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Results for “Bayesian modelling”

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PubMed1989

A Bayesian methodology for scaling radiation studies from animals to man.

This paper describes a Bayesian methodology for integrating studies in experimental animals and humans to obtain a risk estimate for a radionuclide for which no data or very limited human data are available. The method is quite general and is not limited to radiation studies. In fact, it was first developed for chemical toxicants. The methodology is illustrated using studies with rats, beagles, and humans exposed to isotopes of Ra and Pu. The goal is a quantitative risk estimate for bone cancer in humans exposed to internally deposited Pu. The choice of bone cancer as an end point and of Pu as the source of exposure was made partially because of its inherent interest but also because of issues of data availability and suitability. We performed Poisson regression analyses on 13 of 15 data sets. These analyses form the basis for the unifying method of interpreting the entire ensemble of studies. Each of the studies is summarized by the estimated dose-response slope and its estimated standard error. These summary statistics are combined with other available biological and physical information about species differences, physical and metabolic characteristics of isotopes, disease mechanisms, and the like. This information enters the analysis in the form of prior assumptions about the parameters of the Bayesian model combining the studies. The posterior distribution for the bone cancer rate in man from the Bayesian analysis of the 13 studies is updated with the limited data on Pu in humans. This update gives the final probability density for the bone cancer rate in humans exposed to internally deposited Pu. This density has a median of about three cancers per 100 Gy and has a 95% probability interval from 0.8 to 11 bone cancers per 100 Gy.

Animals↗

PubMed2005

Model uncertainty and risk estimation for experimental studies of quantal responses.

Experimental animal studies often serve as the basis for predicting risk of adverse responses in humans exposed to occupational hazards. A statistical model is applied to exposure-response data and this fitted model may be used to obtain estimates of the exposure associated with a specified level of adverse response. Unfortunately, a number of different statistical models are candidates for fitting the data and may result in wide ranging estimates of risk. Bayesian model averaging (BMA) offers a strategy for addressing uncertainty in the selection of statistical models when generating risk estimates. This strategy is illustrated with two examples: applying the multistage model to cancer responses and a second example where different quantal models are fit to kidney lesion data. BMA provides excess risk estimates or benchmark dose estimates that reflects model uncertainty.

Animals↗

PubMed2007

Early prediction of the long term evolution of multiple sclerosis: the Bayesian Risk Estimate for Multiple Sclerosis (BREMS) score.

AIM: To propose a simple tool for early prediction of unfavourable long term evolution of multiple sclerosis (MS). METHODS: A Bayesian model allowed us to calculate, within the first year of disease and for each patient, the Bayesian Risk Estimate for MS (BREMS) score that represents the risk of reaching secondary progression (SP). RESULTS: The median BREMS scores were higher in 158 patients who reached SP within 10 years compared with 1087 progression free patients (0.69 vs 0.30; p<0.0001). The BREMS value was related to SP risk in the whole cohort (p<0.0001) and in the subgroup of 535 patients who had never been treated with immune therapies, thus reasonably representing the natural history of the disease (p<0.000001). CONCLUSIONS: The BREMS score may be useful both to identify patients who are candidates for early or for more aggressive therapies and to improve the design and analysis of clinical therapeutic trials and of observational studies.

Adult↗

PubMed2000

A study of early stopping and model selection applied to the papermaking industry.

This paper addresses the issues of neural network model development and maintenance in the context of a complex task taken from the papermaking industry. In particular, it describes a comparison study of early stopping techniques and model selection, both to optimise neural network models for generalisation performance. The results presented here show that early stopping via use of a Bayesian model evidence measure is a viable way of optimising performance while also making maximum use of all the data. In addition, they show that ten-fold cross-validation performs well as a model selector and as an estimator of prediction accuracy. These results are important in that they show how neural network models may be optimally trained and selected for highly complex industrial tasks where the data are noisy and limited in number.

Algorithms↗

PubMed1987

Bayesian statistical theory in the preoperative diagnosis of pulmonary lesions.

We used a computerized Bayesian algorithm to assist in the preoperative diagnosis of pulmonary lesions. One hundred consecutive patients who were undergoing exploratory thoracotomy for newly discovered pulmonary lesions were prospectively evaluated. The Bayesian model used a total of 44 preoperative clinical and roentgenographic factors to categorize the lesions as benign or malignant. The Bayesian algorithm correctly categorized 96 of the 100 lesions, thereby providing an accuracy of 96 percent. The sensitivity of the model was 98 percent and the specificity was 87 percent. All but two of the 85 malignant lesions were correctly categorized and 13 of the 15 benign lesions were correctly analyzed by the model. These results indicate that computer-assisted diagnosis using the Theorem of Bayes may provide valuable preoperative information for the management of selected patients.

Adolescent↗

PubMed2004

Statistical assessment of mediational effects for logistic mediational models.

The concept of mediation has broad applications in medical health studies. Although the statistical assessment of a mediational effect under the normal assumption has been well established in linear structural equation models (SEM), it has not been extended to the general case where normality is not a usual assumption. In this paper, we propose to extend the definition of mediational effects through causal inference. The new definition is consistent with that in linear SEM and does not rely on the assumption of normality. Here, we focus our attention on the logistic mediation model, where all variables involved are binary. Three approaches to the estimation of mediational effects-Delta method, bootstrap, and Bayesian modelling via Monte Carlo simulation are investigated. Simulation studies are used to examine the behaviour of the three approaches. Measured by 95 per cent confidence interval (CI) coverage rate and root mean square error (RMSE) criteria, it was found that the Bayesian method using a non-informative prior outperformed both bootstrap and the Delta methods, particularly for small sample sizes. Case studies are presented to demonstrate the application of the proposed method to public health research using a nationally representative database. Extending the proposed method to other types of mediational model and to multiple mediators are also discussed.

Adolescent↗

PubMed1999

All maps of parameter estimates are misleading.

Maps are frequently used to display spatial distributions of parameters of interest, such as cancer rates or average pollutant concentrations by county. It is well known that plotting observed rates can have serious drawbacks when sample sizes vary by area, since very high (and low) observed rates are found disproportionately in poorly-sampled areas. Unfortunately, adjusting the observed rates to account for the effects of small-sample noise can introduce an opposite effect, in which the highest adjusted rates tend to be found disproportionately in well-sampled areas. In either case, the maps can be difficult to interpret because the display of spatial variation in the underlying parameters of interest is confounded with spatial variation in sample sizes. As a result, spatial patterns occur in adjusted rates even if there is no spatial structure in the underlying parameters of interest, and adjusted rates tend to look too uniform in areas with little data. We introduce two models (normal and Poisson) in which parameters of interest have no spatial patterns, and demonstrate the existence of spatial artefacts in inference from these models. We also discuss spatial models and the extent to which they are subject to the same artefacts. We present examples from Bayesian modelling, but, as we explain, the artefacts occur generally.

Bayes Theorem↗

PubMed1987

The "constant intake rate" assumption in interim recruitment goal methodology for multicenter clinical trials.

A primary concern of any multihospital clinical trial is the recruitment of a predetermined number of patients during a prespecified interval of time. In several recent papers a Poisson based model was used to estimate the time needed to recruit a predetermined number of patients and the probabilities of recruiting specified fractions of the sample during subintervals. The Poisson model requires the assumption that patients be recruited at a constant rate over the entire length of the interval. In this paper we test the adequacy of this model and assumption using patient intake data from nine multihospital VA clinical trials and propose an alternative Bayesian model.

Bayes Theorem↗

PubMed2001

Risk models used to counsel women for breast and ovarian cancer: a guide for clinicians.

Advances in the identification and treatment of breast and ovarian cancer have lead to a need for reliable estimates of susceptibility risk associated with these two cancers. These estimates may be used in clinical settings to identify individuals at increased risk of developing disease or of being a carrier of a disease susceptibility allele. Accurate assessment of these probabilities is important given the potential implications for medical decision-making including the identification of patients who might benefit from preventive measures, genetic counseling or from entry into clinical trials. A wide range of empirical and statistical models has been proposed, particularly for breast cancer risk prediction, including those that utilize logistic regression or Bayesian modeling. The specific data used to create the various risk models also varies and may include molecular, epidemiologic, or clinical information. This overview presents definitions of risk used in clinical oncology as well as several of the more frequently used methods of risk estimation for breast and ovarian cancer. In addition, the means by which different methods are able to provide a measure of error or uncertainty associated with a given risk estimate will be discussed.

Breast Neoplasms↗

PubMed2005

A Bayesian approach to modeling dynamic effective connectivity with fMRI data.

A state-space modeling approach for examining dynamic relationship between multiple brain regions was proposed in Ho, Ombao and Shumway (Ho, M.R., Ombao, H., Shumway, R., 2005. A State-Space Approach to Modelling Brain Dynamics to Appear in Statistica Sinica). Their approach assumed that the quantity representing the influence of one neuronal system over another, or effective connectivity, is time-invariant. However, more and more empirical evidence suggests that the connectivity between brain areas may be dynamic which calls for temporal modeling of effective connectivity. A Bayesian approach is proposed to solve this problem in this paper. Our approach first decomposes the observed time series into measurement error and the BOLD (blood oxygenation level-dependent) signals. To capture the complexities of the dynamic processes in the brain, region-specific activations are subsequently modeled, as a linear function of the BOLD signals history at other brain regions. The coefficients in these linear functions represent effective connectivity between the regions under consideration. They are further assumed to follow a random walk process so to characterize the dynamic nature of brain connectivity. We also consider the temporal dependence that may be present in the measurement errors. ML-II method (Berger, J.O., 1985. Statistical Decision Theory and Bayesian Analysis (2nd ed.). Springer, New York) was employed to estimate the hyperparameters in the model and Bayes factor was used to compare among competing models. Statistical inference of the effective connectivity coefficients was based on their posterior distributions and the corresponding Bayesian credible regions (Carlin, B.P., Louis, T.A., 2000. Bayes and Empirical Bayes Methods for Data Analysis (2nd ed.). Chapman and Hall, Boca Raton). The proposed method was applied to a functional magnetic resonance imaging data set and results support the theory of attentional control network and demonstrate that this network is dynamic in nature.

Attention↗

PubMedDate not supplied

Lung cancer mortality in a district of La Spezia (Italy) exposed to air pollution from industrial plants.

AIMS AND BACKGROUND: In the last decades, many epidemiological studies have implicated outdoor environmental carcinogens in the onset of lung cancer. The present investigation evaluated lung cancer mortality in two areas of the Province of La Spezia (Northern Italy) exposed to environmental pollution emitted by a coal-fired power station and other industrial sources, including a waste incinerator. METHODS: In the two exposed areas, lung cancer mortality risk for the 1988-1996 calendar period was evaluated using the whole Province population as referent. The corresponding relative risks (RR) were estimated after controlling for age structure, urban/rural gradient and deprivation factors (occupation, education, home ownership, housing conditions and family structure) by a Poisson regression modeling. The geographic pattern of risk for the whole province was evaluated via the Besag, York and Mollié (BYM) bayesian model. RESULTS: Persons living in urban areas showed the highest rates in both sexes. No statistically significant risk excess was found in the two exposed areas among males, after excluding rural and semi-rural zones from the analyses (RR = 1.03 and RR = 0.77). In contrast, a risk excess was observed for females in both exposed areas, which remained elevated and statistically significant (P <0.05) after restriction to urban/semi-urban municipalities and after controlling for deprivation factors (RR = 1.54 and RR = 2.14, respectively). Bayesian mapping confirmed the rural/urban gradient and the risk excess observed in females near the industrial sites. CONCLUSIONS: The risk observed among females is consistent with pollution measurements and with other epidemiologic findings, whereas a strong confounding from occupational exposures and smoking habit could account for the lack of an excess risk in males. However, the ecologic nature of this investigation prevented drawing a causal inference. The pollution-related risk observed in the female gender is an important clue that deserves further epidemiologic attention.

Adult↗

PubMed2006

Variational free energy and the Laplace approximation.

This note derives the variational free energy under the Laplace approximation, with a focus on accounting for additional model complexity induced by increasing the number of model parameters. This is relevant when using the free energy as an approximation to the log-evidence in Bayesian model averaging and selection. By setting restricted maximum likelihood (ReML) in the larger context of variational learning and expectation maximisation (EM), we show how the ReML objective function can be adjusted to provide an approximation to the log-evidence for a particular model. This means ReML can be used for model selection, specifically to select or compare models with different covariance components. This is useful in the context of hierarchical models because it enables a principled selection of priors that, under simple hyperpriors, can be used for automatic model selection and relevance determination (ARD). Deriving the ReML objective function, from basic variational principles, discloses the simple relationships among Variational Bayes, EM and ReML. Furthermore, we show that EM is formally identical to a full variational treatment when the precisions are linear in the hyperparameters. Finally, we also consider, briefly, dynamic models and how these inform the regularisation of free energy ascent schemes, like EM and ReML.

Bayes Theorem↗

PubMed2003

Analysis of a Bayesian repeated measures model for detecting differences in GP prescribing habits.

A linear mixed model is used to detect a change, if any, in the prescribing habits in the UK at the general practice (family medicine) level due to an educational intervention given repeated measures data before and after the intervention and a control group. Inferences are corrected for general practice size and fundholding status. The estimates of the model parameters are obtained using Bayesian inference by applying Gibbs sampling. We develop three different priors for the parameters of the model. These three priors correspond to 'sceptical,' 'reference' and 'enthusiastic' priors in terms of the opinion about the treatment effects that they represent. We compare the results obtained by using these three priors for the parameters in the random effects model.

Anti-Inflammatory Agents, Non-Steroidal↗

PubMed2001

Estimating the Bayesian loss function. A conjoint analysis approach.

Current health economic literature does not provide clear guidelines on how uncertainty around cost-effectiveness estimates should be incorporated into economic decision models. Bayesian analysis is a promising alternative to classical statistics for incorporating uncertainty in economic analysis. Estimating a loss function that relates outcomes to societal welfare is a key component of Bayesian decision analysis. Health economists commonly compute the loss function based on the quality-adjusted life-years associated with each outcome. However, if welfare economics is adopted as the theoretical foundation of the analysis, a loss function based in cost-benefit analysis (CBA) may be more appropriate. CBA has not found wide use in health economics due to practical issues associated with estimating such a loss function. In this paper, we present a method based in conjoint analysis for estimating the CBA loss function that can be applied in practice. We illustrate the use of the methodology using data from a pilot study.

Acute Disease↗

PubMed2006

Bayesian processing of vestibular information.

Complex self-motion stimulations in the dark can be powerfully disorienting and can create illusory motion percepts. In the absence of visual cues, the brain has to use angular and linear acceleration information provided by the vestibular canals and the otoliths, respectively. However, these sensors are inaccurate and ambiguous. We propose that the brain processes these signals in a statistically optimal fashion, reproducing the rules of Bayesian inference. We also suggest that this processing is related to the statistics of natural head movements. This would create a perceptual bias in favour of low velocity and acceleration. We have constructed a Bayesian model of self-motion perception based on these assumptions. Using this model, we have simulated perceptual responses to centrifugation and off-vertical axis rotation and obtained close agreement with experimental findings. This demonstrates how Bayesian inference allows to make a quantitative link between sensor noise and ambiguities, statistics of head movement, and the perception of self-motion.

Acceleration↗

PubMed2004

Sensitivity of Bayes estimators to hyper-parameters with an application to maximum yield from fisheries.

Priors are seldom unequivocal and an important component of Bayesian modeling is assessment of the sensitivity of the posterior to the specified prior distribution. This is especially true in fisheries science where the Bayesian approach has been promoted as a rigorous method for including existing information from previous surveys and from related stocks or species. These informative priors may be highly contested by various interest groups. Here, formulae for the first and second derivatives of Bayes estimators with respect to hyper-parameters of the joint prior density are given. The formula for the second derivative provides a correction to a previously published result. The formulae are shown to reduce to very convenient and easily implemented forms when the hyper-parameters are for exponential family marginal priors. For model parameters with such priors it is shown that the ratio of posterior variance to prior variance can be interpreted as the sensitivity of the posterior mean to the prior mean. This methodology is applied to a nonlinear state-space model for the biomass of South Atlantic albacore tuna and sensitivity of the maximum sustainable yield to the prior specification is examined.

Animals↗

PubMed1992

Ranitidine pharmacokinetics and adverse central nervous system reactions.

BACKGROUND: Treatment with histamine2-receptor antagonists has been associated with adverse central nervous system reactions (CNS-ADRs). Previous studies of cimetidine have shown an association between CNS-ADRs and high cimetidine drug levels. While case reports of ranitidine CNS-ADRs have appeared, we wanted to study a series of patients, some of whom were critically ill, for the presence of CNS-ADRs and to correlate these with ranitidine pharmacokinetics. METHODS: A prospective, observational, open study included 163 consecutive patients, of whom 41 met entry criteria. A nonlinear least-squares regression analysis was used to establish a ranitidine pharmacokinetic dosing model. Ranitidine levels were determined by a high-performance liquid chromatographic assay. Individual ranitidine pharmacokinetics were determined by means of a bayesian model. Observations on 13 possible CNS-ADRs were recorded. The CNS-ADRs were evaluated by the Naranjo rating system. RESULTS: Ranitidine-associated CNS-ADRs, particularly lethargy, confusion, somnolence, and disorientation, occurred more frequently in patients with renal function impairment, and these were associated with higher peak concentrations, average plasma concentrations, and area under the curve. CONCLUSIONS: Ranitidine, when given in conventional doses, can cause CNS-ADRs, particularly in older patients who have substantial renal function impairment. These CNS-ADRs occur as a consequence of altered ranitidine disposition. Ranitidine doses should be reduced when renal function impairment is present, and patients should be carefully observed for CNS-ADRs.

Aged↗

PubMed2002

Bayesian infinite mixture model based clustering of gene expression profiles.

MOTIVATION: The biologic significance of results obtained through cluster analyses of gene expression data generated in microarray experiments have been demonstrated in many studies. In this article we focus on the development of a clustering procedure based on the concept of Bayesian model-averaging and a precise statistical model of expression data. RESULTS: We developed a clustering procedure based on the Bayesian infinite mixture model and applied it to clustering gene expression profiles. Clusters of genes with similar expression patterns are identified from the posterior distribution of clusterings defined implicitly by the stochastic data-generation model. The posterior distribution of clusterings is estimated by a Gibbs sampler. We summarized the posterior distribution of clusterings by calculating posterior pairwise probabilities of co-expression and used the complete linkage principle to create clusters. This approach has several advantages over usual clustering procedures. The analysis allows for incorporation of a reasonable probabilistic model for generating data. The method does not require specifying the number of clusters and resulting optimal clustering is obtained by averaging over models with all possible numbers of clusters. Expression profiles that are not similar to any other profile are automatically detected, the method incorporates experimental replicates, and it can be extended to accommodate missing data. This approach represents a qualitative shift in the model-based cluster analysis of expression data because it allows for incorporation of uncertainties involved in the model selection in the final assessment of confidence in similarities of expression profiles. We also demonstrated the importance of incorporating the information on experimental variability into the clustering model. AVAILABILITY: The MS Windows(TM) based program implementing the Gibbs sampler and supplemental material is available at http://homepages.uc.edu/~medvedm/BioinformaticsSupplement.htm CONTACT: medvedm@email.uc.edu

Bayes Theorem↗