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PubMed1997

Stochastic optimization algorithms of a Bayesian design criterion for Bayesian parameter estimation of nonlinear regression models: application in pharmacokinetics.

This article proposes three stochastic algorithms to optimize a Bayesian design criterion for Bayesian estimation of the parameters of nonlinear regression models; this criterion is the information expected from an experiment. The first algorithm is based on a stochastic version of the simplex with an adaptive sampling procedure. The others are stochastic approximation algorithms: the Kiefer-Wolfowitz and the pseudogradient algorithms. We first present the information criterion and the optimization algorithms. The efficiency of each algorithm for optimizing this Bayesian design criterion is then assessed by a simulation study for a nonlinear model assuming a discrete prior distribution. An application for designing an experiment to estimate the kinetics of radioiodine thyroid uptake is then proposed.

Algorithms↗

PubMed1998

Predicting hospitalisation of patients with diabetes mellitus. An application of the Bayesian discriminant analysis.

The objective of this study was to develop, and subsequently test, a Bayesian discrimination model for the purpose of identifying both the personal and the healthcare system characteristics predictive of hospitalisation for the treatment of patients with diabetes mellitus or commonly observed cormorbidities associated with the disease. First, a Bayesian classification framework was proposed. The model was then tested by using a logit regression technique in order to estimate the probability of one or more hospitalisation events among patients with diabetes. The study used claims data extracted from the Hawaii Medical Service Association (HMSA) Private Business Claims (PBS) files for the 1995 calendar year. Patients under 65 years were identified by paid claims with ICD-9-CM diagnosis codes of 250.xx which gave a sample size of 6841 patients. Age, gender, various pharmacotherapy variables, presence of hypertension, hyperlipidaemia, congestive heart failure, multiple cardiovascular diseases, any combination of commonly observed comorbidities, dialysis services and annual eye examination are highly predictive of 1 or more hospitalisation events. The model shows a predictive power of almost 90%. This study found that multivariate discriminant analysis using a logit regression model successfully identifies: (i) important explanatory variables predictive of hospitalisation; (ii) assigns patients into 1 of 2 mutually exclusive classes; and (iii) offers a benchmark for a comprehensive disease management strategy for patients with more complicated diabetes.

Bayes Theorem↗

PubMed2006

Bayesian analysis of structural equation models with mixed exponential family and ordered categorical data.

Structural equation models are very popular for studying relationships among observed and latent variables. However, the existing theory and computer packages are developed mainly under the assumption of normality, and hence cannot be satisfactorily applied to non-normal and ordered categorical data that are common in behavioural, social and psychological research. In this paper, we develop a Bayesian approach to the analysis of structural equation models in which the manifest variables are ordered categorical and/or from an exponential family. In this framework, models with a mixture of binomial, ordered categorical and normal variables can be analysed. Bayesian estimates of the unknown parameters are obtained by a computational procedure that combines the Gibbs sampler and the Metropolis-Hastings algorithm. Some goodness-of-fit statistics are proposed to evaluate the fit of the posited model. The methodology is illustrated by results obtained from a simulation study and analysis of a real data set about non-adherence of hypertension patients in a medical treatment scheme.

Bayes Theorem↗

PubMed2026

Oncotype DX-guided vs physician-directed chemotherapy and survival in HR+/HER2- breast cancer.

BACKGROUND: Oncotype DX testing guides adjuvant chemotherapy decisions in early-stage hormone receptor-positive/HER2-negative breast cancer, but testing is not universally performed, and outcomes associated with genomic-informed versus clinicopathologic-based chemotherapy decision pathways remain unclear. METHODS: Using the 2022 National Cancer Database Breast Participant User File, we identified women diagnosed from 2010 to 2022 with pathologic T1b-T2, node-negative, hormone receptor-positive/HER2-negative invasive breast cancer who received adjuvant chemotherapy and endocrine therapy. Patients were classified into an Oncotype-guided group, defined by Oncotype DX testing with a recurrence score of 26 or higher, and a physician-directed group, defined by receipt of chemotherapy without genomic testing. The primary outcome was overall survival. Analyses used multivariable Cox models, logistic-IPTW and MLP-IPTW, restricted mean survival time analysis, and a Bayesian latent confounding survival model. RESULTS: Among 56,625 women, 27,278 were in the Oncotype-guided group and 29,347 in the physician-directed group. Median ages were 59 and 56 years, respectively. The Oncotype-guided group had more favorable overall survival than the physician-directed group in multivariable Cox analysis (HR, 0.906; 95% CI, 0.856-0.959; P < 0.001), with similar findings in IPTW analyses. The association was concentrated among patients aged 56 years or older (HR, 0.866; 95% CI, 0.809-0.927; P < 0.001). The Bayesian model showed no strong residual confounding signal. CONCLUSIONS: Among chemotherapy-treated women, an Oncotype-guided pathway was associated with more favorable overall survival than a physician-directed pathway, particularly among older patients, which indicating prognostic heterogeneity selected using genomic versus conventional clinicopathologic information.

Humans↗

PubMed1996

Robustness considerations in Bayesian analysis.

All statistical analyses demand uncertain inputs or assumptions. This is especially true of Bayesian analyses. In addition to the usual concerns about the agreement of the data and model, a Bayesian must contemplate the effect of an uncertain prior specification. The degree to which inferences are robust to changes in the prior is of primary interest. This article discusses some robust techniques that have been suggested in the literature. One goal is to make apparent the relevance of some of these techniques to biostatistical work.

Adrenergic beta-Antagonists↗

PubMed1993

A Bayesian approach to logistic regression models having measurement error following a mixture distribution.

To estimate the parameters in a logistic regression model when the predictors are subject to random or systematic measurement error, we take a Bayesian approach and average the true logistic probability over the conditional posterior distribution of the true value of the predictor given its observed value. We allow this posterior distribution to consist of a mixture when the measurement error distribution changes form with observed exposure. We apply the method to study the risk of alcohol consumption on breast cancer using the Nurses Health Study data. We estimate measurement error from a small subsample where we compare true with reported consumption. Some of the self-reported non-drinkers truly do not drink. The resulting risk estimates differ sharply from those computed by standard logistic regression that ignores measurement error.

Age Factors↗

PubMed2004

Flexible dose-response models for Japanese atomic bomb survivor data: Bayesian estimation and prediction of cancer risk.

Generalised absolute risk models were fitted to the latest Japanese atomic bomb survivor cancer incidence data using Bayesian Markov Chain Monte Carlo methods, taking account of random errors in the DS86 dose estimates. The resulting uncertainty distributions in the relative risk model parameters were used to derive uncertainties in population cancer risks for a current UK population. Because of evidence for irregularities in the low-dose dose response, flexible dose-response models were used, consisting of a linear-quadratic-exponential model, used to model the high-dose part of the dose response, together with piecewise-linear adjustments for the two lowest dose groups. Following an assumed administered dose of 0.001 Sv, lifetime leukaemia radiation-induced incidence risks were estimated to be 1.11 x 10(-2) Sv(-1) (95% Bayesian CI -0.61, 2.38) using this model. Following an assumed administered dose of 0.001 Sv, lifetime solid cancer radiation-induced incidence risks were calculated to be 7.28 x 10(-2) Sv(-1) (95% Bayesian CI -10.63, 22.10) using this model. Overall, cancer incidence risks predicted by Bayesian Markov Chain Monte Carlo methods are similar to those derived by classical likelihood-based methods and which form the basis of established estimates of radiation-induced cancer risk.

Algorithms↗

PubMed2005

Application of Bayesian regularized BP neural network model for analysis of aquatic ecological data-a case study of chlorophyll-a prediction in Nanzui water area of Dongting Lake.

Bayesian regularized BP neural network(BRBPNN) technique was applied in the chlorophyll-a prediction of Nanzui water area in Dongting Lake. Through BP network interpolation method, the input and output samples of the network were obtained. After the selection of input variables using stepwise/multiple linear regression method in SPSS 11.0 software, the BRBPNN model was established between chlorophyll-a and environmental parameters, biological parameters. The achieved optimal network structure was 3-11-1 with the correlation coefficients and the mean square errors for the training set and the test set as 0.999 and 0.00078426, 0.981 and 0.0216 respectively. The sum of square weights between each input neuron and the hidden layer of optimal BRBPNN models of different structures indicated that the effect of individual input parameter on chlorophyll-a declined in the order of alga amount > secchi disc depth (SD) > electrical conductivity (EC). Additionally, it also demonstrated that the contributions of these three factors were the maximal for the change of chlorophyll-a concentration, total phosphorus (TP) and total nitrogen (TN) were the minimal. All the results showed that BRBPNN model was capable of automated regularization parameter selection and thus it may ensure the excellent generation ability and robustness. Thus, this study laid the foundation for the application of BRBPNN model in the analysis of aquatic ecological data(chlorophyll-a prediction) and the explanation about the effective eutrophication treatment measures for Nanzui water area in Dongting Lake.

Bayes Theorem↗

PubMedDate not supplied

Bayesian extensions of the Tobit model for analyzing measures of health status.

Self-reported health status is often measured using utility indices that provide a score intended to summarize an individual's health. Measurements of health status can be subject to a ceiling effect. Frequently, researchers want to examine relationships between determinants of health and measures of health status. In this article, Bayesian extensions of the classical Tobit model are used to study the relationship between health status and predictors of health. The author examined models where the conditional distribution of health status was either normal or lognormal, and allowed for both homoscedasticity and heteroscedasticity. Bayes factors were then used to compare the evidence for a given model against that for a competing model. The author found very strong evidence that the distribution of the Health Utilities Index, conditional on age, gender, income adequacy, and number of chronic conditions, was normal with nonuniform variance, compared to the competing models.

Bayes Theorem↗

PubMed2006

Multi-class cancer classification using multinomial probit regression with Bayesian gene selection.

We consider the problems of multi-class cancer classification from gene expression data. After discussing the multinomial probit regression model with Bayesian gene selection, we propose two Bayesian gene selection schemes: one employs different strongest genes for different probit regressions; the other employs the same strongest genes for all regressions. Some fast implementation issues for Bayesian gene selection are discussed, including preselection of the strongest genes and recursive computation of the estimation errors using QR decomposition. The proposed gene selection techniques are applied to analyse real breast cancer data, small round blue-cell tumours, the national cancer institute's anti-cancer drug-screen data and acute leukaemia data. Compared with existing multi-class cancer classifications, our proposed methods can find which genes are the most important genes affecting which kind of cancer. Also, the strongest genes selected using our methods are consistent with the biological significance. The recognition accuracies are very high using our proposed methods.

Algorithms↗

PubMed2001

Bayesian methods of analysis for cluster randomized trials with binary outcome data.

We explore the potential of Bayesian hierarchical modelling for the analysis of cluster randomized trials with binary outcome data, and apply the methods to a trial randomized by general practice. An approximate relationship is derived between the intracluster correlation coefficient (ICC) and the between-cluster variance used in a hierarchical logistic regression model. By constructing an informative prior for the ICC on the basis of available information, we are thus able implicitly to specify an informative prior for the between-cluster variance. The approach also provides us with a credible interval for the ICC for binary outcome data. Several approaches to constructing informative priors from empirical ICC values are described. We investigate the sensitivity of results to the prior specified and find that the estimate of intervention effect changes very little in this data set, while its interval estimate is more sensitive. The Bayesian approach allows us to assume distributions other than normality for the random effects used to model the clustering. This enables us to gain insight into the robustness of our parameter estimates to the classical normality assumption. In a model with a more complex variance structure, Bayesian methods can provide credible intervals for a difference between two variance components, in order for example to investigate whether the effect of intervention varies across clusters. We compare our results with those obtained from classical estimation, discuss the relative merits of the Bayesian framework, and conclude that the flexibility of the Bayesian approach offers some substantial advantages, although selection of prior distributions is not straightforward.

Bayes Theorem↗

PubMed2005

Individual variation in CD4 cell count trajectory among human immunodeficiency virus-infected men and women on long-term highly active antiretroviral therapy: an application using a Bayesian random change-point model.

The authors evaluated population- and individual-level CD4-positive T-lymphocyte (CD4 cell) count trajectories over a 7-year period (July 1995-March 2004) following initiation of highly active antiretroviral therapy (HAART) in the Multicenter AIDS Cohort Study and the Women's Interagency HIV Study. The study population included 404 human immunodeficiency virus (HIV)-infected men and 609 HIV-infected women who 1) had a CD4 cell count measurement available from their last pre-HAART study visit, 2) provided at least four post-HAART CD4 cell count measurements, and 3) reported HAART usage for at least 80% of the post-HAART visits. The CD4 cell count trajectory was analyzed by means of a Bayesian random change-point model. The results indicated that CD4 cell count trajectories for long-term frequent HAART users can be well modeled with change points at both the population and individual levels. At the population level, regardless of CD4 cell count before HAART initiation, the gains in CD4 cell count ended approximately 2 years after HAART initiation in both men and women. At the individual level, 35% of men in the Multicenter AIDS Cohort Study versus 25% of women in the Women's Interagency HIV Study had a statistically significant change in CD4 cell count trajectory within 7 years after HAART initiation.

Adult↗

PubMed1995

Bayesian analysis of proportional hazards models built from monotone functions.

We consider the usual proportional hazards model in the case where the baseline hazard, the covariate link, and the covariate coefficients are all unknown. Both the baseline hazard and the covariate link are monotone functions and thus are characterized using a dense class of such functions which arises, upon transformation, as a mixture of Beta distribution functions. We take a Bayesian approach for fitting such a model. Since interest focuses more upon the likelihood, we consider vague prior specifications including Jeffreys's prior. Computations are carried out using sampling-based methods. Model criticism is also discussed. Finally, a data set studying survival of a sample of lung cancer patients is analyzed.

Algorithms↗

PubMed2004

Model-based detection of lung nodules in computed tomography exams. Thoracic computer-aided diagnosis.

RATIONALE AND OBJECTIVES: In this study, we developed a prototype model-based computer aided detection (CAD) system designed to automatically detect both solid and subsolid pulmonary nodules in computed tomography (CT) images. By using this CAD algorithm, along with the radiologist's initial interpretation, we aim to improve the sensitivity of radiologic readings of CT lung exams. MATERIALS AND METHODS: We have developed a model-based CAD algorithm through the use of precise mathematic models that capture scanner physics and anatomic information. Our model-based CAD algorithm uses multiple segmentation algorithms to extract noteworthy structures in the lungs and a Bayesian statistical model selection framework to determine the probability of various anatomical events throughout the lung. We tested this algorithm on 50 low-dose CT lung cancer screening cases in which ground truth was produced through readings by three expert chest radiologists. RESULTS: Using this model-based CAD algorithm on 50 low-dose CT cases, we measured potential sensitivity improvements of 7% and 5% in two radiologists with respect to all noncalcified nodules, solid and subsolid, greater than 5 mm in diameter. The third radiologist did not miss any nodules in the ground truth set. The CAD algorithm produced 8.3 false positives per case. CONCLUSION: Our prototype CAD system demonstrates promising results as a tool to improve the quality of radiologic readings by increasing radiologist sensitivity. A significant advantage of this model-based approach is that it can be easily extended to support additional anatomic models as clinical understanding and scanning practices improve.

Algorithms↗

PubMed2004

Variance-modeled posterior inference of microarray data: detecting gene-expression changes in 3T3-L1 adipocytes.

MOTIVATION: Microarrays are becoming an increasingly common tool for observing changes in gene expression over a large cross section of the genome. This experimental tool is particularly valuable for understanding the genome-wide changes in gene transcription in response to thiazolidinedione (TZD) treatment. The TZD class of drugs is known to improve insulin-sensitivity in diabetic patients, and is clinically used in treatment regimens. In cells, TZDs bind to and activate the transcriptional activity of peroxisome proliferator-activated receptor gamma (PPAR-gamma). Large-scale array analyses will provide some insight into the mechanisms of TZD-mediated insulin sensitization. Unfortunately, a theoretical basis for analyzing array data has not kept pace with the rapid adoption of this tool. The methods that are commonly used, particularly the fold-change approach and the standard t-test, either lack statistical rigor or resort to generalized statistical models that do not accurately estimate variability at low replicate numbers. RESULTS: We introduce a statistical framework that models the dependence of measurement variance on the level of gene expression in the context of a Bayesian hierarchical model. We compare several methods of parameter estimation and subsequently apply these to determine a set of genes in 3T3-L1 adipocytes that are differentially regulated in response to TZD treatment. When the number of experimental replicates is low (n = 2-3), this approach appears to qualitatively preserve an equivalent degree of specificity, while vastly improving sensitivity over other comparable methods. In addition, the statistical framework developed here can be readily applied to understand the implicit assumptions made in traditional fold-change approaches to array analysis.

3T3-L1 Cells↗

PubMed2006

Spatial association between speciated fine particles and mortality.

Particulate matter (PM) has been linked to a range of serious cardiovascular and respiratory health problems, including premature mortality. The main objective of our research is to quantify uncertainties about the impacts of fine PM exposure on mortality. We develop a multivariate spatial regression model for the estimation of the risk of mortality associated with fine PM and its components across all counties in the conterminous United States. We characterize different sources of uncertainty in the data and model the spatial structure of the mortality data and the speciated fine PM. We consider a flexible Bayesian hierarchical model for a space-time series of counts (mortality) by constructing a likelihood-based version of a generalized Poisson regression model that combines methods for point-level misaligned data and change of support regression. Our results seem to suggest an increase by a factor of two in the risk of mortality due to fine particles with respect to coarse particles. Our study also shows that in the Western United States, the nitrate and crustal components of the speciated fine PM seem to have more impact on mortality than the other components. On the other hand, in the Eastern United States, sulfate and ammonium explain most of the fine PM effect.

Air Pollutants↗

PubMed2004

A mixed-model approach for the analysis of cDNA microarray gene expression data from extreme-performing pigs after infection with Actinobacillus pleuropneumoniae.

We proposed a novel statistical approach for the analysis of cDNA experiments based on mixed-model methodology combined with mixtures of distributions. Our objective was to detect genes that may be involved in conferring heritable differences in susceptibility to common infections in intensive pig production. We employed a microarray expression profiling strategy and a mixed-model approach to the analysis of the expression data. A cDNA microarray of pig with 6,420 probes from immune tissues and cells was used to compare gene expression in peripheral blood leukocytes of two pigs showing extreme performance in their response to infection with Actinobacillus pleuropneumoniae. Principal components analyses were used to identify the two most extreme-performing pigs after infection (i.e., pigs whose measured responses to infection fell at the extremes). Blood samples and expression profiles from 0 to 24 h after infection were compared using a bivariate, mixed-model approach, in which the effect gene x immunological status interaction was treated as a random effect. Bayesian model-based clustering via mixtures of normal distributions of the resulting BLUP of the random interaction was approached and resulted in a list of 307 differentially expressed genes, of which 179 were down-regulated in the susceptible pig. The majority of the differentially expressed genes were derived from a cDNA library of leukocytes of A. pleuropneumoniae-challenged pigs that were subtracted against leukocytes before the challenge. These results provide evidence that the proposed statistical approach was useful in enhancing the knowledge of the mechanisms involved in the genetics of the immune response.

Actinobacillus Infections↗

PubMed2005

Suboptimal tradeoffs in information seeking.

Explicit information-seeking actions are needed to evaluate alternative actions in problem-solving tasks. Information-seeking costs are often traded off against the utility of information. We present three experiments that show how subjects adapt to the cost and information structures of environments in a map-navigation task. We found that subjects often stabilize at suboptimal levels of performance. A Bayesian satisficing model (BSM) is proposed and implemented in the ACT-R architecture to predict information-seeking behavior. The BSM uses a local decision rule and a global Bayesian learning mechanism to decide when to stop seeking information. The model matched the human data well, suggesting that adaptation to cost and information structures can be achieved by a simple local decision rule. The local decision rule, however, often limits exploration of the environment and leads to suboptimal performance. We propose that suboptimal performance is an emergent property of the dynamic interactions between cognition and the environment.

Bayes Theorem↗