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Cerebral modeling and dynamic Bayesian networks.

The understanding and the prediction of the clinical outcomes of focal or degenerative cerebral lesions, as well as the assessment of rehabilitation procedures, necessitate knowing the cerebral substratum of cognitive or sensorimotor functions. This is achieved by activation studies, where subjects are asked to perform a specific task while data of their brain functioning are obtained through functional neuroimaging techniques. Such studies, as well as animal experiments, have shown that sensorimotor or cognitive functions are the offspring of the activity of large-scale networks of anatomically connected cerebral regions. However, no one-to-one correspondence between activated networks adn functions can be found. Our research aims at understanding how the activation of large-scale networks derives from cerebral information processing mechanisms, which can only explain apparently conflicting activation data. Our work falls at the crossroads of neuroimaging interpretation techniques and computational neuroscience. Since knowledge in cognitive neuroscience is permanently evolving, our research aims more precisely at defining a new modeling formalism and at building a flexible simulator, allowing a quick implementation of the models, for a better interpretation of cerebral functional images. It also aims at providing plausible models, at eht level of large-scale networks, of cerebral information processing mechanisms in humans. In this paper, we propose a formalism, based on dynamic Bayesian networks (DBNs), that respects the following constraints: an oriented, networks architecture, whose nodes (the cerebral structures) can all be different, the implementation of causality--the activation of the structure is caused by upstream nodes' activation--the explicit representation of different time scales (from 1 ms for the cerebral activity to many seconds for a PET scan image acquisition), the representation of cerebral information at the integrated level of neuronal populations, the imprecision of functional neuroimaging data, the nonlinearity and the uncertainty in cerebral mechanisms, and brain's plasticity (learning, reorganization, modulation). One of the main problems, nonlinearity, has been tackled thanks to new extensions of the Kalman filter. The capabilities of the formalism's current version are illustrated by the modeling of a phoneme categorization process, explaining the different cerebral activations in normal and dyslexic subjects.

Bayes Theorem↗

Meta-analysis and the synthesis of evidence.

Use of meta-analytical (quantitative overview) techniques is now commonplace in a large range of medical-research contexts, with a rapid rise in its frequency of use being particularly apparent in the last decade. Many methods of meta-analysis have been proposed and used, from crude 'vote-counting' of studies showing significant or nonsignificant results, through methods for combination of effect-size estimates based on fixed- or random-effects models, to general, linear, mixed models and Bayesian methods. The history of meta-analysis and the advantages and disadvantages of various approaches to it are briefly reviewed in this paper, with reference to its application in health-services research and related fields. Broader approaches to the synthesis of evidence in these contexts using conventional multilevel modelling and hierarchical Bayesian models to address the combination of evidence from disparate types of study are then outlined.

Bayes Theorem↗

A Bayesian approach for population pharmacokinetic modelling of sirolimus.

AIMS: To explore a Bayesian approach for the pharmacokinetic analysis of sirolimus concentration data arising from therapeutic drug monitoring (poorly informative concentration-time point design), and to explore possible covariate relationships for sirolimus pharmacokinetics. METHODS: Sirolimus concentration-time data were available as part of routine clinical care from 25 kidney transplant recipients. Most samples were taken at or near the trough time point at steady state. The data were analyzed using a fully conditional Bayesian approach with PKBUGS (v 1.1)/WinBUGS (v 1.3). Features of the data included noncompliance and missing concentration measurements below the limit of sensitivity of the assay. Informative priors were used. RESULTS: A two-compartment model with proportional residual error provided the best fit to the data (consisting of 315 sirolimus concentration-time points). The typical value for the apparent clearance (CL/F ) was 12.5 l h(-1) at the median age of 44 years. Apparent CL was found to be inversely related to age with a posterior probability of a clinically significant effect of 0.734. CONCLUSIONS: A population pharmacokinetic model was developed for sirolimus using a novel approach. Bayesian modelling with informative priors allowed interpretation of a significant covariate relationship, even using poorly informative data.

Adult↗

Bayesian registration of models using finite element eigenmodes.

This paper is concerned with registering three-dimensional wire-frame organ models. This involves finding correspondences between points on the models of two different examples of the same organ. Such registration is widely used in the processing of medical data; for example in segmentation, or to superimpose functional information on a more detailed structural map. The algorithm described in this paper is based on matching the modes of deformation of organ shapes. Modes with lower spatial frequency characterise large scale organ features whereas small scale variations determine the high frequency modes. First, the organ sizes are normalised using a generalised version of the centroid size metric. The axes of the fundamental frequency modes are then aligned to provide initial rigid-body registration. The registration is refined by matching increasingly high frequency modes using the 'Highest confidence first' algorithm. The matches are evaluated using a Bayesian combination of local prior and likelihood functions. The prior is derived from the Gompertz metric of biological growth and ensures that physically impossible matches are not accepted. The likelihood function is a measure of the similarity between local modal deformation components. The registration algorithm has been applied by the authors in the analysis of three dimensional ultrasound data. Results are presented showing the registration of two liver models derived from 3D ultrasound.

Algorithms↗

Generalization of map estimation in SAAM II: validation against ADAPT II in a glucose model case study.

Bayesian approaches to model identification [e.g., maximum a posteriori (MAP) estimation] are receiving increasing attention in metabolism since important quantitative knowledge has become available in the last decades, e.g., from tracer experiments. By suitably exploiting this knowledge, more complex physiological models than those solely based on experimental data (Fisherian approach) become resolvable. While ADAPT II is the reference software for MAP estimation in pharmacokinetic/pharmacodynamic/metabolic system analysis, another popular, user-friendly and state-of-the-art software is SAAM II. However, SAAM II does not handle a priori information on correlation among parameters, thus allowing a limited version of MAP estimation to be performed. The aim here is twofold. First, we show that this limitation of SAAM II can be easily overcome by resorting to a probability theory result. Second, we test SAAM II vs ADAPT II implementation of MAP estimation in a real case study: the Bayesian identification of a recently proposed two-compartment minimal model of glucose kinetics during an intravenous glucose tolerance test. SAAM II MAP estimates of glucose effectiveness (SG) and insulin sensitivity (S(I)) obtained in a group of 22 healthy humans are in excellent agreement with those of ADAPT II: S(G) = 2.84 +/- 0.27 vs. 2.84 +/- 0.27 (mlmin(-1) kg(-1), mean +/- SD) and S(I) = 11.46 +/- 1.69 vs. 11.47 +/- 1.69 [10(-2) ml kg(-1) min(-1)/ (microU ml(-1))]. The SAAM II vs. ADAPT II estimates are virtually identical (P > 0.44 and 0.68 for S(G) and S(I), respectively) and also closely correlated (p = 0.9998 and 0.9999).

Algorithms↗

Projecting cancer incidence and mortality using Bayesian age-period-cohort models.

BACKGROUND: We present a practical application of an age-period-cohort model in a Bayesian frame-work for making cancer-burden projections. METHODS: Second degree autoregressive smoothing was used on the age, period and cohort effects for estimating future incidence and mortality. RESULTS: We are able to demonstrate the feasibility, flexibility and strengths of this approach. Compared with previously used methods, it performed better for providing point estimates when past trends continued into the future. However, the extremely wide credible intervals need careful interpretation. DISCUSSION: Part of the uncertainty is attributable to the possible inadequacy of the model and not necessarily relevant in the prediction of what would happen if the present trends continue into the future.

Age Factors↗

Bayesian 2-D deconvolution: a model for diffuse ultrasound scattering.

Observed medical ultrasound images are degraded representations of the true acoustic tissue reflectance. The degradation is due to blur and speckle and significantly reduces the diagnostic value of the images. To remove both blur and speckle, we have developed a new statistical model for diffuse scattering in 2-D ultrasound radio frequency images, incorporating both spatial smoothness constraints and a physical model for diffuse scattering. The modeling approach is Bayesian in nature, and we use Markov chain Monte Carlo methods to obtain the restorations. The results from restorations of some real and simulated radio frequency ultrasound images are presented and compared with results produced by Wiener filtering.

Algorithms↗

Exploring the relationship between rationality and bounded rationality in medical knowledge-based systems.

If our goal in Artificial Intelligence in Medicine (AIM) is to engineer systems health-care providers will both use and, in the process, improve their performance, we must concentrate on the development of causal theories of knowledge and problem solving. One broad direction in pursuing this goal is understanding the relationships between existing models of rationality and bounded rationality for similar tasks. Models of rationality refer to those approaches in which the optimal properties of the models are deductively provable, i.e. in which the processing is rational. Representative models of rationality used in AIM are deductive logical models, statistical models such as Bayesian inference models, and decision-analytic models. Models of bounded rationality are those which do not guarantee such optimal properties nor yield to deductive correctness proofs. These models have their roots in cognitive psychology. In this article we show how explicating the relationship between models of rationality and bounded rationality might be done in the case of abductive tasks in medicine. This is done by positioning these modeling approaches within the same framework (an abstract computational model) and interpreting in this context both computational complexity results concerning the nature of the task and empirical results studies of human problem-solving behavior.

Artificial Intelligence↗

Positional entropy during pigeon homing I: application of Bayesian latent state modelling.

In these two companion papers, we introduce a new approach to the analysis of bird navigation which brings together several novel mathematical and technical applications. Miniaturized GPS logging devices provide track data of sufficiently high spatial and temporal resolution that considerable variation in flight behaviour can be observed remotely from the form of the track alone. We analyse a fundamental measure of bird flight track complexity, spatio-temporal entropy, and explore its state-like structure using a probabilistic hidden Markov model. The emergence of a robust three-state structure proves that the technique has analytical power, since this structure was not obvious in the tracks alone. We propose the hypothesis that positional entropy is indicative of underlying navigational uncertainty, and that familiar area navigation may break down into three states of navigational confidence. By interpreting the relationship between these putative states and features on the map, we are able to propose a number of hypothetical navigational strategies feeding into these states. The first of these two papers details the novel technical developments associated with this work and the second paper contains a navigational interpretation of the results particularly with respect to visual features of the landscape.

Animals↗

Positional entropy during pigeon homing II: navigational interpretation of Bayesian latent state models.

In these two companion papers we introduce a new approach to the analysis of bird navigation which brings together several novel mathematical and technical applications. Miniaturized GPS logging devices provide track data of sufficiently high spatial and temporal resolution that considerable variation in flight behaviour can be observed remotely from the form of the track alone. We analyse a fundamental measure of bird flight track complexity, spatio-temporal entropy, and explore its state-like structure using a probabilistic hidden Markov model. The emergence of a robust three-state structure proves that the technique has analytical power, since this structure was not obvious in the tracks alone. We propose the hypothesis that positional entropy is indicative of underlying navigational uncertainty, and that familiar area navigation may break down into three states of navigational confidence. By interpreting the relationship between these putative states and features on the map, we are able to propose a number of hypothetical navigational strategies feeding into these states. The first of these two papers details the novel technical developments associated with this work and the second paper contains a navigational interpretation of the results particularly with respect to visual features of the landscape.

Animals↗

The Chatham Blood Pressure Study. An application of Bayesian growth curve models to a longitudinal study of blood pressure in children.

Recent developments in statistics have produced powerful methods that facilitate the analysis of longitudinal studies. These methods are illustrated by an analysis of a longitudinal study of blood pressure in children. The results of the study show a clear tendency for blood pressure to increase with age, and Asian children tend to have lower blood pressures than their Caucasian counterparts of the same age. There is evidence to support the hypothesis that blood pressures track.

Age Factors↗

Prediction of future serum concentrations with Bayesian fitted pharmacokinetic models: results with data collected by nurses versus trained pharmacy residents.

Recording the times of dosage administration and serum sampling by trained personnel resulted in significantly greater adherence to the protocol of therapeutic drug monitoring and in significantly greater precision in the achievement of desired serum concentration goals of aminoglycoside therapy than when relatively untrained personnel recorded it as a comparatively unemphasized part of their job. This was true even when only data of peak and trough serum concentrations were used. This study demonstrates that thoughtful data collection by appropriately trained nursing, pharmacy, or other clinical personnel is an essential part of therapeutic drug monitoring and plays a significant role in the optimal individualization of drug dosage regimens for patient care.

Aged↗

BGX: a fully Bayesian integrated approach to the analysis of Affymetrix GeneChip data.

We present Bayesian hierarchical models for the analysis of Affymetrix GeneChip data. The approach we take differs from other available approaches in two fundamental aspects. Firstly, we aim to integrate all processing steps of the raw data in a common statistically coherent framework, allowing all components and thus associated errors to be considered simultaneously. Secondly, inference is based on the full posterior distribution of gene expression indices and derived quantities, such as fold changes or ranks, rather than on single point estimates. Measures of uncertainty on these quantities are thus available. The models presented represent the first building block for integrated Bayesian Analysis of Affymetrix GeneChip data: the models take into account additive as well as multiplicative error, gene expression levels are estimated using perfect match and a fraction of mismatch probes and are modeled on the log scale. Background correction is incorporated by modeling true signal and cross-hybridization explicitly, and a need for further normalization is considerably reduced by allowing for array-specific distributions of nonspecific hybridization. When replicate arrays are available for a condition, posterior distributions of condition-specific gene expression indices are estimated directly, by a simultaneous consideration of replicate probe sets, avoiding averaging over estimates obtained from individual replicate arrays. The performance of the Bayesian model is compared to that of standard available point estimate methods on subsets of the well known GeneLogic and Affymetrix spike-in data. The Bayesian model is found to perform well and the integrated procedure presented appears to hold considerable promise for further development.

Bayes Theorem↗

Model evaluation and spatial interpolation by Bayesian combination of observations with outputs from numerical models.

Constructing maps of dry deposition pollution levels is vital for air quality management, and presents statistical problems typical of many environmental and spatial applications. Ideally, such maps would be based on a dense network of monitoring stations, but this does not exist. Instead, there are two main sources of information for dry deposition levels in the United States: one is pollution measurements at a sparse set of about 50 monitoring stations called CASTNet, and the other is the output of the regional scale air quality models, called Models-3. A related problem is the evaluation of these numerical models for air quality applications, which is crucial for control strategy selection. We develop formal methods for combining sources of information with different spatial resolutions and for the evaluation of numerical models. We specify a simple model for both the Models-3 output and the CASTNet observations in terms of the unobserved ground truth, and we estimate the model in a Bayesian way. This provides improved spatial prediction via the posterior distribution of the ground truth, allows us to validate Models-3 via the posterior predictive distribution of the CASTNet observations, and enables us to remove the bias in the Models-3 output. We apply our methods to data on SO2 concentrations, and we obtain high-resolution SO2 distributions by combining observed data with model output. We also conclude that the numerical models perform worse in areas closer to power plants, where the SO2 values are overestimated by the models.

Air Pollution↗

Bayesian hierarchical approach to estimate insulin sensitivity by minimal model.

We adopted Bayesian analysis in combination with hierarchical (population) modelling to estimate simultaneously population and individual insulin sensitivity (SI) and glucose effectiveness (SG) with the minimal model of glucose kinetics using data collected during insulin-modified intravenous glucose tolerance test (IVGTT) and made comparison with the standard non-linear regression analysis. After fasting overnight, subjects with newly presenting Type II diabetes according to World Health Organization criteria (n =65; 53 males, 12 females; age, 54 +/- 9 years; body mass index, 30.4 +/- 5.2 kg/m2; means+/-S.D.) underwent IVGTT consisting of a 0.3 g of glucose bolus/kg of body weight given at time zero for 2 min, followed by 0.05 unit of insulin/kg of body weight at 20 min. Bayesian inference was carried out using vague prior distributions and log-normal distributions to guarantee non-negativity and, thus, physiological plausibility of model parameters and associated credible intervals. Bayesian analysis gave estimates of SI in all subjects. Non-linear regression analysis failed in four cases, where Bayesian analysis-derived SI was located in the lower quartile and was estimated with lower precision. The population means of SI and SG provided by Bayesian analysis and non-linear regression were identical, but the interquartile range given by Bayesian analysis was tighter by approx. 20% for SI and by approx. 15% for SG. Individual insulin sensitivities estimated by the two methods were highly correlated ( rS=0.98; P <0.001). However, the correlation in the lower 20% centile of the insulin-sensitivity range was significantly lower than the correlation in the upper 80% centile ( rS=0.71 compared with rS=0.99; P <0.001). We conclude that the Bayesian hierarchical analysis is an appealing method to estimate SI and SG, as it avoids parameter estimation failures, and should be considered when investigating insulin-resistant subjects.

Adult↗

Nonparametric population modeling of valproate pharmacokinetics in epileptic patients using routine serum monitoring data: implications for dosage.

Therapeutic drug monitoring (TDM) of valproate (VAL) is important in the optimization of its therapy. The aim of the present work was to evaluate the ability of TDM using model-based, goal-oriented Bayesian adaptive control for help in planning, monitoring, and adjusting individualized VAL dosing regimens. USC*PACK software and routine TDM data were used to estimate population and individual pharmacokinetics of two commercially available VAL formulations in epileptic adult and pediatric patients on chronic VAL monotherapy. The population parameter values found were in agreement with values reported earlier. A statistically significant (P < 0.001) difference in median values of the absorption rate constant was found between enteric-coated and sustained-release VAL formulations. In our patients (aged 0.25-53 years), VAL clearance declined with age until adult values were reached at about age 10. Because of the large interindividual variability in PK behavior, the median population parameter values gave poor predictions of the observed VAL serum concentrations. In contrast, the Bayesian individualized models gave good predictions for all subjects in all populations. The Bayesian posterior individualized PK models were based on the population models described here and where most patients had two (a peak and a trough) measured serum concentrations. Repeated consultations and adjusted dosage regimens with some patients allowed us to evaluate any possible influence of dose-dependent VAL clearance on the precision of total VAL concentration predictions based on TDM data and the proposed population models. These nonparametric expectation maximization (NPEM) population models thus provide a useful tool for planning an initial dosage regimen of VAL to achieve desired target peak and trough serum concentration goals, coupled with TDM soon thereafter, as a peak-trough pair of serum concentrations, and Bayesian fitting to individualize the PK model for each patient. The nonparametric PK parameter distributions in these NPEM population models also permit their use by the new method of 'multiple model' dosage design, which allows the target goals to be achieved specifically with maximum precision. Software for both types of Bayesian adaptive control is now available to employ these population models in clinical practice.

Adolescent↗

Bayesian methods for regional-scale eutrophication models.

We demonstrate a Bayesian classification and regression tree (CART) approach to link multiple environmental stressors to biological responses and quantify uncertainty in model predictions. Such an approach can: (1) report prediction uncertainty, (2) be consistent with the amount of data available and (3) be flexible enough to permit updates and improvements. Tree-based methods are a flexible approach useful for variable subset selection and when the analyst suspects global nonlinearity and cannot (or does not want to) specify the functional form of possible interactions a priori. We use the US EPA National Eutrophication Survey data to fit three models demonstrating the methods and to highlight important differences arising from slightly different model specifications. The Bayesian approach offers many advantages, including the estimation of the value of new information and proper probability distributions on the variable of interest as an output, which can be directly used in risk assessment or decision-making.

Bayes Theorem↗