Further insights on the French WISC-IV factor structure through Bayesian structural equation modeling

The interpretation of the Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV) is based on a 4-factor model, which is only partially compatible with the mainstream Cattell-Horn-Carroll (CHC) model of intelligence measurement. The structure of cognitive batteries is frequently analyzed via exploratory factor analysis and/or confirmatory factor analysis. With classical confirmatory factor analysis, almost all crossloadings between latent variables and measures are fixed to zero in order to allow the model to be identified. However, inappropriate zero cross-loadings can contribute to poor model fit, distorted factors, and biased factor correlations; most important, they do not necessarily faithfully reflect theory. To deal with these methodological and theoretical limitations, we used a new statistical approach, Bayesian structural equation modeling (BSEM), among a sample of 249 French-speaking Swiss children (8-12 years). With BSEM, zero-fixed cross-loadings between latent variables and measures are replaced by approximate zeros, based on informative, small-variance priors. Results indicated that a direct hierarchical CHC-based model with 5 factors plus a general intelligence factor better represented the structure of the WISC-IV than did the 4-factor structure and the higher order models. Because a direct hierarchical CHC model was more adequate, it was concluded that the general factor should be considered as a breadth rather than a superordinate factor. Because it was possible for us to estimate the influence of each of the latent variables on the 15 subtest scores, BSEM allowed improvement of the understanding of the structure of intelligence tests and the clinical interpretation of the subtest scores.

Improvement of therapeutic drug monitoring of imatinib by Bayesian prediction of trough levels. Personalized drug dosage

Aims: Plasma concentrations of imatinib differ largely between patients despite same dosage, owing to large inter-individual variability in pharmacokinetic (PK) parameters. As the drug concentration at the end of the dosage interval (Cmin) correlates with treatment response and tolerability, monitoring of Cmin is suggested for therapeutic drug monitoring (TDM) of imatinib. Due to logistic difficulties, random sampling during the dosage interval is however often performed in clinical practice, thus rendering the respective results not informative regarding Cmin values.Objectives: (I) To extrapolate randomly measured imatinib concentrations to more informative Cmin using classical Bayesian forecasting. (II) To extend the classical Bayesian method to account for correlation between PK parameters. (III) To evaluate the predictive performance of both methods.Methods: 31 paired blood samples (random and trough levels) were obtained from 19 cancer patients under imatinib. Two Bayesian maximum a posteriori (MAP) methods were implemented: (A) a classical method ignoring correlation between PK parameters, and (B) an extended one accounting for correlation. Both methods were applied to estimate individual PK parameters, conditional on random observations and covariate-adjusted priors from a population PK model. The PK parameter estimates were used to calculate trough levels. Relative prediction errors (PE) were analyzed to evaluate accuracy (one-sample t-test) and to compare precision between the methods (F-test to compare variances).Results: Both Bayesian MAP methods allowed non-biased predictions of individual Cmin compared to observations: (A) - 7% mean PE (CI95% - 18 to 4 %, p = 0.15) and (B) - 4% mean PE (CI95% - 18 to 10 %, p = 0.69). Relative standard deviations of actual observations from predictions were 22% (A) and 30% (B), i.e. comparable to the intraindividual variability reported. Precision was not improved by taking into account correlation between PK parameters (p = 0.22).Conclusion: Clinical interpretation of randomly measured imatinib concentrations can be assisted by Bayesian extrapolation to maximum likelihood Cmin. Classical Bayesian estimation can be applied for TDM without the need to include correlation between PK parameters. Both methods could be adapted in the future to evaluate other individual pharmacokinetic measures correlated to clinical outcomes, such as area under the curve(AUC).

Bayesian Markov-chain-Monte-Carlo inversion of time-lapse cross hole ground-penetrating radar data to characterize the vadose zone at the Arrenaes field site, Denmark

The ground-penetrating radar (GPR) geophysical method has the potential to provide valuable information on the hydraulic properties of the vadose zone because of its strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR traveltime data can allow for a significant reduction in uncertainty regarding subsurface van Genuchten-Mualem (VGM) parameters. Much of the previous work on the stochastic estimation of VGM parameters from crosshole GPR data has considered the case of steady-state infiltration conditions, which represent only a small fraction of practically relevant scenarios. We explored in detail the dynamic infiltration case, specifically examining to what extent time-lapse crosshole GPR traveltimes, measured during a forced infiltration experiment at the Arreneas field site in Denmark, could help to quantify VGM parameters and their uncertainties in a layered medium, as well as the corresponding soil hydraulic properties. We used a Bayesian Markov-chain-Monte-Carlo inversion approach. We first explored the advantages and limitations of this approach with regard to a realistic synthetic example before applying it to field measurements. In our analysis, we also considered different degrees of prior information. Our findings indicate that the stochastic inversion of the time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions compared with the corresponding priors, which in turn significantly improves knowledge of soil hydraulic properties. Overall, the results obtained clearly demonstrate the value of the information contained in time-lapse GPR data for characterizing vadose zone dynamics.

A comparison of Bayesian and frequentist approaches to incorporating external information for the prediction of prostate cancer risk.

We present the most comprehensive comparison to date of the predictive benefit of genetics in addition to currently used clinical variables, using genotype data for 33 single-nucleotide polymorphisms (SNPs) in 1,547 Caucasian men from the placebo arm of the REduction by DUtasteride of prostate Cancer Events (REDUCE®) trial. Moreover, we conducted a detailed comparison of three techniques for incorporating genetics into clinical risk prediction. The first method was a standard logistic regression model, which included separate terms for the clinical covariates and for each of the genetic markers. This approach ignores a substantial amount of external information concerning effect sizes for these Genome Wide Association Study (GWAS)-replicated SNPs. The second and third methods investigated two possible approaches to incorporating meta-analysed external SNP effect estimates - one via a weighted PCa 'risk' score based solely on the meta analysis estimates, and the other incorporating both the current and prior data via informative priors in a Bayesian logistic regression model. All methods demonstrated a slight improvement in predictive performance upon incorporation of genetics. The two methods that incorporated external information showed the greatest receiver-operating-characteristic AUCs increase from 0.61 to 0.64. The value of our methods comparison is likely to lie in observations of performance similarities, rather than difference, between three approaches of very different resource requirements. The two methods that included external information performed best, but only marginally despite substantial differences in complexity.

Hydrogeophysical data integration at larger scales: Application of Bayesian sequential simulation for the characterization of heterogeneous alluvial aquifers

Knowledge of the spatial distribution of hydraulic conductivity (K) within an aquifer is critical for reliable predictions of solute transport and the development of effective groundwater management and/or remediation strategies. While core analyses and hydraulic logging can provide highly detailed information, such information is inherently localized around boreholes that tend to be sparsely distributed throughout the aquifer volume. Conversely, larger-scale hydraulic experiments like pumping and tracer tests provide relatively low-resolution estimates of K in the investigated subsurface region. As a result, traditional hydrogeological measurement techniques contain a gap in terms of spatial resolution and coverage, and they are often alone inadequate for characterizing heterogeneous aquifers. Geophysical methods have the potential to bridge this gap. The recent increased interest in the application of geophysical methods to hydrogeological problems is clearly evidenced by the formation and rapid growth of the domain of hydrogeophysics over the past decade (e.g., Rubin and Hubbard, 2005).

Sparse regularization for fiber ODF reconstruction: from the suboptimality of ℓ2 and ℓ1 priors to ℓ0.

Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a large variety of methods have been recently proposed to shorten the acquisition times. Among them, spherical deconvolution approaches have gained a lot of interest for their ability to reliably recover the intra-voxel fiber configuration with a relatively small number of data samples. To overcome the intrinsic instabilities of deconvolution, these methods use regularization schemes generally based on the assumption that the fiber orientation distribution (FOD) to be recovered in each voxel is sparse. The well known Constrained Spherical Deconvolution (CSD) approach resorts to Tikhonov regularization, based on an ℓ(2)-norm prior, which promotes a weak version of sparsity. Also, in the last few years compressed sensing has been advocated to further accelerate the acquisitions and ℓ(1)-norm minimization is generally employed as a means to promote sparsity in the recovered FODs. In this paper, we provide evidence that the use of an ℓ(1)-norm prior to regularize this class of problems is somewhat inconsistent with the fact that the fiber compartments all sum up to unity. To overcome this ℓ(1) inconsistency while simultaneously exploiting sparsity more optimally than through an ℓ(2) prior, we reformulate the reconstruction problem as a constrained formulation between a data term and a sparsity prior consisting in an explicit bound on the ℓ(0)norm of the FOD, i.e. on the number of fibers. The method has been tested both on synthetic and real data. Experimental results show that the proposed ℓ(0) formulation significantly reduces modeling errors compared to the state-of-the-art ℓ(2) and ℓ(1) regularization approaches.

Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science

Continuing developments in science and technology mean that the amounts of information forensic scientists are able to provide for criminal investigations is ever increasing. The commensurate increase in complexity creates difficulties for scientists and lawyers with regard to evaluation and interpretation, notably with respect to issues of inference and decision. Probability theory, implemented through graphical methods, and specifically Bayesian networks, provides powerful methods to deal with this complexity. Extensions of these methods to elements of decision theory provide further support and assistance to the judicial system. Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science provides a unique and comprehensive introduction to the use of Bayesian decision networks for the evaluation and interpretation of scientific findings in forensic science, and for the support of decision-makers in their scientific and legal tasks. Includes self-contained introductions to probability and decision theory. Develops the characteristics of Bayesian networks, object-oriented Bayesian networks and their extension to decision models. Features implementation of the methodology with reference to commercial and academically available software. Presents standard networks and their extensions that can be easily implemented and that can assist in the reader's own analysis of real cases. Provides a technique for structuring problems and organizing data based on methods and principles of scientific reasoning. Contains a method for the construction of coherent and defensible arguments for the analysis and evaluation of scientific findings and for decisions based on them. Is written in a lucid style, suitable for forensic scientists and lawyers with minimal mathematical background. Includes a foreword by Ian Evett. The clear and accessible style of this second edition makes this book ideal for all forensic scientists, applied statisticians and graduate students wishing to evaluate forensic findings from the perspective of probability and decision analysis. It will also appeal to lawyers and other scientists and professionals interested in the evaluation and interpretation of forensic findings, including decision making based on scientific information.

Decision-theoretic analysis of forensic sampling criteria using Bayesian decision networks

Sampling issues represent a topic of ongoing interest to the forensic science community essentially because of their crucial role in laboratory planning and working protocols. For this purpose, forensic literature described thorough (Bayesian) probabilistic sampling approaches. These are now widely implemented in practice. They allow, for instance, to obtain probability statements that parameters of interest (e.g., the proportion of a seizure of items that present particular features, such as an illegal substance) satisfy particular criteria (e.g., a threshold or an otherwise limiting value). Currently, there are many approaches that allow one to derive probability statements relating to a population proportion, but questions on how a forensic decision maker - typically a client of a forensic examination or a scientist acting on behalf of a client - ought actually to decide about a proportion or a sample size, remained largely unexplored to date. The research presented here intends to address methodology from decision theory that may help to cope usefully with the wide range of sampling issues typically encountered in forensic science applications. The procedures explored in this paper enable scientists to address a variety of concepts such as the (net) value of sample information, the (expected) value of sample information or the (expected) decision loss. All of these aspects directly relate to questions that are regularly encountered in casework. Besides probability theory and Bayesian inference, the proposed approach requires some additional elements from decision theory that may increase the efforts needed for practical implementation. In view of this challenge, the present paper will emphasise the merits of graphical modelling concepts, such as decision trees and Bayesian decision networks. These can support forensic scientists in applying the methodology in practice. How this may be achieved is illustrated with several examples. The graphical devices invoked here also serve the purpose of supporting the discussion of the similarities, differences and complementary aspects of existing Bayesian probabilistic sampling criteria and the decision-theoretic approach proposed throughout this paper.

Bayesian classification criterion for forensic multivariate data

This study presents a classification criteria for two-class Cannabis seedlings. As the cultivation of drug type cannabis is forbidden in Switzerland, law enforcement authorities regularly ask laboratories to determine cannabis plant's chemotype from seized material in order to ascertain that the plantation is legal or not. In this study, the classification analysis is based on data obtained from the relative proportion of three major leaf compounds measured by gas-chromatography interfaced with mass spectrometry (GC-MS). The aim is to discriminate between drug type (illegal) and fiber type (legal) cannabis at an early stage of the growth. A Bayesian procedure is proposed: a Bayes factor is computed and classification is performed on the basis of the decision maker specifications (i.e. prior probability distributions on cannabis type and consequences of classification measured by losses). Classification rates are computed with two statistical models and results are compared. Sensitivity analysis is then performed to analyze the robustness of classification criteria.

Advanced mapping of environmental data: Geostatistics, Machine Learning and Bayesian Maximum Entropy

This book combines geostatistics and global mapping systems to present an up-to-the-minute study of environmental data. Featuring numerous case studies, the reference covers model dependent (geostatistics) and data driven (machine learning algorithms) analysis techniques such as risk mapping, conditional stochastic simulations, descriptions of spatial uncertainty and variability, artificial neural networks (ANN) for spatial data, Bayesian maximum entropy (BME), and more.

Detection of nandrolone metabolites in urine after a football game in professional and amateur players: a Bayesian comparison.

Nandrolone (19-nortestosterone) is a widely used anabolic steroid in sports where strength plays an essential role. Once nandrolone has been metabolised, two major metabolites are excreted in urine, 19-norandrosterone (NA) and 19-noretiocholanolone (NE). In 1997, in France, quite a few sportsmen had concentrations of 19-norandrosterone very close to the IOC cut off limit (2ng/ml). At that time, a debate took place about the capability of the human male body to produce by itself these metabolites without any intake of nandrolone or related compounds. The International Football Federation (FIFA) was very concerned with this problematic, especially because the World Cup was about to start in France. In this respect, a statistical study was held with all football players from the first and second divisions of the Swiss Football National League. All players gave a urine sample after effort and around 6% of them showed traces of 19-norandrosterone. These results were compared with amateur football players (control group) and around 6% of them had very small amounts of 19-norandrosterone and/or 19-noretiocholanolone in urine after effort, whereas none of them had detectable traces of one or the other metabolite before effort. The origin of these compounds in urine after a strenuous physical activity is still unknown, but three hypotheses can be put forward. First, an endogenous production of nandrolone metabolites takes place. Second, nandrolone metabolites are released from the fatty tissues after an intake of nandrolone, some related compounds or some contaminated nutritive supplements. Finally, the sportsmen may have taken something during or just before the football game.

Multiple-scale hydrological and geophysical data integration through non-linear Bayesian sequential simulation

Significant progress has been made with regard to the quantitative integration of geophysical and hydrological data at the local scale. However, extending the corresponding approaches to the scale of a field site represents a major, and as-of-yet largely unresolved, challenge. To address this problem, we have developed downscaling procedure based on a non-linear Bayesian sequential simulation approach. The main objective of this algorithm is to estimate the value of the sparsely sampled hydraulic conductivity at non-sampled locations based on its relation to the electrical conductivity logged at collocated wells and surface resistivity measurements, which are available throughout the studied site. The in situ relationship between the hydraulic and electrical conductivities is described through a non-parametric multivariatekernel density function. Then a stochastic integration of low-resolution, large-scale electrical resistivity tomography (ERT) data in combination with high-resolution, local-scale downhole measurements of the hydraulic and electrical conductivities is applied. The overall viability of this downscaling approach is tested and validated by comparing flow and transport simulation through the original and the upscaled hydraulic conductivity fields. Our results indicate that the proposed procedure allows obtaining remarkably faithful estimates of the regional-scale hydraulic conductivity structure and correspondingly reliable predictions of the transport characteristics over relatively long distances.

An empirical hierarchical Bayesian unification of occupational exposure assessment methods.

In occupational exposure assessment of airborne contaminants, exposure levels can either be estimated through repeated measurements of the pollutant concentration in air, expert judgment or through exposure models that use information on the conditions of exposure as input. In this report, we propose an empirical hierarchical Bayesian model to unify these approaches. Prior to any measurement, the hygienist conducts an assessment to generate prior distributions of exposure determinants. Monte-Carlo samples from these distributions feed two level-2 models: a physical, two-compartment model, and a non-parametric, neural network model trained with existing exposure data. The outputs of these two models are weighted according to the expert's assessment of their relevance to yield predictive distributions of the long-term geometric mean and geometric standard deviation of the worker's exposure profile (level-1 model). Bayesian inferences are then drawn iteratively from subsequent measurements of worker exposure. Any traditional decision strategy based on a comparison with occupational exposure limits (e.g. mean exposure, exceedance strategies) can then be applied. Data on 82 workers exposed to 18 contaminants in 14 companies were used to validate the model with cross-validation techniques. A user-friendly program running the model is available upon request.

Therapeutic drug monitoring of imatinib: Bayesian and alternative methods to predict trough levels

Background: The imatinib trough plasma concentration (C(min)) correlates with clinical response in cancer patients. Therapeutic drug monitoring (TDM) of plasma C(min) is therefore suggested. In practice, however, blood sampling for TDM is often not performed at trough. The corresponding measurement is thus only remotely informative about C(min) exposure. Objectives: The objectives of this study were to improve the interpretation of randomly measured concentrations by using a Bayesian approach for the prediction of C(min), incorporating correlation between pharmacokinetic parameters, and to compare the predictive performance of this method with alternative approaches, by comparing predictions with actual measured trough levels, and with predictions obtained by a reference method, respectively. Methods: A Bayesian maximum a posteriori (MAP) estimation method accounting for correlation (MAP-ρ) between pharmacokinetic parameters was developed on the basis of a population pharmacokinetic model, which was validated on external data. Thirty-one paired random and trough levels, observed in gastrointestinal stromal tumour patients, were then used for the evaluation of the Bayesian MAP-ρ method: individual C(min) predictions, derived from single random observations, were compared with actual measured trough levels for assessment of predictive performance (accuracy and precision). The method was also compared with alternative approaches: classical Bayesian MAP estimation assuming uncorrelated pharmacokinetic parameters, linear extrapolation along the typical elimination constant of imatinib, and non-linear mixed-effects modelling (NONMEM) first-order conditional estimation (FOCE) with interaction. Predictions of all methods were finally compared with 'best-possible' predictions obtained by a reference method (NONMEM FOCE, using both random and trough observations for individual C(min) prediction). Results: The developed Bayesian MAP-ρ method accounting for correlation between pharmacokinetic parameters allowed non-biased prediction of imatinib C(min) with a precision of ±30.7%. This predictive performance was similar for the alternative methods that were applied. The range of relative prediction errors was, however, smallest for the Bayesian MAP-ρ method and largest for the linear extrapolation method. When compared with the reference method, predictive performance was comparable for all methods. The time interval between random and trough sampling did not influence the precision of Bayesian MAP-ρ predictions. Conclusion: Clinical interpretation of randomly measured imatinib plasma concentrations can be assisted by Bayesian TDM. Classical Bayesian MAP estimation can be applied even without consideration of the correlation between pharmacokinetic parameters. Individual C(min) predictions are expected to vary less through Bayesian TDM than linear extrapolation. Bayesian TDM could be developed in the future for other targeted anticancer drugs and for the prediction of other pharmacokinetic parameters that have been correlated with clinical outcomes.