, avoiding the censored data problem and more accurately describing statistical error when estimating dose-response behavior. This paper applies the Bayesian hierarchical models to logistic and MPN data from published papers for the ultraviolet (UV) inactivation of Cryptosporidium. Results are compared to those from three alternative models. The Bayesian model estimates a significantly lower UV dose for a given level of Cryptosporidium inactivation than the alternative models, due mainly to the reduced model uncertainty.

Animals↗
PubMed2006

Bringing metabolic networks to life: integration of kinetic, metabolic, and proteomic data.

BACKGROUND: Translating a known metabolic network into a dynamic model requires reasonable guesses of all enzyme parameters. In Bayesian parameter estimation, model parameters are described by a posterior probability distribution, which scores the potential parameter sets, showing how well each of them agrees with the data and with the prior assumptions made. RESULTS: We compute posterior distributions of kinetic parameters within a Bayesian framework, based on integration of kinetic, thermodynamic, metabolic, and proteomic data. The structure of the metabolic system (i.e., stoichiometries and enzyme regulation) needs to be known, and the reactions are modelled by convenience kinetics with thermodynamically independent parameters. The parameter posterior is computed in two separate steps: a first posterior summarises the available data on enzyme kinetic parameters; an improved second posterior is obtained by integrating metabolic fluxes, concentrations, and enzyme concentrations for one or more steady states. The data can be heterogeneous, incomplete, and uncertain, and the posterior is approximated by a multivariate log-normal distribution. We apply the method to a model of the threonine synthesis pathway: the integration of metabolic data has little effect on the marginal posterior distributions of individual model parameters. Nevertheless, it leads to strong correlations between the parameters in the joint posterior distribution, which greatly improve the model predictions by the following Monte-Carlo simulations. CONCLUSION: We present a standardised method to translate metabolic networks into dynamic models. To determine the model parameters, evidence from various experimental data is combined and weighted using Bayesian parameter estimation. The resulting posterior parameter distribution describes a statistical ensemble of parameter sets; the parameter variances and correlations can account for missing knowledge, measurement uncertainties, or biological variability. The posterior distribution can be used to sample model instances and to obtain probabilistic statements about the model's dynamic behaviour.

Bayes Theorem↗
PubMed2002

Minimal model S(I)=0 problem in NIDDM subjects: nonzero Bayesian estimates with credible confidence intervals.

The minimal model of glucose kinetics, in conjunction with an insulin-modified intravenous glucose tolerance test, is widely used to estimate insulin sensitivity (S(I)). Parameter estimation usually resorts to nonlinear least squares (NLS), which provides a point estimate, and its precision is expressed as a standard deviation. Applied to type 2 diabetic subjects, NLS implemented in MINMOD software often predicts S(I)=0 (the so-called "zero" S(I) problem), whereas general purpose modeling software systems, e.g., SAAM II, provide a very small S(I) but with a very large uncertainty, which produces unrealistic negative values in the confidence interval. To overcome these difficulties, in this article we resort to Bayesian parameter estimation implemented by a Markov chain Monte Carlo (MCMC) method. This approach provides in each individual the S(I) a posteriori probability density function, from which a point estimate and its confidence interval can be determined. Although NLS results are not acceptable in four out of the ten studied subjects, Bayes estimation implemented by MCMC is always able to determine a nonzero point estimate of S(I) together with a credible confidence interval. This Bayesian approach should prove useful in reanalyzing large databases of epidemiological studies.

Bayes Theorem↗
PubMed2004

A comparison of learning algorithms for Bayesian networks: a case study based on data from an emergency medical service.

Due to the uncertainty of many of the factors that influence the performance of an emergency medical service, we propose using Bayesian networks to model this kind of system. We use different algorithms for learning Bayesian networks in order to build several models, from the hospital manager's point of view, and apply them to the specific case of the emergency service of a Spanish hospital. This first study of a real problem includes preliminary data processing, the experiments carried out, the comparison of the algorithms from different perspectives, and some potential uses of Bayesian networks for management problems in the health service.

Algorithms↗