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PubMed1985

Bayesian pharmacokinetic/pharmacodynamic forecasting of prothrombin response to warfarin therapy: preliminary evaluation.

The ability of a pharmacokinetic/pharmacodynamic Bayesian forecasting computer program to predict prothrombin response to warfarin therapy was investigated. The performance of the program was evaluated retrospectively in an inpatient study population of 45 subjects. Predictions of prothrombin response at discharge, based on zero to five serially measured prothrombin ratios, were compared. Precision of prediction was measured by root mean squared error (rmse), bias was measured by average prediction error, and significance (p less than 0.05) was determined by 95% confidence intervals and correlation coefficients. Eleven (3.8%) predictions exceeded established limitations of the pharmacokinetic/pharmacodynamic model and were excluded from data analysis. Correlations between measured and predicted prothrombin ratios for all methods were significant. The five prothrombin ratio feedbacks provided the most accurate predictions (rmse 0.219). These predictions were significantly better than the population parameter (rmse 0.418), one (rmse 0.401), and two (rmse 0.459) prothrombin ratio feedback predictions. The predictions based on population parameters and one prothrombin ratio feedback were significantly biased. When provided with sufficient feedback, the bias was not apparent and the predictive performance improved with each additional prothrombin ratio. The predictive performance of the four and five prothrombin ratio feedbacks is sufficient to provide clinically useful dosage guidelines early in the course of warfarin therapy. The population parameter estimates require further delineation in order to improve the performance of limited prothrombin ratio feedback predictions.

Bayes Theorem↗
PubMedDate not supplied

Markov chain Monte Carlo estimation of a multiparameter decision model: consistency of evidence and the accurate assessment of uncertainty.

Decision models are usually populated 1 parameter at a time, with 1 item of information informing each parameter. Often, however, data may not be available on the parameters themselves but on several functions of parameters, and there may be more items of information than there are parameters to be estimated. The authors show how in these circumstances all the model parameters can be estimated simultaneously using Bayesian Markov chain Monte Carlo methods. Consistency of the information and/or the adequacy of the model can also be assessed within this framework. Statistical evidence synthesis using all available data should result in more precise estimates of parameters and functions of parameters, and is compatible with the emphasis currently placed on systematic use of evidence. To illustrate this, WinBUGS software is used to estimate a simple 9-parameter model of the epidemiology of HIV in women attending prenatal clinics, using information on 12 functions of parameters, and to thereby compute the expected net benefit of 2 alternative prenatal testing strategies, universal testing and targeted testing of high-risk groups. The authors demonstrate improved precision of estimates, and lower estimates of the expected value of perfect information, resulting from the use of all available data.

AIDS Serodiagnosis↗
PubMed2002

On the probability model for asthma attacks.

In environmental epidemiology, the impact of environmental agents on symptoms or health status is of interest. This influence is described quantitatively in the theory of Whittemore & Keller (1979). They formulated a logistic model for individuals that is useful in evaluation of panel studies in which each participant protocols whether he does or does not have a certain symptom each day. In the present paper an equation for the prevalence of symptoms in the study population that is defined as the fraction of symptomatic subjects is deduced from the model for individuals. The model for the aggregated quantity depends on the individuals' parameters in a nonlinear manner. The relationship between the individual-based model and the corresponding population-based model is illustrated by means of a simulated panel. Bayesian estimates of the parameters are calculated and compared for both approaches. Bayesian inference enables to apply the prevalence model to a population of non-identical individuals. For such a heterogeneous population, we observe an attenuation of environmental effects on the aggregated symptom prevalence in comparison to the individual-based approach. The presented theory is applicable not only to panel studies but also in time-series analysis of prevalences and incidences.

Asthma↗
PubMed2005

Resolving deep phylogenetic relationships in salamanders: analyses of mitochondrial and nuclear genomic data.

Phylogenetic relationships among salamander families illustrate analytical challenges inherent to inferring phylogenies in which terminal branches are temporally very long relative to internal branches. We present new mitochondrial DNA sequences, approximately 2,100 base pairs from the genes encoding ND1, ND2, COI, and the intervening tRNA genes for 34 species representing all 10 salamander families, to examine these relationships. Parsimony analysis of these mtDNA sequences supports monophyly of all families except Proteidae, but yields a tree largely unresolved with respect to interfamilial relationships and the phylogenetic positions of the proteid genera Necturus and Proteus. In contrast, Bayesian and maximum-likelihood analyses of the mtDNA data produce a topology concordant with phylogenetic results from nuclear-encoded rRNA sequences, and they statistically reject monophyly of the internally fertilizing salamanders, suborder Salamandroidea. Phylogenetic simulations based on our mitochondrial DNA sequences reveal that Bayesian analyses outperform parsimony in reconstructing short branches located deep in the phylogenetic history of a taxon. However, phylogenetic conflicts between our results and a recent analysis of nuclear RAG-1 gene sequences suggest that statistical rejection of a monophyletic Salamandroidea by Bayesian analyses of our mitochondrial genomic data is probably erroneous. Bayesian and likelihood-based analyses may overestimate phylogenetic precision when estimating short branches located deep in a phylogeny from data showing substitutional saturation; an analysis of nucleotide substitutions indicates that these methods may be overly sensitive to a relatively small number of sites that show substitutions judged uncommon by the favored evolutionary model.

Animals↗
PubMed2005

Bayesian normalization and identification for differential gene expression data.

Commonly accepted intensity-dependent normalization in spotted microarray studies takes account of measurement errors in the differential expression ratio but ignores measurement errors in the total intensity, although the definitions imply the same measurement error components are involved in both statistics. Furthermore, identification of differentially expressed genes is usually considered separately following normalization, which is statistically problematic. By incorporating the measurement errors in both total intensities and differential expression ratios, we propose a measurement-error model for intensity-dependent normalization and identification of differentially expressed genes. This model is also flexible enough to incorporate intra-array and inter-array effects. A Bayesian framework is proposed for the analysis of the proposed measurement-error model to avoid the potential risk of using the common two-step procedure. We also propose a Bayesian identification of differentially expressed genes to control the false discovery rate instead of the ad hoc thresholding of the posterior odds ratio. The simulation study and an application to real microarray data demonstrate promising results.

Bayes Theorem↗
PubMed1999

Statistical limitations in functional neuroimaging. I. Non-inferential methods and statistical models.

Functional neuroimaging (FNI) provides experimental access to the intact living brain making it possible to study higher cognitive functions in humans. In this review and in a companion paper in this issue, we discuss some common methods used to analyse FNI data. The emphasis in both papers is on assumptions and limitations of the methods reviewed. There are several methods available to analyse FNI data indicating that none is optimal for all purposes. In order to make optimal use of the methods available it is important to know the limits of applicability. For the interpretation of FNI results it is also important to take into account the assumptions, approximations and inherent limitations of the methods used. This paper gives a brief overview over some non-inferential descriptive methods and common statistical models used in FNI. Issues relating to the complex problem of model selection are discussed. In general, proper model selection is a necessary prerequisite for the validity of the subsequent statistical inference. The non-inferential section describes methods that, combined with inspection of parameter estimates and other simple measures, can aid in the process of model selection and verification of assumptions. The section on statistical models covers approaches to global normalization and some aspects of univariate, multivariate, and Bayesian models. Finally, approaches to functional connectivity and effective connectivity are discussed. In the companion paper we review issues related to signal detection and statistical inference.

Bayes Theorem↗
PubMed2006

Bayesian spatio-temporal approach for EEG source reconstruction: conciliating ECD and distributed models.

Characterizing the cortical activity sources of electroencephalography (EEG)/magnetoencephalography data is a critical issue since it requires solving an ill-posed inverse problem that does not admit a unique solution. Two main different and complementary source models have emerged: equivalent current dipoles (ECD) and distributed linear (DL) models. While ECD models remain highly popular since they provide an easy way to interpret the solutions, DL models (also referred to as imaging techniques) are known to be more realistic and flexible. In this paper, we show how those two representations of the brain electromagnetic activity can be cast into a common general framework yielding an optimal description and estimation of the EEG sources. From this extended source mixing model, we derive a hybrid approach whose key aspect is the separation between temporal and spatial characteristics of brain activity, which allows to dramatically reduce the number of DL model parameters. Furthermore, the spatial profile of the sources, as a temporal invariant map, is estimated using the entire time window data, allowing to significantly enhance the information available about the spatial aspect of the EEG inverse problem. A Bayesian framework is introduced to incorporate distinct temporal and spatial constraints on the solution and to estimate both parameters and hyperparameters of the model. Using simulated EEG data, the proposed inverse approach is evaluated and compared with standard distributed methods using both classical criteria and ROC curves.

Algorithms↗
PubMed2005

Investigating the functional role of callosal connections with dynamic causal models.

The anatomy of the corpus callosum has been described in considerable detail. Tracing studies in animals and human postmortem experiments are currently complemented by diffusion-weighted imaging, which enables noninvasive investigations of callosal connectivity to be conducted. In contrast to the wealth of anatomical data, little is known about the principles by which interhemispheric integration is mediated by callosal connections. Most importantly, we lack insights into the mechanisms that determine the functional role of callosal connections in a context-dependent fashion. These mechanisms can now be disclosed by models of effective connectivity that explain neuroimaging data from paradigms that manipulate interhemispheric interactions. In this article, we demonstrate that dynamic causal modeling (DCM), in conjunction with Bayesian model selection (BMS), is a powerful approach to disentangling the various factors that determine the functional role of callosal connections. We first review the theoretical foundations of DCM and BMS before demonstrating the application of these techniques to empirical data from a single subject.

Algorithms↗
PubMed2001

Factors influencing the prediction of steady state concentrations of digoxin.

The prediction error in the Bayesian analysis program for digoxin was evaluated in Japanese patients, and factors influencing the accuracy were investigated. Serum concentrations of digoxin were monitored two times and were compared with the predicted values obtained by using the Bayesian analysis program. The prediction error at the first time was 43.1%. Although this estimation error was reasonably restored at the second time of monitoring, the prediction error remained at 26.6%. These data suggested that unknown factors not included in the program affected the serum concentration of digoxin. Retrospective research of the digoxin serum concentrations in the patients suggested the coadministration of the drugs, which were the P-glycoprotein modulators, as well as the unexpected alteration of the serum creatinine, were the important factors influencing the prediction of the drug serum concentrations. We next examined the inhibitory effect of quinidine, verapamil and spironolactone on the transcellular transport of digoxin by using human P-glycoprotein overexpressing LLC-GA5-COL150 cells. Quinidine, verapamil and spironolactone could inhibit the transcellular transport of digoxin by 50%. In addition, the reduction of the renal clearance by 50%, which could possibly be caused by this inhibition, led to the increase of 36% in the steady state through concentrations of digoxin in the physiological pharmacokinetic model. In conclusion, the prediction of long-term serum concentration-time profiles of digoxin, based on the Bayesian analysis, will be disturbed by the coadministration of the P-glycoprotein modulators and the unexpected alteration of the serum creatinine.

Adolescent↗
PubMed2006

Analysis of single-molecule FRET trajectories using hidden Markov modeling.

The analysis of single-molecule fluorescence resonance energy transfer (FRET) trajectories has become one of significant biophysical interest. In deducing the transition rates between various states of a system for time-binned data, researchers have relied on simple, but often arbitrary methods of extracting rates from FRET trajectories. Although these methods have proven satisfactory in cases of well-separated, low-noise, two- or three-state systems, they become less reliable when applied to a system of greater complexity. We have developed an analysis scheme that casts single-molecule time-binned FRET trajectories as hidden Markov processes, allowing one to determine, based on probability alone, the most likely FRET-value distributions of states and their interconversion rates while simultaneously determining the most likely time sequence of underlying states for each trajectory. Together with a transition density plot and Bayesian information criterion we can also determine the number of different states present in a system in addition to the state-to-state transition probabilities. Here we present the algorithm and test its limitations with various simulated data and previously reported Holliday junction data. The algorithm is then applied to the analysis of the binding and dissociation of three RecA monomers on a DNA construct.

Algorithms↗
PubMed2004

Comparison of the accuracies of several phylogenetic methods using protein and DNA sequences.

A biologically realistic method was used to simulate evolutionary trees. The method uses a real DNA coding sequence as the starting point, simulates mutation according to the mutational spectrum of Escherichia coli-including base substitutions, insertions, and deletions-and separates the processes of mutation and selection. Trees of 8, 16, 32, and 64 taxa were simulated with average branch lengths of 50, 100, 150, 200, and 250 changes per branch. The resulting sequences were aligned with ClustalX, and trees were estimated by Neighbor Joining, Parsimony, Maximum Likelihood, and Bayesian methods from both DNA sequences and the corresponding protein sequences. The estimated trees were compared with the true trees, and both topological and branch length accuracies were scored. Over the variety of conditions tested, Bayesian trees estimated from DNA sequences that had been aligned according to the alignment of the corresponding protein sequences were the most accurate, followed by Maximum Likelihood trees estimated from DNA sequences and Parsimony trees estimated from protein sequences.

Amino Acid Sequence↗
PubMed2000

Correctness of local probability in graphical models with loops.

Graphical models, such as Bayesian networks and Markov networks, represent joint distributions over a set of variables by means of a graph. When the graph is singly connected, local propagation rules of the sort proposed by Pearl (1988) are guaranteed to converge to the correct posterior probabilities. Recently a number of researchers have empirically demonstrated good performance of these same local propagation schemes on graphs with loops, but a theoretical understanding of this performance has yet to be achieved. For graphical models with a single loop, we derive an analytical relationship between the probabilities computed using local propagation and the correct marginals. Using this relationship we show a category of graphical models with loops for which local propagation gives rise to provably optimal maximum a posteriori assignments (although the computed marginals will be incorrect). We also show how nodes can use local information in the messages they receive in order to correct their computed marginals. We discuss how these results can be extended to graphical models with multiple loops and show simulation results suggesting that some properties of propagation on single-loop graphs may hold for a larger class of graphs. Specifically we discuss the implication of our results for understanding a class of recently proposed error-correcting codes known as turbo codes.

Bayes Theorem↗
PubMed1998

Classification of foetal heart rate sequences based on fractal features.

Visual inspection of foetal heart rate (FHR) sequences is an important means of foetal well-being evaluation. The application of fractal features for classifying physiologically relevant FHR sequence patterns is reported. The use of fractal features is motivated by the difficulties exhibited by traditional classification schemes to discriminate some classes of FHR sequence and by the recognition that this type of signal exhibits features on different scales of observation, just as fractal signals do. To characterise the signals by fractal features, two approaches are taken. The first modes the FHR sequences as temporal fractals. The second uses techniques from the chaos-theory field and aims to model the attractor based on FHR sequences. The fractal features determined by both approaches are used to design a Bayesian classification scheme. Classification results for three classes are presented; they are quite satisfactory and illustrate the importance of this type of methodology.

Bayes Theorem↗
PubMedDate not supplied

Improved system for object detection and star/galaxy classification via local subspace analysis.

The two traditional tasks of object detection and star/galaxy classification in astronomy can be automated by neural networks because the nature of the problems is that of pattern recognition. A typical existing system can be further improved by using one of the local Principal Component Analysis (PCA) models. Our analysis in the context of object detection and star/galaxy classification reveals that local PCA is not only superior to global PCA in feature extraction, but is also superior to gaussian mixture in clustering analysis. Unlike global PCA which performs PCA for the whole data set, local PCA applies PCA individually to each cluster of data. As a result, local PCA often outperforms global PCA for data of multi-modes. Moreover, since local PCA can effectively avoid the trouble of having to specify a large number of free elements of each covariance matrix of gaussian mixture, it can give a better description of local subspace structures of each cluster when applied on high dimensional data with small sample size. In this paper, the local PCA model proposed by Xu [IEEE Trans. Neural Networks 12 (2001) 822] under the general framework of Bayesian Ying Yang (BYY) normalization learning will be adopted. Endowed with the automatic model selection ability of BYY learning, the BYY normalization learning-based local PCA model can cope with those object detection and star/galaxy classification tasks with unknown model complexity. A detailed algorithm for implementation of the local PCA model will be proposed, and experimental results using both synthetic and real astronomical data will be demonstrated.

Astronomy↗
PubMed2003

Bayesian methods for chromosome dosimetry following a criticality accident.

Radiation doses received during a criticality accident will be from a combination of fission spectrum neutrons and gamma rays. It is desirable to estimate the total dose, as well as the neutron and gamma doses. Present methods for dose estimation with chromosome aberrations after a criticality accident use point estimates of the neutron to gamma dose ratio obtained from personnel dosemeters and/or accident reconstruction calculations. In this paper a Bayesian approach to dose estimation with chromosome aberrations is developed which allows the uncertainty of the dose ratio to be considered. Posterior probability densities for the total and the neutron and gamma doses were derived.

Bayes Theorem↗
PubMed1992

Graph-grammar productions for the modeling of medical dilemmas.

We introduce graph-grammar production rules, which can guide physicians to construct models for normative decision making. A physician describes a medical decision problem using standard terminology, and the graph-grammar system matches a graph-manipulation rule to each of the standard terms. With minimal help from the physician, these graph-manipulation rules can construct an appropriate Bayesian probabilistic network. The physician can then assess the necessary probabilities and utilities to arrive at a rational decision. The grammar relies on prototypical forms that we have observed in models of medical dilemmas. We have found graph grammars to be a concise and expressive formalism for describing prototypical forms, and we believe such grammars can greatly facilitate the modeling of medical dilemmas and medical plans.

Bayes Theorem↗
PubMed1998

Guideline generation from data by induction of decision tables using a Bayesian network framework.

Decision tables can be used to represent practice guidelines effectively. In this study we adopt the powerful probabilistic framework of Bayesian Networks (BN) for the induction of decision tables. We discuss the simplest BN model, the Naive Bayes and extend it to the Two-Stage Naive Bayes. We show that reversal of edges in Naive Bayes and Two-stage Naive Bayes results in simple decision table and hierarchical decision table respectively. We induce these graphical models for dementia severity staging using the Clinical Dementia Rating Scale (CDRS) database from the University of California, Irvine, Alzheimer's Disease Research Center. These induced models capture the two-stage methodology clinicians use in computing the global CDR score by first computing the six category scores of memory, orientation, judgment and problem solving, community affairs, home and hobbies and personal care, and then the global CDRS. The induced Two-Stage models also attain a clinically acceptable performance when compared to domain experts and could serve as useful guidelines for dementia severity staging.

Algorithms↗
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↗