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PubMed2026

A Bayesian framework for multivariate differential analysis.

Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a hierarchical formulation with moderated-variance estimators for each analyte directly injected into the t-statistic. While standard hypothesis testing strategies are recognised for their low computational cost, allowing for quick extraction of the most differential among thousands of elements, they generally overlook key aspects such as handling missing values, inter-element correlations, and uncertainty quantification. The present paper proposes a fully Bayesian framework for differential analysis, leveraging a conjugate hierarchical formulation for both the mean and the variance. Inference is performed by computing the posterior distribution of compared experimental conditions and sampling from the distribution of differences. This approach provides well-calibrated uncertainty quantification at a similar computational cost as hypothesis testing by leveraging closed-form equations. Furthermore, a natural extension enables multivariate differential analysis that accounts for possible inter-element correlations. We also demonstrate that, in this Bayesian treatment, missing at random data should generally be ignored in univariate settings, and further derive a tailored approximation that handles multiple imputation for the multivariate setting. We argue that probabilistic statements in terms of effect size and associated uncertainty are better suited to practical decision-making. Therefore, we finally propose simple and intuitive inference criteria, such as the overlap coefficient, which express group similarity as a probability rather than traditional, and often misleading, p-values. The performance of this approach is evaluated through an extensive empirical study using both synthetic and controlled real-world proteomics datasets. Overall, we believe that this Bayesian framework for (multivariate) differential analysis provides a valuable and intuitive counterpart to standard methods at a comparable computational cost.

Bayes Theorem↗

PubMed2005

Bayesian random effects meta-analysis of trials with binary outcomes: methods for the absolute risk difference and relative risk scales.

In a recent Statistics in Medicine paper, Warn, Thompson and Spiegelhalter (WTS) made a comparison between the Bayesian approach to the meta-analysis of binary outcomes and a popular Classical approach that uses summary (two-stage) techniques. They included approximate summary (two-stage) Bayesian techniques in their comparisons in an attempt undoubtedly to make the comparison less unfair. But, as this letter will argue, there are techniques from the Classical approach that are closer-those based directly on the likelihood-and they failed to make comparisons with these. Here the differences between Bayesian and Classical approaches in meta-analysis applications reside solely in how the likelihood functions are converted into either credibility intervals or confidence intervals. Both summarize, contrast and combine data using likelihood functions. Conflating what Bayes actually offers to meta-analysts-a means of converting likelihood functions to credibility intervals-with the use of likelihood functions themselves to summarize, contrast and combine studies is at best misleading.

Bayes Theorem↗

PubMed1995

Bayesian approaches to random-effects meta-analysis: a comparative study.

Current methods for meta-analysis still leave a number of unresolved issues, such as the choice between fixed- and random-effects models, the choice of population distribution in a random-effects analysis, the treatment of small studies and extreme results, and incorporation of study-specific covariates. We describe how a full Bayesian analysis can deal with these and other issues in a natural way, illustrated by a recent published example that displays a number of problems. Such analyses are now generally available using the BUGS implementation of Markov chain Monte Carlo numerical integration techniques. Appropriate proper prior distributions are derived, and sensitivity analysis to a variety of prior assumptions carried out. Current methods are briefly summarized and compared to the full Bayes analysis.

Bayes Theorem↗

PubMed2026

Minimally invasive versus open abdominoperineal resection and the risk of postoperative perineal hernia: a systematic review and meta-analysis.

BACKGROUND: The impact of minimally invasive surgery on the risk of postoperative perineal hernia after abdominoperineal resection (APR) or extralevator abdominoperineal excision (ELAPE) remains uncertain. This study compares perineal hernia rates and perioperative outcomes between minimally invasive and open approaches. METHODS: PubMed, Scopus, Web of Science, and Cochrane Library were searched through June 2026. Pooled odds ratios (ORs) and mean differences (MDs) with 95% confidence intervals (CIs) were calculated using random-effects models. A Bayesian meta-analysis was additionally performed for the primary outcome. RESULTS: Four comparative observational studies involving 763 patients were included; 249 underwent minimally invasive APR/ELAPE, and 514 underwent open APR/ELAPE. Postoperative perineal hernia was significantly more frequent following minimally invasive surgery (OR 4.13; 95% CI 2.24-7.61; p < 0.001). Intraoperative blood loss was significantly lower in the minimally invasive group (MD - 156.5 mL; 95% CI - 298.4 to - 14.5; p = 0.03), as was operative time (MD - 41.7 min; 95% CI - 60.8 to - 22.5; p < 0.01). No significant differences were observed in hospital stay (MD - 2.5 days; 95% CI - 5.4 to 0.4; p = 0.09) or 30-day readmission rates (OR 1.41; 95% CI 0.82-2.42; p = 0.209). Bayesian analysis yielded a posterior mean OR of 4.04 (95% CrI 1.96-8.36), corresponding to a 99.9% posterior probability that minimally invasive surgery increases the risk of postoperative perineal hernia. CONCLUSION: Minimally invasive APR/ELAPE was associated with an increased risk of postoperative perineal hernia compared with the open approach. Strategies to reduce this complication while preserving the benefits of minimally invasive surgery warrant further investigation.

Humans↗

PubMed2006

Genomewide scan for real-word reading subphenotypes of dyslexia: novel chromosome 13 locus and genetic complexity.

Dyslexia is a common learning disability exhibited as a delay in acquiring reading skills despite adequate intelligence and instruction. Reading single real words (real-word reading, RWR) is especially impaired in many dyslexics. We performed a genome scan, using variance components (VC) linkage analysis and Bayesian Markov chain Monte Carlo (MCMC) joint segregation and linkage analysis, for three quantitative measures of RWR in 108 multigenerational families, with follow up of the strongest signals with parametric LOD score analyses. We used single-word reading efficiency (SWE) to assess speed and accuracy of RWR, and word identification (WID) to assess accuracy alone. Adjusting SWE for WID provided a third measure of RWR efficiency. All three methods of analysis identified a strong linkage signal for SWE on chromosome 13q. Based on multipoint analysis with 13 markers we obtained a MCMC intensity ratio (IR) of 53.2 (chromosome-wide P < 0.004), a VC LOD score of 2.29, and a parametric LOD score of 2.94, based on a quantitative-trait model from MCMC segregation analysis (SA). A weaker signal for SWE on chromosome 2q occurred in the same location as a significant linkage peak seen previously in a scan for phonological decoding. MCMC oligogenic SA identified three models of transmission for WID, which could be assigned to two distinct linkage peaks on chromosomes 12 and 15. Taken together, these results indicate a locus for efficiency and accuracy of RWR on chromosome 13, and a complex model for inheritance of RWR accuracy with loci on chromosomes 12 and 15.

Adolescent↗

PubMed1999

Bayesian monitoring of phase II trials in cancer chemoprevention.

Early randomized Phase II cancer chemoprevention trials which assess short-term biological activity are critical to the decision process to advance to late Phase II/Phase III trials. We have adapted published Bayesian interim analysis methods (Spiegelhalter et al., J. R. Statist. Soc A, 1994; 157: 357-416) which give greater flexibility and simplicity of inference to the monitoring of randomized controlled Phase II trials using intermediate endpoints. The Bayesian stopping rule is designed to stop the trial more quickly when the evidence suggests ineffectiveness rather than when it suggests biological activity, thus allowing resources to be concentrated on those agents that show the most promise in this early stage of testing. We investigate frequentist performance characteristics of the proposed method through simulation of randomized placebo controlled trials with a growth factor intermediate end-point using mean and variance values derived from the literature. Simulation results show expected error rates and trial size similar to other commonly used group sequential methods for this setting. These results suggest that the Bayesian approach to interim analysis is well suited for monitoring small randomized controlled Phase II chemoprevention trials for early detection of either inactive or promising agents.

Antineoplastic Agents↗

PubMed2005

The cost-effectiveness of basiliximab induction in "old-to-old" kidney transplant programs: Bayesian estimation, simulation, and uncertainty analysis.

INTRODUCTION: Markov models are employed in economic analyses to evaluate all possible expectations in a dilemna. The introduction of a new clinical protocol (Basiliximab induction with calcineurin-sparing protocols) for a group of kidney transplant recipients receiving organs from marginal donors was validated with a Markov simulation model, demonstrating the usefulness of combining simulation with Bayesian estimation methods for analysis of cost-effectiveness data collected alongside a clinical trial. We sought to determine whether calcineurin-sparing protocols using anti-interleukin-2/antibody induction (Simulect) would show a beneficial effect on initial kidney function and reduce transplantation costs upon admission, clinical incidences, graft function, and complications during the first month after transplant. PATIENTS AND METHODS: A Markov Chain Monte Carlo (MCMC) was used to estimate a system of generalized linear models relating costs and outcomes to a kidney transplant process affected by treatment under alternative therapies. The Markov simulation model was established following three chains: a calcineurin-free regimen with Basiliximab induction (chain A); a calcineurin-sparing protocol with Basiliximab induction (chain B); and a conventional immunosuppressive regimen (chain C). The MCMC draws were used as parameters in simulations that yielded inferences about the relative cost-effectiveness of the novel therapy under a variety of scenarios. After designing the Markov chain and cohorts, 31 patients from the "old-to-old" program were assigned; eight to chain A; eight to chain B; and 15 to chain C. A year after transplantation a cost-benefit study was performed guided by the three branches of the Markov model. RESULTS: The Markov model showed a benefit of induction therapies in elderly patients. A cost-benefit model showed that after a year, there was a clear benefit from calcineurin-free plus Basiliximab induction therapies, with a slight benefit from calcineurin-sparing protocols. CONCLUSIONS: Markov models are extremely useful when introducing new clinical therapies. The approach allows flexibility in assessing treatment using various premises and quantifies the global effect of parametric uncertainty on a decision maker's confidence to adopt one therapy over another. In our transplant program, a cost-effective analysis of outcomes in old patients using the Markov model showed a clear benefit of calcineurin-sparing protocols with Basixilimab induction.

Age Factors↗

PubMed1999

A Bayesian approach to stochastic cost-effectiveness analysis.

The aim of this paper is to briefly outline a Bayesian approach to cost-effectiveness analysis (CEA). Historically, frequentists have been cautious of Bayesian methodology, which is often held as synonymous with a subjective approach to statistical analysis. In this paper, the potential overlap between Bayesian and frequentist approaches to CEA is explored--the focus being on the empirical and uninformative prior-based approaches to Bayesian methods rather than the use of subjective beliefs. This approach emphasizes the advantage of a Bayesian interpretation for decision-making while retaining the robustness of the frequentist approach. In particular the use of cost-effectiveness acceptability curves is examined. A traditional frequentist approach is equivalent to a Bayesian approach assuming no prior information, while where there is pre-existing information available from which to construct a prior distribution, an empirical Bayes approach is equivalent to a frequentist approach based on pooling the available data. Cost-effectiveness acceptability curves directly address the decision-making problem in CEA. Although it is argued that their interpretation as the probability that an intervention is cost-effective given the data requires a Bayesian interpretation, this should generate no misgivings for the frequentist.

Bayes Theorem↗

PubMed2006

A northern glacial refugium for bank voles (Clethrionomys glareolus).

There is controversy and uncertainty on how far north there were glacial refugia for temperate species during the Pleistocene glaciations and in the extent of the contribution of such refugia to present-day populations. We examined these issues using phylogeographic analysis of a European woodland mammal, the bank vole (Clethrionomys glareolus). A Bayesian coalescence analysis indicates that a bank vole population survived the height of the last glaciation (approximately 25,000-10,000 years B.P.) in the vicinity of the Carpathians, a major central European mountain chain well north of the Mediterranean areas typically regarded as glacial refugia for temperate species. Parameter estimates from the fitted isolation with migration model show that the divergence of the Carpathian population started at least 22,000 years ago, and it was likely followed by only negligible immigration from adjacent regions, suggesting the persistence of bank voles in the Carpathians through the height of the last glaciation. On the contrary, there is clear evidence for gene flow out of the Carpathians, demonstrating the contribution of the Carpathian population to the colonization of Europe after the Pleistocene. These findings are consistent with data from animal and plant fossils recovered in the Carpathians and provide the clearest phylogeographic evidence to date of a northern glacial refugium for temperate species in Europe.

Animals↗

PubMed2003

Reliability of Bayesian posterior probabilities and bootstrap frequencies in phylogenetics.

Many empirical studies have revealed considerable differences between nonparametric bootstrapping and Bayesian posterior probabilities in terms of the support values for branches, despite claimed predictions about their approximate equivalence. We investigated this problem by simulating data, which were then analyzed by maximum likelihood bootstrapping and Bayesian phylogenetic analysis using identical models and reoptimization of parameter values. We show that Bayesian posterior probabilities are significantly higher than corresponding nonparametric bootstrap frequencies for true clades, but also that erroneous conclusions will be made more often. These errors are strongly accentuated when the models used for analyses are underparameterized. When data are analyzed under the correct model, nonparametric bootstrapping is conservative. Bayesian posterior probabilities are also conservative in this respect, but less so.

Bayes Theorem↗

PubMed2002

Bayesian random effects meta-analysis of trials with binary outcomes: methods for the absolute risk difference and relative risk scales.

When conducting a meta-analysis of clinical trials with binary outcomes, a normal approximation for the summary treatment effect measure in each trial is inappropriate in the common situation where some of the trials in the meta-analysis are small, or the observed risks are close to 0 or 1. This problem can be avoided by making direct use of the binomial distribution within trials. A fully Bayesian method has already been developed for random effects meta-analysis on the log-odds scale using the BUGS implementation of Gibbs sampling. In this paper we demonstrate how this method can be extended to perform analyses on both the absolute and relative risk scales. Within each approach we exemplify how trial-level covariates, including underlying risk, can be considered. Data from 46 trials of the effect of single-dose ibuprofen on post-operative pain are analysed and the results contrasted with those derived from classical and Bayesian summary statistic methods. The clinical interpretation of the odds ratio scale is not straightforward. The advantages and flexibility of a fully Bayesian approach to meta-analysis of binary outcome data, considered on an absolute risk or relative risk scale, are now available.

Anti-Inflammatory Agents, Non-Steroidal↗

PubMed1999

Comparison of the Bayesian approach and a limited sampling model for the estimation of AUC and Cmax: a computer simulation analysis.

OBJECTIVES: To compare two limited sampling methods (Bayesian and the limited sampling model) for the estimation of AUC and Cmax following a single oral dose of a hypothetical drug. METHODS: The plasma concentration vs time data sets for 50 subjects using a linear one- or two-compartment pharmacokinetic model were generated by simulation. The limited sampling model (LSM) was developed using samples from 10 subjects using one or two time points. The simulated plasma concentrations were also used for Bayesian evaluation. Bayesian analysis was performed on Non-Mem and mean pharmacokinetic parameters used for simulation were assumed as population pharmacokinetic parameters. In addition a test drug was also used to compare the predicted AUC and Cmax for the two approaches. RESULTS: Both methods were validated in 40 subjects for the hypothetical drug and in 12 subjects for the test drug. Both methods provided good estimates of AUC and Cmax. CONCLUSION: The results indicate that the LSM is similar to the Bayesian method and may be used in lieu of the Bayesian approach in estimating AUC and Cmax using one or two samples in clinical settings without detailed pharmacokinetic studies.

Area Under Curve↗

PubMed2004

Non-adult dental age assessment: correspondence analysis and linear regression versus Bayesian predictions.

This study focuses on the evaluation of factors influencing the quality (accuracy and reliability) of non-adult dental age assessment from radiographic stages of permanent teeth (excluding the third molar). We used four distinct cross-sectional samples of 1,528 healthy children: 3 of known geographic origin (Ivory Coast, Iran and France) and 1 additional sample of children whose grandparents originated from a different continent. Two different methods of calculations are compared: the correspondence analysis combined with linear regression (CAR) and Bayesian predictions (with no independence assumption). Our results indicate that the quality of age assessment does not seem to depend predominantly on the use of geographic-specific standards. In the case of Bayesian predictions, we observed a clear trend in favour of significantly higher accuracy and reliability levels when using non-geographic-specific standards. One of the main advantage of Bayesian predictions over maximum likelihood methods of estimation is an overall increase in accuracy with high levels of reliability on a fraction of the test sample and, importantly, across all age categories (contrary to methods based on regression analysis). Importantly, in the case of Bayesian non-adult predictions, and contrary to age estimation techniques based on regression, a better quality does not depend on age.

Adolescent↗

PubMed2005

Propagation of population pharmacokinetic information using a Bayesian approach: comparison with meta-analysis.

We investigated the propagation of population pharmacokinetic information across clinical studies by applying Bayesian techniques. The aim was to summarize the population pharmacokinetic estimates of a study in appropriate statistical distributions in order to use them as Bayesian priors in consequent population pharmacokinetic analyses. Various data sets of simulated and real clinical data were fitted with WinBUGS, with and without informative priors. The posterior estimates of fittings with non-informative priors were used to build parametric informative priors and the whole procedure was carried on in a consecutive manner. The posterior distributions of the fittings with informative priors where compared to those of the meta-analysis fittings of the respective combinations of data sets. Good agreement was found, for the simulated and experimental datasets when the populations were exchangeable, with the posterior distribution from the fittings with the prior to be nearly identical to the ones estimated with meta-analysis. However, when populations were not exchangeble an alternative parametric form for the prior, the natural conjugate prior, had to be used in order to have consistent results. In conclusion, the results of a population pharmacokinetic analysis may be summarized in Bayesian prior distributions that can be used consecutively with other analyses. The procedure is an alternative to meta-analysis and gives comparable results. It has the advantage that it is faster than the meta-analysis, due to the large datasets used with the latter and can be performed when the data included in the prior are not actually available.

Administration, Oral↗

PubMed2004

Analysis of lesion detectability in Bayesian emission reconstruction with nonstationary object variability.

Bayesian methods based on the maximum a posteriori principle (also called penalized maximum-likelihood methods) have been developed to improve image quality in emission tomography. To explore the full potential of Bayesian reconstruction for lesion detection, we derive simplified theoretical expressions that allow fast evaluation of the detectability of a lesion in Bayesian reconstruction. This work is builded on the recent progress on the theoretical analysis of image properties of statistical reconstructions and the development of numerical observers. We explicitly model the nonstationary variation of the lesion and background without assuming that they are locally stationary. The results can be used to choose the optimum prior parameters for the maximum lesion detectability. The theoretical results are validated using Monte Carlo simulations. The comparisons show good agreement between the theoretical predictions and the Monte Carlo results. We also demonstrate that the lesion detectability can be reliably estimated using one noisy data set.

Algorithms↗

PubMed2003

Application of Bayesian spatial statistical methods to analysis of haplotypes effects and gene mapping.

We propose a method to analyze haplotype effects using ideas derived from Bayesian spatial statistics. We assume that two haplotypes that are similar to one another in structure are likely to have similar risks, and define a distance metric to specify the appropriate level of closeness between the two haplotypes. Through the choice of distance metric, varying levels of population genetics theory can be incorporated into the modeling process, including some that allow estimation of the location of the disease causing mutation(s). This location can be estimated, along with the other parameters of the model, using Markov chain Monte Carlo (MCMC) estimation methods. We demonstrate the effectiveness of the model on two real datasets, a well-known dataset used to fine-map the gene for cystic fibrosis, and one used to localize the gene for Friedreich's ataxia.

Bayes Theorem↗

PubMed2003

Molecular systematics and adaptive radiation of Hawaii's endemic Damselfly genus Megalagrion (Odonata: Coenagrionidae).

Damselflies of the endemic Hawaiian genus Megalagrion have radiated into a wide variety of habitats and are an excellent model group for the study of adaptive radiation. Past phylogenetic analysis based on morphological characters has been problematic. Here, we examine relationships among 56 individuals from 20 of the 23 described species using maximum likelihood (ML) and Bayesian phylogenetic analysis of mitochondrial (1287 bp) and nuclear (1039 bp) DNA sequence data. Models of evolution were chosen using the Akaike information criterion. Problems with distant outgroups were accommodated by constraining the best ML ingroup topology but allowing the outgroups to attach to any ingroup branch in a bootstrap analysis. No strong contradictions were obtained between either data partition and the combined data set. Areas of disagreement are mainly confined to clades that are strongly supported by the mitochondrial DNA and weakly supported by the elongation factor 1alpha data because of lack of changes. However, the combined analysis resulted in a unique tree. Correlation between Bayesian posterior probabilities and bootstrap percentages decreased in concert with decreasing information in the data partitions. In cases where nodes were supported by single characters bootstrap proportions were dramatically reduced compared with posterior probabilities. Two speciation patterns were evident from the phylogenetic analysis. First, most speciation is interisland and occurred as members of established ecological guilds colonized new volcanoes after they emerged from the sea. Second, there are several instances of rapid radiation into a variety of specialized habitats, in one case entirely within the island of Kauai. Application of a local clock procedure to the mitochondrial DNA topology suggests that two of these radiations correspond to the development of habitat on the islands of Kauai and Oahu. About 4.0 million years ago, species simultaneously moved into fast streams and plant leaf axils on Kauai, and about 1.5 million years later another group moved simultaneously to seeps and terrestrial habitats on Oahu. Results from the local clock analysis also strongly suggest that Megalagrion arrived in Hawaii about 10 million years ago, well before the emergence of Kauai. Date estimates were more sensitive to the particular node that was fixed in time than to the model of local branch evolution used. We propose a general model for the development of endemic damselfly species on Hawaiian Islands and document five potential cases of hybridization (M. xanthomelas x M. pacificum, M. eudytum x M. vagabundum, M. orobates x M. oresitrophum, M. nesiotes x M. oahuense, and M. mauka x M. paludicola).

Adaptation, Biological↗

PubMed2001

Bayesian estimation and test for factor analysis model with continuous and polytomous data in several populations.

The main purpose of this paper is to develop a Bayesian approach for the multisample factor analysis model with continuous and polytomous variables. Joint Bayesian estimates of the thresholds, the factor scores and the structural parameters subjected to some simple constraints across groups are obtained simultaneously. The Gibbs sampler is used to produce the joint Bayesian estimates. It is shown that the conditional distributions involved in the implementation are the familiar uniform, gamma, normal, univariate truncated normal and Wishart distributions. The Bayes factor is introduced to test hypotheses involving constraints among the structural parameters of the factor analysis models across groups. Two procedures for computing the test statistics are developed, one based on the Schwarz criterion (or Bayesian information criterion), while the other computes the posterior densities and likelihood ratios by means of draws from the appropriate conditional distributions via the Gibbs sampler. The empirical performance of the proposed Bayesian procedure and its sensitivity to prior distributions are illustrated by some simulation results and two real-life examples.

Bayes Theorem↗