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PubMed2002

Decision analytical economic modelling within a Bayesian framework: application to prophylactic antibiotics use for caesarean section.

Economic evaluation of health care interventions based on decision analytic modelling can generate valuable information for health policy decision makers. However, the usefulness of the results obtained depends on the quality of the data input into the model; that is, the accuracy of the estimates for the costs, effectiveness, and transition probabilities between the different health states of the model. The aim of this paper is to review the use of Bayesian decision models in economic evaluation and to demonstrate how the individual components required for decision analytical modelling (i.e., systematic review incorporating meta-analyses, estimation of transition probabilities, evaluation of the model, and sensitivity analysis) may be addressed simultaneously in one coherent Bayesian model evaluated using Markov Chain Monte Carlo simulation implemented in the specialist Bayesian statistics software WinBUGS. To illustrate the method described, a simple probabilistic decision model is developed to evaluate the cost implications of using prophylactic antibiotics in caesarean section to reduce the incidence of wound infection. The advantages of using the Bayesian statistical approach outlined compared to the conventional classical approaches to decision analysis include the ability to: (i) perform all necessary analyses, including all intermediate analyses (e.g., meta-analyses) required to derive model parameters, in a single coherent model; (ii) incorporate expert opinion either directly or regarding the relative credibility of different data sources; (iii) use the actual posterior distributions for parameters of interest (opposed to making distributional assumptions necessary for the classical formulation); and (iv) incorporate uncertainty for all model parameters.

Antibiotic Prophylaxis↗

PubMed2006

Stochastic complexities of general mixture models in variational Bayesian learning.

In this paper, we focus on variational Bayesian learning of general mixture models. Variational Bayesian learning was proposed as an approximation of Bayesian learning. While it has provided computational tractability and good generalization in many applications, little has been done to investigate its theoretical properties. The asymptotic form was obtained for the stochastic complexity, or the free energy in the variational Bayesian learning of a mixture of exponential-family distributions, which is the main contribution this paper makes. We reveal that the stochastic complexities become smaller than those of regular statistical models, which implies that the advantages of Bayesian learning are still retained in variational Bayesian learning. Moreover, the derived bounds indicate what influence the hyperparameters have on the learning process, and the accuracy of the variational Bayesian approach as an approximation of true Bayesian learning.

Animals↗

PubMed2006

Predicting coronary heart disease mortality--assessing uncertainties in population forecasts and death probabilities by using Bayesian inference.

BACKGROUND: Predictions concerning people and their health are influenced by many factors and have many sources of uncertainty. Even so predictions can give useful guidelines for health care planning. We present a Bayesian model based on past observations and prior knowledge to predict coronary heart disease (CHD) mortality in selected areas of Finland until the year 2030. METHODS: CHD mortality data are based on official statistics. The study area consists of one western and two eastern parts of Finland. The modelling of the probability of death follows a Bayesian age-period-cohort model. Two models are used, one assuming that the trend from 1970 to 2002 will continue and the other that mortality will stay at the attained level. RESULTS: If the observed trend in CHD mortality were to continue, death probabilities would decrease significantly among men aged 50-69 and women aged 50-59. In the older age groups (men aged 70 and women 60 years or more) the changes were found to be negligible. If the trend continues, the number of CHD deaths will decrease from 2002 to 2030 significantly among men [81% decrease; 95% credible interval (95% CI) 54-96%] and women (90%; 67-100%) aged 50-59. In the age group 60-79 the changes will be smaller and non-significant. In the oldest age group (80-99 years) the predicted increase in the number of deaths will be great, from 284 to 1297 (95% CI 474-2620) in men and from 722 to 1970 (717-4017) in women. CONCLUSIONS: Our predictions emphasize the significance of maintaining the recent decline of CHD mortality among middle-aged adults. Special attention should be paid to CHD mortality among men and women aged 80 and over. Considerable improvements in prevention and treatment are needed to compensate for the effects of ageing of the population.

Age Factors↗

PubMed2005

Identifying interacting SNPs using Monte Carlo logic regression.

Interactions are frequently at the center of interest in single-nucleotide polymorphism (SNP) association studies. When interacting SNPs are in the same gene or in genes that are close in sequence, such interactions may suggest which haplotypes are associated with a disease. Interactions between unrelated SNPs may suggest genetic pathways. Unfortunately, data sets are often still too small to definitively determine whether interactions between SNPs occur. Also, competing sets of interactions could often be of equal interest. Here we propose Monte Carlo logic regression, an exploratory tool that combines Markov chain Monte Carlo and logic regression, an adaptive regression methodology that attempts to construct predictors as Boolean combinations of binary covariates such as SNPs. The goal of Monte Carlo logic regression is to generate a collection of (interactions of) SNPs that may be associated with a disease outcome, and that warrant further investigation. As such, the models that are fitted in the Markov chain are not combined into a single model, as is often done in Bayesian model averaging procedures. Instead, the most frequently occurring patterns in these models are tabulated. The method is applied to a study of heart disease with 779 participants and 89 SNPs. A simulation study is carried out to investigate the performance of the Monte Carlo logic regression approach.

Haplotypes↗

PubMed2004

The Precautionary Principle and statistical approaches to uncertainty.

The central challenge from the Precautionary Principle to statistical methodology is to help delineate (preferably quantitatively) the possibility that some exposure is hazardous, even in cases where this is not established beyond reasonable doubt. The classical approach to hypothesis testing is unhelpful, because lack of significance can be due either to uninformative data or to genuine lack of effect (the Type II error problem). Its inversion, bioequivalence testing, might sometimes be a model for the Precautionary Principle in its ability to "prove the null hypothesis". Current procedures for setting safe exposure levels are essentially derived from these classical statistical ideas, and we outline how uncertainties in the exposure and response measurements affect the no observed adverse effect level, the Benchmark approach and the "Hockey Stick" model. A particular problem concerns model uncertainty: usually these procedures assume that the class of models describing dose/response is known with certainty; this assumption is, however, often violated, perhaps particularly often when epidemiological data form the source of the risk assessment, and regulatory authorities have occasionally resorted to some average based on competing models. The recent methodology of the Bayesian model averaging might be a systematic version of this, but is this an arena for the Precautionary Principle to come into play?

Bayes Theorem↗

PubMed2005

Decision support for diagnosis of lyme disease.

This paper describes the development of a Bayesian model for diagnosis of patients suspected of Lyme disease, and the integration of such a model into a medical information system. A Bayesian network incorporating the clinical history and laboratory results has been constructed. Because many of the symptoms are not exclusive to Lyme disease and they develop over time, the clinical history is important for making the correct diagnosis. The model is based on time slices, where each time slice contains the observed pathological picture from one consultation with for example, the general practitioner. Since the time intervals between consultations typically are not equivalent, we have developed a novel method that can handle non-equivalent time intervals between the time slices in the network. The method is based on a description of the general development pattern of Lyme disease, which is implemented in a model that states the conditional probabilities of experiencing a certain pathological picture given time since infection. The model has been integrated into a web-based medical information system, called Borrelia Systems, which has enabled us to evaluate the model during a progressive diagnostic process. The integration has been accomplished through the development of a Bayesian Application Framework. This framework specifies a communication data structure in XML providing a graphical user interface and database components, which can be used when developing systems that are based on Bayesian networks. The framework generalizes the integration of Bayesian networks so that it is possible to switch network without manually having to update or change the system.

Bayes Theorem↗

PubMed2004

Analysis of melanoma onset: assessing familial aggregation by using estimating equations and fitting variance components via Bayesian random effects models.

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

Adolescent↗

PubMed1999

Bayesian survival analysis using a MARS model.

A Bayesian multivariate adaptive regression spline fitting approach is used to model univariate and multivariate survival data with censoring. The possible models contain the proportional hazards model as a subclass and automatically detect departures from this. A reversible jump Markov chain Monte Carlo algorithm is described to obtain the estimate of the hazard function as well as the survival curve.

Algorithms↗

PubMed2000

Combining physician's subjective and physiology-based objective mortality risk predictions.

OBJECTIVE: None of the currently available physiology-based mortality risk prediction models incorporate subjective judgements of healthcare professionals, a source of additional information that could improve predictor performance and make such systems more acceptable to healthcare professionals. This study compared the performance of subjective mortality estimates by physicians and nurses with a physiology-based method, the Pediatric Risk of Mortality (PRISM) III. Then, healthcare provider estimates were combined with PRISM III estimates using Bayesian statistics. The performance of the Bayesian model was then compared with the original two predictions. DESIGN: Concurrent cohort study. SETTING: A tertiary pediatric intensive care unit at a university affiliated children's hospital. PATIENTS: Consecutive admissions to the pediatric intensive care unit. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: For each of the 642 consecutive eligible patients, an exact mortality estimate and the degree of certainty (continuous scale from 1 to 5) associated with the estimate was collected from the attending, fellow, resident, and nurse responsible for the patient's care. Bayesian statistics were used to combine the PRISM III and certainty weighted subjective predictions to create a third Bayesian estimate of mortality. PRISM III discriminated survivors from nonsurvivors very well (area under curve [AUC], 0.924) as did the physicians and nurses (AUCs attendings, 0.953; fellows, 0.870; residents, 0.923; nurses, 0.935). Although the AUCs of the healthcare providers were not significantly different from the AUCs of PRISM III, the Bayesian AUCs were higher than both the healthcare providers' AUCs (p < or = .09 for all) and PRISM III AUCs. Similarly, the calibration statistics for the Bayesian estimates were superior to the calibration statistics for both the healthcare providers and PRISM III models. CONCLUSIONS: The results of this study demonstrated that healthcare providers' subjective mortality predictions and PRISM III mortality predictions perform equally well. The Bayesian model that combined provider and PRISM III mortality predictions was more accurate than either provider or PRISM III alone and may be more acceptable to physicians. A methodology using subjective outcome predictions could be more relevant to individual patient decision support.

Adolescent↗

PubMed2006

Bayesian semiparametric dynamic frailty models for multiple event time data.

Many biomedical studies collect data on times of occurrence for a health event that can occur repeatedly, such as infection, hospitalization, recurrence of disease, or tumor onset. To analyze such data, it is necessary to account for within-subject dependency in the multiple event times. Motivated by data from studies of palpable tumors, this article proposes a dynamic frailty model and Bayesian semiparametric approach to inference. The widely used shared frailty proportional hazards model is generalized to allow subject-specific frailties to change dynamically with age while also accommodating nonproportional hazards. Parametric assumptions on the frailty distribution are avoided by using Dirichlet process priors for a shared frailty and for multiplicative innovations on this frailty. By centering the semiparametric model on a conditionally conjugate dynamic gamma model, we facilitate posterior computation and lack-of-fit assessments of the parametric model. Our proposed method is demonstrated using data from a cancer chemoprevention study.

Algorithms↗

PubMed1998

Model-based, goal-oriented, individualised drug therapy. Linkage of population modelling, new 'multiple model' dosage design, bayesian feedback and individualised target goals.

This article examines the use of population pharmacokinetic models to store experiences about drugs in patients and to apply that experience to the care of new patients. Population models are the Bayesian prior. For truly individualised therapy, it is necessary first to select a specific target goal, such as a desired serum or peripheral compartment concentration, and then to develop the dosage regimen individualised to best hit that target in that patient. One must monitor the behaviour of the drug by measuring serum concentrations or other responses, hopefully obtained at optimally chosen times, not only to see the raw results, but to also make an individualised (Bayesian posterior) model of how the drug is behaving in that patient. Only then can one see the relationship between the dose and the absorption, distribution, effect and elimination of the drug, and the patient's clinical sensitivity to it; one must always look at the patient. Only by looking at both the patient and the model can it be judged whether the target goal was correct or needs to be changed. The adjusted dosage regimen is again developed to hit that target most precisely starting with the very next dose, not just for some future steady state. Nonparametric population models have discrete, not continuous, parameter distributions. These lead naturally into the multiple model method of dosage design, specifically to hit a desired target with the greatest possible precision for whatever past experience and present data are available on that drug--a new feature for this goal-oriented, model-based, individualised drug therapy. As clinical versions of this new approach become available from several centers, it should lead to further improvements in patient care, especially for bacterial and viral infections, cardiovascular therapy, and cancer and transplant situations.

Anti-Arrhythmia Agents↗

PubMed1997

A Weibull regression model with gamma frailties for multivariate survival data.

Frequently in the analysis of survival data, survival times within the same group are correlated due to unobserved co-variates. One way these co-variates can be included in the model is as frailties. These frailty random block effects generate dependency between the survival times of the individuals which are conditionally independent given the frailty. Using a conditional proportional hazards model, in conjunction with the frailty, a whole new family of models is introduced. By considering a gamma frailty model, often the issue is to find an appropriate model for the baseline hazard function. In this paper a flexible baseline hazard model based on a correlated prior process is proposed and is compared with a standard Weibull model. Several model diagnostics methods are developed and model comparison is made using recently developed Bayesian model selection criteria. The above methodologies are applied to the McGilchrist and Aisbett (1991) kidney infection data and the analysis is performed using Markov Chain Monte Carlo methods.

Bayes Theorem↗

PubMed2004

Comparison of Bayesian, classical, and heuristic approaches in identifying acute disease events in lung transplant recipients.

This study compares a typical heuristic algorithm with classical and Bayesian regression models in ascertaining the presence of acute bronchopulmonary disease events in lung transplant recipients. These models attempt to predict whether an epoch will end in an event, based on the preceding two weeks of data. The data consist of 150 two-week epochs of daily to biweekly spirometry and symptom covariates for 30 subjects over 60 subject-years. Seventy-five 'event' epochs end on a day when an acute bronchopulmonary disease event is documented in the medical record; 75 randomly selected 'non-event' epochs end on a day when no event is documented. The data are partitioned by randomly assigning 15 subjects for training and the remaining 15 subjects for testing. For cross-validation, a second random partition is generated from the same data set. The statistical models are trained and tested on both partitions. For the heuristic algorithm, its historical event classifications on the same test cases are used. Classification performance on both partitions of all models is compared using receiver operating characteristic curves, sensitivity and specificity, and a Shannon information score. Data partition did not appreciably affect statistical model performance. All statistical models, unlike the heuristic algorithm, performed significantly different than chance (family significance < 0.05, Pearson independence chi-square, Bonferroni multiple correction), and better than the heuristic algorithm. The best models were Bayesian changepoint models. Through a clinically oriented discussion, a case classified by all of these algorithms is presented, suggesting the clinical usefulness of the Bayesian approach compared with the classical and heuristic approaches.

Acute Disease↗

PubMed2026

On the origin of animals and placental mammals: a critique of literalist readings of the fossil record.

The fossil record is incomplete, as evidenced by the pervasive presence of ghost lineages throughout the Tree of Life. For example, across placental mammals, at least 720 Myr of basal lineages are ghost lineages, that is, lineages that have left no fossil evidence of their past history. In contrast, some studies have suggested that the fossil record is a faithful temporal archive of evolutionary history and thus the times of diversification of clades must be close to the ages of their oldest fossils. Such literalist interpretations have been contradicted by analysis of molecular datasets which, in many cases, indicate that groups including placental mammals and animals may have originated at times substantially older than their fossil records. Some of those studies have further argued that, in the case of animals and placental mammals, molecular clocks are uninformative, suffer from characteristic pathologies, and thus cannot distinguish between recent and ancient hypotheses of diversification. Here, we reexamine these two cases and show, using Bayesian model selection theory, that the explosive diversification models previously proposed for animals and placental mammals have a posterior probability of ∼0. We show the characteristic pathologies purportedly discovered do not exist, highlight errors in previous analyses, and provide advice on best practice for molecular-clock dating analysis.

Animals↗

PubMed2004

Comprehensive decision analytical modelling in economic evaluation: a Bayesian approach.

Decision analytical models are widely used in economic evaluation of health care interventions with the objective of generating valuable information to assist health policy decision-makers to allocate scarce health care resources efficiently. The whole decision modelling process can be summarised in four stages: (i) a systematic review of the relevant data (including meta-analyses), (ii) estimation of all inputs into the model (including effectiveness, transition probabilities and costs), (iii) sensitivity analysis for data and model specifications, and (iv) evaluation of the model. The aim of this paper is to demonstrate how the individual components of decision modelling, outlined above, may be addressed simultaneously in one coherent Bayesian model (sometimes known as a comprehensive decision analytical model) and evaluated using Markov Chain Monte Carlo simulation implemented in the specialist software WinBUGS. To illustrate the method described, it is applied to two illustrative examples: (1) The prophylactic use of neurominidase inhibitors for the prevention of influenza. (2) The use of taxanes for the second-line treatment of advanced breast cancer. The advantages of integrating the four stages outlined into one comprehensive decision analytical model, compared to the conventional 'two-stage' approach, are discussed.

Adolescent↗

PubMed2026

Weathering the storm: Most maternal and environmental drivers of individual reproductive success do not scale up to population recruitment in a large herbivore.

Population growth depends upon individual survival and reproduction, but do drivers of individual reproductive success scale up to population recruitment? Factors affecting individuals may have little effect on population dynamics if individuals within a population experience different conditions. When seasonal resource availability is unpredictable and breeding season long, average conditions over a breeding cycle may poorly reflect the environment experienced by many individuals. We compared the drivers of individual reproductive success and population recruitment in an asynchronously breeding large herbivore, the eastern grey kangaroo (Macropus giganteus). We analysed 18 years of individual-based data using multivariate hierarchical Bayesian models to first identify the causal mechanisms relating population density, environmental conditions and maternal traits to individual success. We then assessed whether the drivers of individual reproductive success scaled up to determine population recruitment. Most maternal and environmental covariates strongly influenced individual reproductive success, with distinct effects on juvenile survival before and after pouch exit. Maternal traits had a greater influence in the pouch, whereas environmental conditions became increasingly important once young exited the pouch. Most drivers of individual reproductive success did not affect population recruitment. Recruitment increased with population density and mean body condition of adult females. Weather harshness had a weak positive effect on recruitment, which appeared independent of female age structure, previous recruitment or forage. Most drivers of individual reproductive success did not scale up to population recruitment. Birth asynchrony could buffer population recruitment against environmental variation such that variables affecting individual reproduction have little impact at the population level. Large herbivores that reproduce asynchronously may therefore be more resilient to environmental variability than synchronous breeders.

Bayesian modelling↗

PubMed2000

Predictive inference, causal reasoning, and model assessment in nonparametric Bayesian analysis: a case study.

This paper continues our earlier analysis of a data set on acute ear infections in small children, presented in Andreev and Arjas (1998). The main goal here is to provide a method, based on the use of predictive distributions, for assessing the possible causal influence which the type of day care will have on the incidence of ear infections. A closely related technique is used for the assessment of the nonparametric Bayesian intensity model applied in the paper. Two graphical methods, supported by formal tests, are suggested for this purpose.

Algorithms↗

PubMed2004

Population pharmacokinetics of pyrimethamine and sulfadoxine in children treated for congenital toxoplasmosis.

The population pharmacokinetics of pyrimethamine (PYR) and sulfadoxine (SDX) for a group of 32 children with congenital toxoplasmosis was investigated by nonparametric modeling analysis. A one-compartment model was used as the structural model, and individual pharmacokinetic parameters were estimated by Bayesian modeling. PYR (1.25 mg/kg of body weight) and SDX (25 mg/kg) were administered orally every 10 days for 1 year, with adjustment of the dose to body weight every 3 months. Drug concentrations were measured by high-performance liquid chromatography. A total of 101 measurements in serum were available for both drugs. Mean absorption rate constants, volumes of distribution, elimination rate constants, and half-lives were 0.915 h(-1), 4.379 liters/kg, 0.00839 h(-1), and 5.5 days for PYR and 1.659 h(-1), 0.392 liters/kg, 0.00526 h(-1), and 6.6 days for SDX, respectively. Wide interindividual variability was observed. The estimated minimum and maximum concentrations of PYR in serum differed 8- and 25-fold among patients, respectively, and those of SDX differed 4- and 5-fold, respectively. Increases in the concentration of PYR were observed for eight children, and increases in the SDX concentration were observed for seven children. Serum PYR-SDX concentrations are unpredictable even when the dose is standardized for body weight. The concentrations of the PYR-SDX combination that are most efficacious for children have not yet been established. A model such as ours, associated with long-term follow-up, is needed to study the correlation between exposure to these two drugs and clinical outcome in children.

Antiprotozoal Agents↗