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PubMed1991

A computational model of approximate Bayesian inference for associating clinical algorithms with decision analyses.

The lack of rationale or explanation is a major deficiency of clinical algorithms. To address this issue, the authors present a computational model for associating decision analyses with clinical algorithms. Automata theory is used to model categorical reasoning with approximate Bayesian inference based on probability intervals. This approximation reduces the number of computations to linear-order instead of the exponential-order combinations of clinical findings in exact Bayes. The linkage of decision analyses and clinical algorithms by means of this model exploits a new concept of "regular" clinical algorithms and their equivalency in theory and provides valuable perspectives in practice for developers of clinical algorithms.

Algorithms↗
PubMed1998

Assessing placebo response using Bayesian hierarchical survival models.

The National Institute of Mental Health (NIMH) Collaborative Study of Long-Term Maintenance Drug Therapy in Recurrent Affective Illness was a multicenter randomized controlled clinical trial designed to determine the efficacy of a pharmacotherapy for the prevention of the recurrence of unipolar affective disorders. The outcome of interest in this study was the time until the recurrence of a depressive episode. The data show much heterogeneity between centers for the placebo group. The aim of this paper is to use Bayesian hierarchical survival models to investigate the heterogeneity of placebo effects among centers in the NIMH study. This heterogeneity is explored in terms of the marginal posterior distributions of parameters of interest and predictive distributions of future observations. The Gibbs sampling algorithm is used to approximate posterior and predictive distributions. Sensitivity of results to the assumption of a constant hazard survival distribution at the first stage of the hierarchy is examined by comparing results derived from a two component exponential mixture and a two component exponential changepoint model to the results derived from an exponential model. The second component of the mixture and changepoint models is assumed to be a surviving fraction. For each of these first stage parametric models sensitivity of results to second stage prior distributions is also examined.

Bayes Theorem↗
PubMed2006

Dragon Promoter Mapper (DPM): a Bayesian framework for modelling promoter structures.

UNLABELLED: Dragon Promoter Mapper (DPM) is a tool to model promoter structure of co-regulated genes using methodology of Bayesian networks. DPM exploits an exhaustive set of motif features (such as motif, its strand, the order of motif occurrence and mutual distance between the adjacent motifs) and generates models from the target promoter sequences, which may be used to (1) detect regions in a genomic sequence which are similar to the target promoters or (2) to classify other promoters as similar or not to the target promoter group. DPM can also be used for modelling of enhancers and silencers. AVAILABILITY: http://defiant.i2r.a-star.edu.sg/projects/BayesPromoter/ CONTACT: vlad@sanbi.ac.za SUPPLEMENTARY INFORMATION: Manual for using DPM web server is provided at http://defiant.i2r.a-star.edu.sg/projects/BayesPromoter/html/manual/manual.htm.

Algorithms↗
PubMed1998

A Bayesian hierarchical survival model for the institutional effects in a multi-centre cancer clinical trial.

In randomized clinical trials comparing treatment effects on diseases such as cancer, a multi-centre trial is usually conducted to accrue the required number of patients in a reasonable period of time. While we interpret the average treatment effect, it is necessary to examine the homogeneity of the observed treatment effects across institutions, that is, treatment-by-institution interaction. If the homogeneity is confirmed, the conclusions concerning treatment effects can be generalized to a broader patient population. In this paper, a Bayesian hierarchical survival model is used to investigate the institutional effects on the efficacy of treatment as well as on the baseline risk. The marginal posterior distributions are estimated by a Markov chain Monte Carlo method, that is, Gibbs sampling, to overcome current computational limitations. The robustness of the inferences to the distributional assumption for the random effects is also examined. We illustrate the methods with analyses of data from a multi-centre cancer clinical trial, which investigated the efficacy of immunochemotherapy as an adjuvant treatment after curative resection of gastric cancer. In this trial there is little difference in the treatment effects across institutions and the treatment is shown to be effective, while there appears to be substantial variation in the baseline risk across institutions. This result indicates that the observed treatment effects might be generalized to a broader patient population.

Adjuvants, Immunologic↗
PubMed1998

Gibbs sampler for the logistic model in the analysis of longitudinal binary data.

Logistic mixed-effects models constitute a natural framework to study longitudinal binary response variables when the question addressed with the data is related to covariate effects within persons. However, the computations of the likelihoods are generally tedious and require the resolution of integrals which have no analytical solution. In this paper, we study a logistic mixed-effects model in a Bayesian framework and use the Gibbs sampler to overcome the current computational limitations. From a study of side-effects occurring during plasma exchanges, we explore the issues of bayesian formulation, model parametrization, choice of the prior distributions, diagnosing convergence, comparison between models and model adequacy. Finally, we show that a Bayesian random-effects model is useful to facilitate prediction.

Bayes Theorem↗
PubMed2004

The heritability of breast cancer: a Bayesian correlated frailty model applied to Swedish twins data.

The aim of this study was to investigate the role of genes and environment in susceptibility to breast cancer and to give an estimate of heritability in the propensity to develop the disease. To do this we applied an interdisciplinary approach, merging models developed in the field of demography and survival analysis - so-called frailty models - and models coming from quantitative genetics and epidemiology, namely genetic models. In our study, the inferential problem was solved in a Bayesian framework and the numerical work was carried out using MCMC methods. We used the special information coming from twin data, particularly breast cancer data, from the Swedish Twin Register. The application of a correlated log-normal frailty model leads to a very large estimate of the population heterogeneity (sigma = 6.7), and relatively small correlations between co-twins' frailties - around 0.3 for monozygotic and 0.1 for dizygotic twins. Comparing three different genetic models (an ACE, an AE and an ADE model), we furthermore concluded that genetic effects would explain globally almost 30% of the total variability of propensity to breast cancer. Environmental effects would be predominant in determining breast cancer susceptibility and these effects would be primarily individual-specific, that is, non-shared effects. Finally, a model which includes dominance genetic effects (ADE model) is preferred for genetic and statistical reasons.

Bayes Theorem↗
PubMed2006

A Bayesian semi-parametric model for colorectal cancer incidences.

A Bayesian semi-parametric model is proposed to capture the interaction among demographic effects (age and gender), spatial effects (county) and temporal effects of colorectal cancer incidences simultaneously. In particular, an extension of multivariate conditionally autoregressive (CAR) processes to a partially informative Gaussian demographic spatial temporal CAR (DSTCAR) process for a spatial-temporal setting is proposed. The precision matrix of the Gaussian DSTCAR process is the Kronecker product of several components. The spatial component is modelled with a CAR prior. A pth order intrinsic autoregressive prior (IAR(p)) is implemented for the temporal component to estimate a smoothed and non-parametric temporal trend. The demographic component is modelled with a Wishart prior. Data analysis shows significant spatial correlation only exists in the age group of 50-59. Males and females in their 50s and 60s show fairly strong correlation. The hypothesis testing based on Bayes factor suggests that gender correlation cannot be ignored in this model.

Adult↗
PubMed2006

Using a Bayesian belief network model to categorize length of stay for radical prostatectomy patients.

A clinical pathway implements best medical practices and represents sequencing and timing of interventions by clinicians for a particular clinical presentation. We used a Bayesian belief network (BBN) to model a clinical pathway for radical prostatectomy and to categorize patient's length of stay (LOS) as being met or delayed given the patient's outcomes and activities. A BBN model constructed from historical data collected as part of a retrospective chart study represents probabilistic dependencies between specific events from the pathway and identifies events directly affecting LOS. Preliminary evaluation of a BBN model on an independent test sample of patients' data shows that model reliably categorizes LOS for the second and third day after the surgery (with overall accuracy of 82 and 84%, respectively).

Bayes Theorem↗
PubMed2006

Fusion of Hidden Markov Random Field models and its Bayesian estimation.

In this paper, we present a Hidden Markov Random Field (HMRF) data-fusion model. The proposed model is applied to the segmentation of natural images based on the fusion of colors and textons into Julesz ensembles. The corresponding Exploration/ Selection/Estimation (ESE) procedure for the estimation of the parameters is presented. This method achieves the estimation of the parameters of the Gaussian kernels, the mixture proportions, the region labels, the number of regions, and the Markov hyper-parameter. Meanwhile, we present a new proof of the asymptotic convergence of the ESE procedure, based on original finite time bounds for the rate of convergence.

Algorithms↗
PubMed2006

Disease mapping in veterinary epidemiology: a Bayesian geostatistical approach.

Model-based geostatistics and Bayesian approaches are useful in the context of veterinary epidemiology when point data have been collected by appropriate study design. We take advantage of an example of Epidemiological Surveillance on urban settings where a two-stage sampling design with first stage transects is applied to study the risk of dog parasite infection in the city of Naples, 2004-2005. We specified Bayesian Gaussian spatial exponential models and Bayesian kriging were performed to predict the continuous risk surface of parasite infection on the study region. We compared the results with those obtained by the application of hierarchical Bayesian models on areal data (proportion of positive specimens by transect). The models results were consistent with each other and the Bayesian geostatistical approach proved to be more accurate in identifying areas at risk of zoonotic parasitic diseases. In general, larger risk areas were identified at the city border where wild dogs mixed with domestic dogs and human or urban barriers were less present.

Animal Diseases↗
PubMed2003

Assessment of homogeneity vs. heterogeneity of residual variance in random regression test-day models in a Bayesian analysis.

Test-day first-lactation milk yields from Holstein cows were analyzed with a set of random regression models based on Legendre polynomials of varying order on additive genetic and permanent environmental effects. Homogeneity and heterogeneity of residual variance, assuming three and 30 arbitrary measurement error classes of different length were considered. Unknown parameters were estimated within a Bayesian framework. Bayes factors and a checking function for the cross-validation predictive densities of the data were the tools chosen for selecting among competing models. Residual variances obtained from 30 arbitrary intervals were nearly constant between d 70 and 300 and tended to increase towards the extremes of the lactation, especially at the onset. In early lactation, the temporary measurement errors were found to be larger and highly variable. A high order of the regression submodels employed for modeling the permanent environmental deviations tended to strongly correct the heterogeneity of the residual variance. Accordingly, the assumption of homogeneity of residual variance was the most plausible specification under both comparison criteria when the number of random regression coefficients was set to five. Otherwise, the heterogeneity assumption, using three or 30 error classes, was better supported, depending on the criterion and on the order of the submodel fitted for the permanent environmental effect.

Analysis of Variance↗
PubMed2005

Estimating the intensity of infection with Schistosoma japonicum in villagers of leyte, Philippines. Part I: a Bayesian cumulative logit model. The schistosomiasis transmission and ecology project (STEP).

Intensity profiles for helminths are used to describe population infection status, monitor effectiveness of control programs, and provide accurate data to validate transmission models. This study aims to accurately predict age/gender specific intensity profiles of endemic schistosomiasis japonica infection in the Philippines. Poor sensitivity of the Kato-Katz test and large heterogeneity in infection levels across villages complicate these predictions. Data from 1,989 individuals living in three endemic villages were analyzed with a Bayesian cumulative-logit model adjusting for nonproportional odds, variation between villages, and measurement error. The posterior uncertainty regarding the proportion of individuals in each egg category was high compared with that estimated using a model ignoring measurement error and villages' heterogeneity. The intensity profiles were very different in children less than 7 years old compared with older children and adults. This model could easily be adapted to other parasitic infections or outcomes where an analysis by category would be recommended.

Animals↗
PubMed2006

Evaluation of antiangiogenic treatment effects on tumors' microcirculation by Bayesian physiological pharmacokinetic modeling and magnetic resonance imaging.

A physiological pharmacokinetic (PBPK) model was used to estimate tumor microcirculation in nude mice with a grafted tumor. The kinetics of a rapid clearance blood pool agent, Vistarem, were investigated by dynamic MRI after bolus administration. Signal enhancements were recorded in arterial blood and in tumor tissue. To analyze these data, we developed a whole-body mathematical model of the agent's biodistribution using physiological parameters. The model included six compartments: arterial and venous plasma, tumor (split into capillaries and interstitium), and the rest of the body (also split into capillaries and interstitium). As an application, changes in tumor microcirculation parameters were evaluated in mice receiving either an antiangiogenic treatment (ZD4190) or a placebo. The analysis was performed in a Bayesian framework, and the model was fitted to experimental data using Markov Chain Monte Carlo techniques. Results showed a significant difference in tumor microcirculation between the two groups of mice when the microcirculation parameters are considered together. This whole-body physiological model enables to analyze jointly data in tumor tissue and in arterial blood. This leads to accurate estimates of microcirculation parameters and the evaluation of their uncertainty.

Animals↗
PubMed2000

Bayesian analysis of lactation curves of Holstein-Friesian cattle using a nonlinear model.

A Bayesian procedure was developed for fitting Wood's incomplete Gamma function to test-day milk records of Spanish Holstein Friesian cattle. Each parameter of Wood's function was considered as a dependent variable in a submodel that accounted for systematic effects and genetic relationships among animals. Marginal posterior distributions of model parameters were obtained using Gibbs sampling. Variables of economic interest, such as 305-d yield, persistency, peak yield, and days in milk at peak day were predicted as functions of Wood's function curve parameters. Heritability estimates were 0.26, 0.32, and 0.19 for parameters of Wood's function and 0.26, 0.14, 0.26, and 0.05 for 305-d yield, persistency, peak yield, and days in milk at peak yield. These estimates indicate that it is possible to modify the shape of the lactation curve through genetic selection. Genetic correlations between parameters of Wood's curve and the aforementioned functions of these parameters suggest that selection for 305-d milk yield would result in higher and later peak yield, but only a slight improvement in persistency is expected.

Animals↗
PubMed2006

Bayesian random-effect model for predicting outcome fraught with heterogeneity--an illustration with episodes of 44 patients with intractable epilepsy.

OBJECTIVE: The study aimed to develop a predictive model to deal with data fraught with heterogeneity that cannot be explained by sampling variation or measured covariates. METHODS: The random-effect Poisson regression model was first proposed to deal with over-dispersion for data fraught with heterogeneity after making allowance for measured covariates. Bayesian acyclic graphic model in conjunction with Markov Chain Monte Carlo (MCMC) technique was then applied to estimate the parameters of both relevant covariates and random effect. Predictive distribution was then generated to compare the predicted with the observed for the Bayesian model with and without random effect. Data from repeated measurement of episodes among 44 patients with intractable epilepsy were used as an illustration. RESULTS: The application of Poisson regression without taking heterogeneity into account to epilepsy data yielded a large value of heterogeneity (heterogeneity factor = 17.90, deviance = 1485, degree of freedom (df) = 83). After taking the random effect into account, the value of heterogeneity factor was greatly reduced (heterogeneity factor = 0.52, deviance = 42.5, df = 81). The Pearson chi2 for the comparison between the expected seizure frequencies and the observed ones at two and three months of the model with and without random effect were 34.27 (p = 1.00) and 1799.90 (p < 0.0001), respectively. CONCLUSION: The Bayesian acyclic model using the MCMC method was demonstrated to have great potential for disease prediction while data show over-dispersion attributed either to correlated property or to subject-to-subject variability.

Adolescent↗
PubMed2003

A Bayesian semiparametric joint hierarchical model for longitudinal and survival data.

This article proposes a new semiparametric Bayesian hierarchical model for the joint modeling of longitudinal and survival data. We relax the distributional assumptions for the longitudinal model using Dirichlet process priors on the parameters defining the longitudinal model. The resulting posterior distribution of the longitudinal parameters is free of parametric constraints, resulting in more robust estimates. This type of approach is becoming increasingly essential in many applications, such as HIV and cancer vaccine trials, where patients' responses are highly diverse and may not be easily modeled with known distributions. An example will be presented from a clinical trial of a cancer vaccine where the survival outcome is time to recurrence of a tumor. Immunologic measures believed to be predictive of tumor recurrence were taken repeatedly during follow-up. We will present an analysis of this data using our new semiparametric Bayesian hierarchical joint modeling methodology to determine the association of these longitudinal immunologic measures with time to tumor recurrence.

Bayes Theorem↗
PubMed2006

Development of a pharmacokinetic and Bayesian optimal sampling model for individualization of oral busulfan in hematopoietic stem cell transplantation.

Therapeutic drug monitoring is used to minimize toxicity and maximize the therapeutic efficacy of busulfan, which shows high intra- and interpatient pharmacokinetic variability and erratic oral absorption. This study was designed to develop a pharmacokinetic model that could accommodate the erratic oral absorption of busulfan and to use this model to develop an optimal sparse pharmacokinetic sampling strategy to improve the precision and efficiency of therapeutic drug monitoring. Twenty-one pharmacokinetic profiles were collected from 12 patients receiving oral busulfan before hematopoietic stem cell transplantation. Each pharmacokinetic profile was defined by 5 to 9 plasma concentrations. Candidate pharmacokinetic models were initially fit to the data by maximum likelihood, with model discrimination by Akaike's Information Criterion. Maximum likelihood results were used to derive Bayesian previous parameter estimates, and D-optimal design was used to determine optimal sparse sampling strategies. Each candidate sampling strategy was tested in each patient by comparing the resultant Css obtained from the sparse strategy to the actual Css derived from each patient's full pharmacokinetic dataset. The final model was a 1-compartment model, with oral busulfan absorbed in 1 to 3 phases, and fit the data well. All limited sampling models tested were unbiased in their results, and a 4-sample scheme proved to adequately characterize busulfan pharmacokinetics, and should allow for a reduced sampling frequency for therapeutic drug monitoring.

Administration, Oral↗
PubMed1995

Comparison of 2- and 3-compartment models for the Bayesian estimation of methotrexate pharmacokinetics.

Moderate and high-dose methotrexate was given by a 4-h infusion to 10 patients. The pharmacokinetics of methotrexate, determined by fluorescence polarization immuno-assay, was successively described by a 2- and a 3-compartment open model with elimination from the central compartment. Population pharmacokinetic parameters were obtained by non-linear regression from 8 data points for each course and were subsequently used to fit the same data by the Bayesian estimation method. According to Akaike's information criterion, the 3-compartment model was found statistically superior in 7 patients out of 10. Using this model clearance was well predicted (+/- 5%) by the Bayesian method with only 2 points taken at the end of the infusion and 24 h after. The prediction was less good for the steady-state volume of distribution (+/- 18%) and the half-lives (+/- 20-30%). This procedure enables a good estimation of individual pharmacokinetic parameters for methotrexate, specially with clearance, at minimal cost and minimal disturbance for the patient.

Adolescent↗