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PubMed1999

A new method for spectral decomposition using a bilinear Bayesian approach.

A frequent problem in analysis is the need to find two matrices, closely related to the underlying measurement process, which when multiplied together reproduce the matrix of data points. Such problems arise throughout science, for example, in imaging where both the calibration of the sensor and the true scene may be unknown and in localized spectroscopy where multiple components may be present in varying amounts in any spectrum. Since both matrices are unknown, such a decomposition is a bilinear problem. We report here a solution to this problem for the case in which the decomposition results in matrices with elements drawn from positive additive distributions. We demonstrate the power of the methodology on chemical shift images (CSI). The new method, Bayesian spectral decomposition (BSD), reduces the CSI data to a small number of basis spectra together with their localized amplitudes. We apply this new algorithm to a 19F nonlocalized study of the catabolism of 5-fluorouracil in human liver, 31P CSI studies of a human head and calf muscle, and simulations which show its strengths and limitations. In all cases, the dataset, viewed as a matrix with rows containing the individual NMR spectra, results from the multiplication of a matrix of generally nonorthogonal basis spectra (the spectral matrix) by a matrix of the amplitudes of each basis spectrum in the the individual voxels (the amplitude matrix). The results show that BSD can simultaneously determine both the basis spectra and their distribution. In principle, BSD should solve this bilinear problem for any dataset which results from multiplication of matrices representing positive additive distributions if the data overdetermine the solutions.

Adenosine Triphosphate↗

PubMed2002

A Bayesian re-assessment of two Phase II trials of gemcitabine in metastatic nasopharyngeal cancer.

The Simon two-stage minimax design is a popular statistical design used in Phase II clinical trials. The analysis of the data arising from the design typically involves the use of frequentist statistics. This paper presents an alternative, Bayesian, approach to the design and analysis of Phase II clinical trials. In particular, we consider how a Bayesian approach could have affected the design, analysis and interpretation of two parallel Phase II trials of the National Cancer Centre Singapore, on the activity of gemcitabine in chemotherapy-naïve and in previously treated patients with metastatic nasopharyngeal carcinoma. We begin by explaining the Bayesian methodology and contrasting it with the frequentist approach. We then carry out a Bayesian analysis of the trial results. The conclusions drawn using the Bayesian approach were in general agreement with those obtained from the frequentist analysis. However they had the advantage of allowing for different and potentially more useful interpretations to be made regarding the trial results, as well as for the incorporation of external sources of information. In particular, using a Bayesian trial design, we were able to take into account the results of the parallel trial results when deciding whether to continue each trial beyond the interim stage.

Antimetabolites, Antineoplastic↗

PubMed2004

Bayesian model accounting for within-class biological variability in Serial Analysis of Gene Expression (SAGE).

BACKGROUND: An important challenge for transcript counting methods such as Serial Analysis of Gene Expression (SAGE), "Digital Northern" or Massively Parallel Signature Sequencing (MPSS), is to carry out statistical analyses that account for the within-class variability, i.e., variability due to the intrinsic biological differences among sampled individuals of the same class, and not only variability due to technical sampling error. RESULTS: We introduce a Bayesian model that accounts for the within-class variability by means of mixture distribution. We show that the previously available approaches of aggregation in pools ("pseudo-libraries") and the Beta-Binomial model, are particular cases of the mixture model. We illustrate our method with a brain tumor vs. normal comparison using SAGE data from public databases. We show examples of tags regarded as differentially expressed with high significance if the within-class variability is ignored, but clearly not so significant if one accounts for it. CONCLUSION: Using available information about biological replicates, one can transform a list of candidate transcripts showing differential expression to a more reliable one. Our method is freely available, under GPL/GNU copyleft, through a user friendly web-based on-line tool or as R language scripts at supplemental web-site.

Astrocytoma↗

PubMed2006

Insights into protein-protein interfaces using a Bayesian network prediction method.

Identifying the interface between two interacting proteins provides important clues to the function of a protein, and is becoming increasing relevant to drug discovery. Here, surface patch analysis was combined with a Bayesian network to predict protein-protein binding sites with a success rate of 82% on a benchmark dataset of 180 proteins, improving by 6% on previous work and well above the 36% that would be achieved by a random method. A comparable success rate was achieved even when evolutionary information was missing, a further improvement on our previous method which was unable to handle incomplete data automatically. In a case study of the Mog1p family, we showed that our Bayesian network method can aid the prediction of previously uncharacterised binding sites and provide important clues to protein function. On Mog1p itself a putative binding site involved in the SLN1-SKN7 signal transduction pathway was detected, as was a Ran binding site, previously characterized solely by conservation studies, even though our automated method operated without using homologous proteins. On the remaining members of the family (two structural genomics targets, and a protein involved in the photosystem II complex in higher plants) we identified novel binding sites with little correspondence to those on Mog1p. These results suggest that members of the Mog1p family bind to different proteins and probably have different functions despite sharing the same overall fold. We also demonstrated the applicability of our method to drug discovery efforts by successfully locating a number of binding sites involved in the protein-protein interaction network of papilloma virus infection. In a separate study, we attempted to distinguish between the two types of binding site, obligate and non-obligate, within our dataset using a second Bayesian network. This proved difficult although some separation was achieved on the basis of patch size, electrostatic potential and conservation. Such was the similarity between the two interacting patch types, we were able to use obligate binding site properties to predict the location of non-obligate binding sites and vice versa.

Animals↗

PubMed2004

Reconstruction of gene networks using Bayesian learning and manipulation experiments.

MOTIVATION: The analysis of high-throughput experimental data, for example from microarray experiments, is currently seen as a promising way of finding regulatory relationships between genes. Bayesian networks have been suggested for learning gene regulatory networks from observational data. Not all causal relationships can be inferred from correlation data alone. Often several equivalent but different directed graphs explain the data equally well. Intervention experiments where genes are manipulated can help to narrow down the range of possible networks. RESULTS: We describe an active learning algorithm that suggests an optimized sequence of intervention experiments. Simulation experiments show that our selection scheme is better than an unguided choice of interventions in learning the correct network and compares favorably in running time and results with methods based on value of information calculations.

Algorithms↗

PubMed2006

A deformable grid-matching approach for microarray images.

A fundamental step of microarray image analysis is the detection of the grid structure for the accurate location of each spot, representing the state of a given gene in a particular experimental condition. This step is known as gridding and belongs to the class of deformable grid matching problems which are well known in literature. Most of the available microarray gridding approaches require human intervention; for example, to specify landmarks, some points in the spot grid, or even to precisely locate individual spots. Automating this part of the process can allow high throughput analysis. This paper focuses on the development of a fully automated procedure for the problem of automatic microarray gridding. It is grounded on the Bayesian paradigm and on image analysis techniques. The procedure has two main steps. The first step, based on the Radon transform, is aimed at generating a grid hypothesis; the second step accounts for local grid deformations. The accuracy and properties of the procedure are quantitatively assessed over a set of synthetic and real images; the results are compared with well-known methods available from the literature.

Algorithms↗

PubMed1998

Mining biomedical time series by combining structural analysis and temporal abstractions.

This paper describes the combination of Structural Time Series analysis and Temporal Abstractions for the interpretation of data coming from home monitoring of diabetic patients. Blood Glucose data are analyzed by a novel Bayesian technique for time series analysis. The results obtained are post-processed using Temporal Abstractions in order to extract knowledge that can be exploited "at the point of use" from physicians. The proposed data analysis procedure can be viewed as a Knowledge Discovery in Data Base process that is applied to time-varying data. The work here described is part of a Web-based telemedicine system for the management of Insulin Dependent Diabetes Mellitus patients, called T-IDDM.

Algorithms↗

PubMed1989

Comparison of Bayesian with group sequential methods for monitoring clinical trials.

We describe some problems with applying methods based on classical sequential analysis to monitoring clinical trials. A Bayesian method is developed and the boundaries are compared with frequentist schemes. For the examples chosen, the Bayesian boundaries can be quite similar to those obtained from Pocock and O'Brien and Fleming (OBF) rules, depending on the choice of prior distribution. They converge less rapidly than OBF's but more rapidly than Pocock's. In general the Bayesian methods provide the same desirable features as frequentist methods, without sacrificing flexibility and simplicity of interpretation.

Bayes Theorem↗

PubMed1998

Flexible Bayesian modelling for survival data.

The analysis of failure time data often involves two strong assumptions. The proportional hazards assumption postulates that hazard rates corresponding to different levels of explanatory variables are proportional. The additive effects assumption specifies that the effect associated with a particular explanatory variable does not depend on the levels of other explanatory variables. A hierarchical Bayes model is presented, under which both assumptions are relaxed. In particular, time-dependent covariate effects are explicitly modelled, and the additivity of effects is relaxed through the use of a modified neural network structure. The hierarchical nature of the model is useful in that it parsimoniously penalizes violations of the two assumptions, with the strength of the penalty being determined by the data.

Bayes Theorem↗

PubMed2005

The Bradford Hill considerations on causality: a counterfactual perspective.

Bradford Hill's considerations published in 1965 had an enormous influence on attempts to separate causal from non-causal explanations of observed associations. These considerations were often applied as a checklist of criteria, although they were by no means intended to be used in this way by Hill himself. Hill, however, avoided defining explicitly what he meant by "causal effect". This paper provides a fresh point of view on Hill's considerations from the perspective of counterfactual causality. I argue that counterfactual arguments strongly contribute to the question of when to apply the Hill considerations. Some of the considerations, however, involve many counterfactuals in a broader causal system, and their heuristic value decreases as the complexity of a system increases; the danger of misapplying them can be high. The impacts of these insights for study design and data analysis are discussed. The key analysis tool to assess the applicability of Hill's considerations is multiple bias modelling (Bayesian methods and Monte Carlo sensitivity analysis); these methods should be used much more frequently.

Journal Article↗

PubMed2005

Estimation of individual admixture: analytical and study design considerations.

The genome of an admixed individual represents a mixture of alleles from different ancestries. In the United States, the two largest minority groups, African-Americans and Hispanics, are both admixed. An understanding of the admixture proportion at an individual level (individual admixture, or IA) is valuable for both population geneticists and epidemiologists who conduct case-control association studies in these groups. Here we present an extension of a previously described frequentist (maximum likelihood or ML) approach to estimate individual admixture that allows for uncertainty in ancestral allele frequencies. We compare this approach both to prior partial likelihood based methods as well as more recently described Bayesian MCMC methods. Our full ML method demonstrates increased robustness when compared to an existing partial ML approach. Simulations also suggest that this frequentist estimator achieves similar efficiency, measured by the mean squared error criterion, as Bayesian methods but requires just a fraction of the computational time to produce point estimates, allowing for extensive analysis (e.g., simulations) not possible by Bayesian methods. Our simulation results demonstrate that inclusion of ancestral populations or their surrogates in the analysis is required by any method of IA estimation to obtain reasonable results.

Black or African American↗

PubMed2000

Bayesian estimation of range for microsatellite loci.

Microsatellite loci have become important in population genetics because of their high level of polymorphism in natural populations, very frequent occurrence throughout the genome, and apparently high mutation rate. Observed repeat numbers (alleles size) in natural populations and expectations based on computer simulations suggest that the range of repeat numbers at a microsatellite locus is restricted. This range is a key parameter that should be properly estimated in order to proceed with calculations of divergence times in phylogenetic studies and to better investigate the within- and between-population variability. The 'plug-in' estimate of range based on the minimum and maximum value observed in a sample is not satisfactory because of the relatively large number of alleles in comparison with typical sample sizes. In this paper, a set of data from 30 dinucleotide microsatellite loci is analysed under the assumption of independence among loci. Bayesian inference on range for one locus is obtained by assuming that constraints on range values exist as sharp bounds. Closed-form calculations and robustness revealed by our analysis suggest that the proposed Bayesian approach might be routinely used by researchers to classify microsatellite loci according to the estimated value of their allelic range.

Bayes Theorem↗

PubMed2005

An analysis of the costs of treating schizophrenia in Spain: a hierarchical Bayesian approach.

BACKGROUND: Health care decisions should incorporate cost of illness and treatment data, particularly for disorders such as schizophrenia with a high morbidity rate and a disproportionately low allocation of resources. Previous cost of illness analyses may have disregarded geographical aspects relevant for resource consumption and unit cost calculation. AIMS: To compare the utilisation of resources and the care costs of schizophrenic patients in four mental-health districts in Spain (in Madrid, Catalonia, Navarra and Andalusia), and to analyse factors that determine the costs and the differences between areas. METHODS: A treated prevalence bottom-up three year follow-up design was used for obtaining data concerning socio-demography, clinical evolution and the utilisation of services. 1997 reference prices were updated for years 1998-2000 in euros. We propose two different scenarios, varying in the prices applied. In the first (Scenario 0) the reference prices are those obtained for a single geographic area, and so the cost variations are only due to differences in the use of resources. In the second situation (Scenario 1), we analyse the variations in resource utilisation at different levels, using the prices applicable to each healthcare area. Bayesian hierarchical models are used to discuss the factors that determine such costs and the differences between geographic areas. RESULTS: In scenario 0, the estimated mean cost was 4918.948 euros for the first year. In scenario 1 the highest cost was in Gava (Catalonia) and the lowest in Loja (Andalusia). Mean costs were respectively 4547.24 and 2473.98 euros. With respect to the evolution of costs over time, we observed an increase during the second year and a reduction during the third year. Geographical differences appeared in follow-up costs. The variables related to lower treatment costs were: residence in the family household, higher patient age and being in work. On the contrary, the number of relapses is directly related to higher treatment costs. No differences were observed between health areas concerning resource utilisation. DISCUSSION: Calculating the costs of a given disease involves two principal factors: the resource utilisation and the prices. In most studies, emphasis is placed on the analysis of resource utilisation. Other evaluations, however, have recognized the implications of incorporating different prices into the final results. In this study we show both scenarios. The factors that determine the cost of schizophrenia for the Spanish case are similar to the factors encountered in studies carried out in other countries. IMPLICATIONS FOR HEALTH POLICIES: Treatment costs may be reduced by the prevention of psychotic symptoms and relapse. IMPLICATIONS FOR FUTURE RESEARCH: The use of the same price data in multicentre studies may not be realistic. More effort should be made to obtain price data from all the centres or countries participating in a study. In the present study, only direct healthcare and social costs have been included. Future research should consider informal and indirect costs.

Adult↗

PubMedDate not supplied

Bayesian communication of research results over the World Wide Web.

The World Wide Web provides a unique opportunity to reconsider how the results of scientific studies can best be presented to clinicians. For decades statisticians, philosophers, medical investigators, and others interested in data analysis have assumed that the Bayesian paradigm is the proper approach for reporting the findings of scientific analyses for use by client computers and readers. At the heart of that approach is the inclusion of the reader's preexisting knowledge and beliefs. Yet, to date, the methods for inclusion have been too complicated for non-statisticians to use. We believe that the World Wide Web provides an ideal environment for putting the Bayesian paradigm into practice: the author publishes the data from the server side, the reader uses the client to represent her or his prior belief, a downloaded program (a Java applet) combines the two. This article describes a prototype implementation for two-arm clinical trials with normally distributed outcomes.

Bayes Theorem↗

PubMed2005

Taxonomic utility of a phylogenetic analysis of phosphoglycerate kinase proteins of Archaea, Bacteria, and Eukaryota: insights by Bayesian analyses.

We studied 131 protein sequences of the essentially ubiquitous glycolytic enzyme 3-phosphoglycerate kinase (3-PGK) by Bayesian analyses in three Domains: 15 Archaea, 83 Bacteria, and 33 Eukaryota. The posterior distribution of phylogenetic trees developed were based on a uniform prior, the WAG model of protein evolution, Metropolis-Hastings sampling in a Markov chain Monte Carlo analysis, and a package of diagnostics to critically evaluate the validity of the analyses. The 15 Archaea separated with high posterior probability. The archaean Phyla Euryarchaeota and the apparently Euryarchaeota derived Crenarchaeota were monophyletic. The 33 Eukaryota separated into two main groups: the non-chlorophyllous forms with coherent sub-groupings of Euglenozoa, Alveolata, Fungi, and Metazoa and all the chlorophyllous species studied: the Plantae (Viridaeplantae), chlorophyllous Stramenopiles, and the chlorophyllous Bacteria. This association supports other opinions concerning the related lineage of cyanobacteria and the Plantae. The 3-PGK sequences from 83 Bacteria in almost every instance associated by their recognized taxal group: alpha-, beta-, gamma-, epsilon-proteobacteria, Chlamydia, Actinobacteridae, and Firmicutes. Firmicutes sequences were subdivided into three apparently monophyletic groups: the anaerobic Clostridia, the spore-forming Bacillales and a group containing the Mollicutes, Lactobacillales and non-spore-forming Bacillales. The 3-PGK-gene tree assemblage was notable both for its pervasive clustering in three Domains according to recognized taxonomic groupings of Class, Order, Family, and Genus. The 3-PGK enzyme or 3-PGK-like activity may have played a central role in the metabolism of the Universal Ancestor.

Archaea↗

PubMed1976

A Bayesian approach to health project estimation.

This paper illustrates how a Bayesian statistical approach was used to estimate the outcomes of the National Tuberculosis Program in India. Such an estimate, it is argued, is necessary for a proper judgement about a project's social usefulness. The process of medical care delivery is reduced to a set of conditioned probabilities. The numbers are estimated using as source material medical records, the results of medical research, and the opinion of experts. Bayesian methods of estimation are used and their value is discussed. The final discussion contains a brief treatment of the role of project analysis in public decision making. The place of Bayesian methods in project analysis is briefly illustrated, demonstrating their operational value in the field of public health decision making.

Bayes Theorem↗

PubMed2001

Meta-analysis of randomized trials of terazosin in the treatment of benign prostatic hyperplasia.

OBJECTIVES: To determine the effectiveness of the long-acting alpha(1)-adrenergic receptor blocking agent terazosin compared with placebo on lower urinary tract symptoms and peak urinary flow rate in men with clinical benign prostatic hyperplasia. METHODS: A formal meta-analysis of all nine randomized trials of terazosin using both an Empirical Bayes and a fully Bayesian approach was conducted. A pooled analysis was conducted on those studies in which patients had a baseline assessment of prostate volume by transrectal ultrasonography. RESULTS: No evidence of heterogeneity was found in the estimated effects of terazosin on the change in peak flow rates in the studies. Terazosin treatment was associated with an increase in the peak flow rate of 1.4 mL/s (95% confidence interval [1.0, 1.7]) compared with placebo. Terazosin resulted in an average reduction of 2.2 points over placebo (95% confidence interval [1.6, 3.0]) regarding the common symptom score (range 0 to 36 points). A mild heterogeneity was found across the studies, with the decrease in symptom score slightly greater with longer treatment duration. No evidence was found that the baseline prostate volume influenced the effect of terazosin. CONCLUSIONS: Terazosin was effective and superior to placebo in reducing symptoms and increasing the peak urinary flow rate. The effect of terazosin on the peak urinary flow rate was apparent in studies as short as 8 weeks. Most importantly, the effect of terazosin on symptoms and peak urinary flow rate was independent of the baseline prostate size for the range of prostate volumes reported.

Adrenergic alpha-Antagonists↗

PubMed1991

Assessment of theophylline compliance in general practice using a 'compliance index' based on apparent drug clearance.

The monitoring of compliance in outpatients using serum drug levels suffers from the difficulty of relating concentrations to changes in dosage. Clearance is independent of dose for most drugs, and may be predicted using a Bayesian based forecasting program. This paper describes how the apparent clearance obtained following a single drug analysis can be compared with the Bayesian population value to derive a Compliance Index. In compliant individuals with stable hepatic and renal function this index should remain constant. We evaluated the usefulness of the Compliance Index in general practice with patients prescribed theophylline. Of 54 patients examined on up to five occasions, only 12% were deemed to be fully compliant at all times. Compliance improved during the study, but worsened again once regular consultation ceased. The results indicate that such a Compliance Index is a viable method of assessing compliance with the aid of concentration measurements.

Adolescent↗