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Results for “Bayesian analysis”

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At least 811 records · Page 45Linked to original sources

PubMed1999

Application of Bayesian inference to fMRI data analysis.

The methods of Bayesian statistics are applied to the analysis of fMRI data. Three specific models are examined. The first is the familiar linear model with white Gaussian noise. In this section, the Jeffreys' Rule for noninformative prior distributions is stated and it is shown how the posterior distribution may be used to infer activation in individual pixels. Next, linear time-invariant (LTI) systems are introduced as an example of statistical models with nonlinear parameters. It is shown that the Bayesian approach can lead to quite complex bimodal distributions of the parameters when the specific case of a delta function response with a spatially varying delay is analyzed. Finally, a linear model with auto-regressive noise is discussed as an alternative to that with uncorrelated white Gaussian noise. The analysis isolates those pixels that have significant temporal correlation under the model. It is shown that the number of pixels that have a significantly large auto-regression parameter is dependent on the terms used to account for confounding effects.

Artifacts↗

PubMed1997

Bayesian design and analysis of two x two factorial clinical trials.

The 2 x 2 factorial design has been advocated for improving the efficiency of clinical trials. Most such trials are designed on the assumption that there is no interaction between the levels of the factors and outcome. This assumption is often problematic, however, because interactions are usually possible in clinical trials and the sample sizes often used provide little power in testing for interactions. We consider the use of Bayesian methods for the design and analysis of 2 x 2 factorial clinical trials. This approach avoids the need to dichotomize one's assumptions that interactions either do or do not exist and provides a flexible approach to the design and analysis of such clinical trials. Exact results are developed for balanced factorial designs with normal response. Approximations are then presented for factorial designs based on the logistic model for binary response or the proportional hazards model for time-to-event data. The resulting approximate posterior distributions are normal and hence no extensive computations are required. Suggestions for specification of prior distributions are presented.

Antineoplastic Agents, Phytogenic↗

PubMed2002

Bayesian framework for least-squares support vector machine classifiers, gaussian processes, and kernel Fisher discriminant analysis.

The Bayesian evidence framework has been successfully applied to the design of multilayer perceptrons (MLPs) in the work of MacKay. Nevertheless, the training of MLPs suffers from drawbacks like the nonconvex optimization problem and the choice of the number of hidden units. In support vector machines (SVMs) for classification, as introduced by Vapnik, a nonlinear decision boundary is obtained by mapping the input vector first in a nonlinear way to a high-dimensional kernel-induced feature space in which a linear large margin classifier is constructed. Practical expressions are formulated in the dual space in terms of the related kernel function, and the solution follows from a (convex) quadratic programming (QP) problem. In least-squares SVMs (LS-SVMs), the SVM problem formulation is modified by introducing a least-squares cost function and equality instead of inequality constraints, and the solution follows from a linear system in the dual space. Implicitly, the least-squares formulation corresponds to a regression formulation and is also related to kernel Fisher discriminant analysis. The least-squares regression formulation has advantages for deriving analytic expressions in a Bayesian evidence framework, in contrast to the classification formulations used, for example, in gaussian processes (GPs). The LS-SVM formulation has clear primal-dual interpretations, and without the bias term, one explicitly constructs a model that yields the same expressions as have been obtained with GPs for regression. In this article, the Bayesian evidence framework is combined with the LS-SVM classifier formulation. Starting from the feature space formulation, analytic expressions are obtained in the dual space on the different levels of Bayesian inference, while posterior class probabilities are obtained by marginalizing over the model parameters. Empirical results obtained on 10 public domain data sets show that the LS-SVM classifier designed within the Bayesian evidence framework consistently yields good generalization performances.

Artificial Intelligence↗

PubMedDate not supplied

A comparison of Bayesian and maximum likelihood methods to determine the performance of a point of care test for Helicobacter pylori in the office setting.

OBJECTIVE: Evaluations of point of care tests (PCT) are often hampered by a lack of appropriate gold standards. This study aimed to compare the results of a Bayesian statistical analysis and a maximum likelihood method to evaluate the performance of a PCT for Helicobacter pylori in primary care. METHODS: The Helisal Rapid Blood Test (Cortecs Diagnostics) was performed in 311 patients from 6 primary care centers, and a concurrent venous sample was taken for 2 enzyme-linked immunosorbent assays (ELISA) performed at the laboratory, blind to the PCT result. The Bayesian analysis was conducted using Markov Chain Monte Carlo methods (WinBUGS). The performance characteristics of the PCT and the 2 ELISA tests were estimated together with 95% credible intervals (95% CIs). RESULTS: The estimate of prevalence of H. pylori in this population was 64% (95% CI, 59% to 70%), the sensitivity and specificity of the PCT were 89% (84% to 94%) and 84% (77% to 91%), respectively (likelihood ratios positive 5.6, negative 0.13). The equivalent maximum likelihood results were prevalence, 65%; sensitivity, 90%; and specificity, 83%. CONCLUSIONS: The Helisal Rapid Blood Test performed as well as laboratory-based ELISA tests in this cohort of patients. The Bayesian analysis and the maximum likelihood method gave similar results, the Bayesian method also simultaneously estimating 95% CIs.

Aged↗

PubMed2006

A Bayesian design and analysis for dose-response using informative prior information.

We wish to use prior information on an existing drug in the design and analysis of a dose-response study for a new drug candidate within the same pharmacological class. Using the Bayesian methodology, this prior information can be used quantitatively and the randomization can be weighted in favor of the new compound, where there is less information. An Emax model is used to describe the dose-response of the existing drug. The estimates from this model are used to provide informative prior information used for the design and analysis of the new study to establish the relative potency between the new compound and the existing drug therapy. The assumption is made that the data from previous trials and the new study are exchangeable. The impact of departures from this assumption can be quantified through simulations and by assessing the operating characteristics of various scenarios. Simulations show that relatively modest sample sizes can yield informative results about the magnitude of the relative potency using this approach. The operating characteristics are good when assessing model estimates against clinically important changes in relative potency.

Algorithms↗

PubMed2002

Multiscale and Bayesian approaches to data analysis in genomics high-throughput screening.

Tremendous amounts of data are produced by high-throughput screening methods currently employed in drug discovery and product development. A typical cDNA microarray or oligonucleotide-based gene chip experiment easily generates over 10,000 data points for each array or chip. The challenge of inferring meaningful information is formidable given the size and number of these datasets. This paper reviews the current status of statistical tools available for gene expression analysis, with emphasis on Bayesian approaches and multiscale wavelet filtering. Fundamental concepts of Bayesian and multiscale modeling are discussed from the perspective of their potential to address important issues related to the analysis of gene expression data, such as the fact that genomic data often have non-Gaussian distributions and feature localization and multiple scales in both frequency and measurement dimension. Recent publications in these areas are reviewed. Wavelet filtering and the advantages of multiscale methods are demonstrated by application to publicly available gene expression data from the National Cancer Institute (NCI). Multiscale methods, including multiscale principal component analysis (MSPCA), are applied to extract gene subsets and to visualize data in multidimensions for comparisons. Similarity in cell lines and gene selection are effectively visualized and quantitatively compared.

Animals↗

PubMed1999

Bayesian design and analysis of active control clinical trials.

We consider the design and analysis of active control clinical trials, i.e., clinical trials comparing an experimental treatment E to a control treatment C considered to be effective. Direct comparison of E to placebo P, or no treatment, is sometimes ethically unacceptable. Much discussion of the design and analysis of such clinical trials has focused on whether the comparison of E to C should be based on a test of the null hypothesis of equivalence, on a test of a nonnull hypothesis that the difference is of some minimally medically important size delta, or on one or two-sided confidence intervals. These approaches are essentially the same for study planning. They all suffer from arbitrariness in specifying the size of the difference delta that must be excluded. We propose an alternative Bayesian approach to the design and analysis of active control trials. We derive the posterior probability that E is superior to P or that E is at least k% as good as C and that C is more effective than P. We also derive approximations for use with logistic and proportional hazard models. Selection of prior distributions is discussed, and results are illustrated using data from an active control trial of a drug for the treatment of unstable angina.

Angina, Unstable↗

PubMed2005

A hierarchical Bayesian birth cohort analysis from incomplete registry data: evaluating the trends in the age of onset of insulin-dependent diabetes mellitus (T1DM).

Childhood diabetes is one of the major non-communicable diseases in children under 15 years of age. It requires a life-long insulin treatment and may lead to serious complications. Along with the worldwide increase in the incidence several countries have recently reported a decreasing trend in the age of onset of the disease. The aim of this study is to analyse long-term data on the incidence of the childhood diabetes in Finland from the birth cohorts perspective. The annual incidence data were available for the period 1965--1996 which translates into 1951--1996 birth cohorts. Hence the data consist of completely and partially observed cohorts. Bayesian modelling was employed in the analysis. Several different priors and cohort combinations were tried in order to determine the sensitivity of the results. The cumulative birth cohort incidence of diabetes was determined to have an increasing average annual trend of 2.5 per cent. Although the average birth cohort-specific age of onset was estimated to have decreased slightly over the years of observation, the trend could be a result of random variation.

Adolescent↗

PubMed1999

The diagnostic power of motor unit potential analysis: an objective bayesian approach.

The notion of a "myopathic" or "neuropathic" electromyogram (EMG) is usually based on qualitative visual and acoustical impressions. Conventional quantification defines abnormality but not diagnosis, which requires interpretation of patterns of change. Discriminant analysis is a model for this multivariate decision. It tells how probable it is that a motor unit potential (MUP) comes from a normal, myopathic, or neuropathic muscle. Accumulation of single MUP information by a sequential Bayesian algorithm produced diagnostic probabilities above 0.95 in 91% of all muscles (223 biceps brachii muscles from 80 patients with motoneuron disorders, 56 patients with neuropathies, 71 patients with myopathies, and 34 controls). Two muscles from patients with neurogenic disorders were misclassified as "myopathic." Misclassification was more frequent only in myositis (4 of 28 muscles) and in oculopharyngeal muscular dystrophy (2 of 4 muscles). MUP discriminant classification was as sensitive as, and more specific than, conventional quantitative EMG, which discriminated between myopathic and neuropathic in only 22% of the muscles. This rate was 59% for discriminant analysis. As a knowledge-based expert system, MUP discriminant analysis successfully distinguishes between myopathic, neuropathic, and unclassifiable MUP samples. It discloses more information than conventional quantitative MUP analysis.

Action Potentials↗

PubMed1993

On the use of Bayesian probability theory for analysis of exponential decay data: an example taken from intravoxel incoherent motion experiments.

Traditionally, the method of nonlinear least squares (NLLS) analysis has been used to estimate the parameters obtained from exponential decay data. In this study, we evaluated the use of Bayesian probability theory to analyze such data; specifically, that resulting from intravoxel incoherent motion NMR experiments. Analysis was done both on simulated data to which different amounts of Gaussian noise had been added and on actual data derived from rat brain. On simulated data, Bayesian analysis performed substantially better than NLLS under conditions of relatively low signal-to-noise ratio. Bayesian probability theory also offers the advantages of: a) not requiring initial parameter estimates and hence not being susceptible to errors due to incorrect starting values and b) providing a much better representation of the uncertainty in the parameter estimates in the form of the probability density function. Bayesian analysis of rat brain data was used to demonstrate the shape of the probability density function from data sets of different quality.

Animals↗

PubMed2001

Estimating the Bayesian loss function. A conjoint analysis approach.

Current health economic literature does not provide clear guidelines on how uncertainty around cost-effectiveness estimates should be incorporated into economic decision models. Bayesian analysis is a promising alternative to classical statistics for incorporating uncertainty in economic analysis. Estimating a loss function that relates outcomes to societal welfare is a key component of Bayesian decision analysis. Health economists commonly compute the loss function based on the quality-adjusted life-years associated with each outcome. However, if welfare economics is adopted as the theoretical foundation of the analysis, a loss function based in cost-benefit analysis (CBA) may be more appropriate. CBA has not found wide use in health economics due to practical issues associated with estimating such a loss function. In this paper, we present a method based in conjoint analysis for estimating the CBA loss function that can be applied in practice. We illustrate the use of the methodology using data from a pilot study.

Acute Disease↗

PubMed2005

Inequality constrained analysis of variance: a Bayesian approach.

Researchers often have one or more theories or expectations with respect to the outcome of their empirical research. When researchers talk about the expected relations between variables if a certain theory is correct, their statements are often in terms of one or more parameters expected to be larger or smaller than one or more other parameters. Stated otherwise, their statements are often formulated using inequality constraints. In this article, a Bayesian approach to evaluate analysis of variance or analysis of covariance models with inequality constraints on the (adjusted) means is presented. This evaluation contains two issues: estimation of the parameters given the restrictions using the Gibbs sampler and model selection using Bayes factors in the case of competing theories. The article concludes with two illustrations: a one-way analysis of covariance and an analysis of a three-way table of ordered means.

Analysis of Variance↗

PubMed2005

BGX: a fully Bayesian integrated approach to the analysis of Affymetrix GeneChip data.

We present Bayesian hierarchical models for the analysis of Affymetrix GeneChip data. The approach we take differs from other available approaches in two fundamental aspects. Firstly, we aim to integrate all processing steps of the raw data in a common statistically coherent framework, allowing all components and thus associated errors to be considered simultaneously. Secondly, inference is based on the full posterior distribution of gene expression indices and derived quantities, such as fold changes or ranks, rather than on single point estimates. Measures of uncertainty on these quantities are thus available. The models presented represent the first building block for integrated Bayesian Analysis of Affymetrix GeneChip data: the models take into account additive as well as multiplicative error, gene expression levels are estimated using perfect match and a fraction of mismatch probes and are modeled on the log scale. Background correction is incorporated by modeling true signal and cross-hybridization explicitly, and a need for further normalization is considerably reduced by allowing for array-specific distributions of nonspecific hybridization. When replicate arrays are available for a condition, posterior distributions of condition-specific gene expression indices are estimated directly, by a simultaneous consideration of replicate probe sets, avoiding averaging over estimates obtained from individual replicate arrays. The performance of the Bayesian model is compared to that of standard available point estimate methods on subsets of the well known GeneLogic and Affymetrix spike-in data. The Bayesian model is found to perform well and the integrated procedure presented appears to hold considerable promise for further development.

Bayes Theorem↗

PubMed2006

Sparse Bayesian kernel survival analysis for modeling the growth domain of microbial pathogens.

Survival analysis is a branch of statistics concerned with the time elapsing before "failure," with diverse applications in medical statistics and the analysis of the reliability of electrical or mechanical components. We introduce a parametric accelerated life survival analysis model based on kernel learning methods that, at least in principal, is able to learn arbitrary dependencies between a vector of explanatory variables and the scale of the distribution of survival times. The proposed kernel survival analysis method is then used to model the growth domain of Clostridium botulinum, the food processing and storage conditions permitting the growth of this foodborne microbial pathogen, leading to the production of the neurotoxin responsible for botulism. A Bayesian training procedure, based on the evidence framework, is used for model selection and to provide a credible interval on model predictions. The kernel survival analysis models are found to be more accurate than models based on more traditional survival analysis techniques but also suggest a risk assessment of the foodborne botulism hazard would benefit from the collection of additional data.

Artificial Intelligence↗

PubMed2004

Bayesian integrated functional analysis of microarray data.

MOTIVATION: The statistical analysis of microarray data usually proceeds in a sequential manner, with the output of the previous step always serving as the input of the next one. However, the methods currently used in such analyses do not properly account for the fact that the intermediate results may not always be correct, then leading to cumulating error in the inferences drawn based on such steps. RESULTS: Here we show that, by an application of hierarchical Bayesian methodology, this sequential procedure can be replaced by a single joint analysis, while systematically accounting for the uncertainties in this process. Moreover, we can also integrate relevant functional information available from databases into such an analysis, thereby increasing the reliability of the biological conclusions that are drawn. We illustrate these points by analysing real data and by showing that the genes can be divided into categories of interest, with the defining characteristic depending on the biological question that is considered. We contend that the proposed method has advantages at two levels. First, there are gains in the statistical and biological results from the analysis of this particular dataset. Second, it opens up new possibilities in analysing microarray data in general.

Algorithms↗

PubMed2002

A Bayesian fixed effects analysis of the Mantel-Haenszel model applied to meta-analysis.

When performing a meta analysis, it is often necessary to combine results from several 2 x 2 contingency tables. The Mantel-Haenszel model assumes a common measure of association between the treatment and outcome variables across the tables. A Bayesian method is described for drawing inferences regarding the measure of association, for checking the plausibility of the Mantel-Haenszel model, and for drawing inferences regarding the success rates for the individual studies. While the methodology is readily extendable to random effects models, a fixed effects approach avoids the complex statistical modelling of a mixture distribution which is required for the good application of random effects models.

Anti-Bacterial Agents↗

PubMedDate not supplied

A hierarchical Bayesian meta-analysis of randomised clinical trials of drug-eluting stents.

BACKGROUND: Drug-eluting stents (DES) are associated with lower restenosis rates than bare-metal stents (BMS), but the benefits and safety of the new devices have not been systematically quantified across different trials. We undertook a meta-analysis of randomised trials comparing BMS and stents eluting sirolimus or paclitaxel. METHODS: A systematic literature search aimed to identify all randomised clinical trials with 6-12 months of clinical follow-up. Results were pooled by a hierarchical Bayesian random-effects model with prespecified stratification for drug and the presence of carrier polymer. The primary outcomes examined were rates of death, myocardial infarction, target-lesion revascularisation, major adverse cardiac events (death, myocardial infarction, and target-vessel revascularisation), and angiographic restenosis. FINDINGS: We identified 11 eligible trials involving 5103 patients. The pooled mortality rates were low for both DES and BMS with no evidence of any difference between them (odds ratio 1.11 [95% credible interval 0.61-2.06]). Pooled rates of myocardial infarction showed no between-group difference (0.92 [0.65-1.25]). The rate of major adverse cardiac events was 7.8% with DES and 16.4% with BMS (0.42 [0.32-0.53]), and the angiographic restenosis rates were also lower for DES (8.9% vs 29.3%; 0.18 [0.06-0.40]). The pooled rates of major adverse cardiac events for each DES type and the respective BMS were: for sirolimus, 6.8% versus 21.0% (0.28 [0.17-0.41]); for polymer-based paclitaxel 8.7% versus 16.7% (0.47 [0.25-0.71]); and for non-polymer-based paclitaxel 7.7% versus 9.5% (0.64 [0.42-1.00]). We did not observe higher rates of edge restenosis, stent thrombosis, or late incomplete stent apposition with DES, although the credible intervals were wide. INTERPRETATION: Sirolimus-eluting and polymeric paclitaxel-eluting stents are effective at decreasing rates of angiographic restenosis and major adverse cardiac events compared with BMS. However, there is no evidence that they affect mortality or myocardial-infarction rates. They also appear to be safe in the short to medium term, although definitive conclusions are not possible. Larger studies with longer follow-up are needed to define better the role of these new devices.

Angioplasty, Balloon, Coronary↗

PubMed2006

Bayesian item fit analysis for unidimensional item response theory models.

Assessing item fit for unidimensional item response theory models for dichotomous items has always been an issue of enormous interest, but there exists no unanimously agreed item fit diagnostic for these models, and hence there is room for further investigation of the area. This paper employs the posterior predictive model-checking method, a popular Bayesian model-checking tool, to examine item fit for the above-mentioned models. An item fit plot, comparing the observed and predicted proportion-correct scores of examinees with different raw scores, is suggested. This paper also suggests how to obtain posterior predictive p-values (which are natural Bayesian p-values) for the item fit statistics of Orlando and Thissen that summarize numerically the information in the above-mentioned item fit plots. A number of simulation studies and a real data application demonstrate the effectiveness of the suggested item fit diagnostics. The suggested techniques seem to have adequate power and reasonable Type I error rate, and psychometricians will find them promising.

Algorithms↗