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PubMed2002

Finding and fixing systems weaknesses: probabilistic methods and applications of engineering risk analysis.

Methods of engineering risk analysis are based on a functional analysis of systems and on the probabilities (generally Bayesian) of the events and random variables that affect their performances. These methods allow identification of a system's failure modes, computation of its probability of failure or performance deterioration per time unit or operation, and of the contribution of each component to the probabilities and consequences of failures. The model has been extended to include the human decisions and actions that affect components' performances, and the management factors that affect behaviors and can thus be root causes of system failures. By computing the risk with and without proposed measures, one can then set priorities among different risk management options under resource constraints. In this article, I present briefly the engineering risk analysis method, then several illustrations of risk computations that can be used to identify a system's weaknesses and the most cost-effective way to fix them. The first example concerns the heat shield of the space shuttle orbiter and shows the relative risk contribution of the tiles in different areas of the orbiter's surface. The second application is to patient risk in anesthesia and demonstrates how the engineering risk analysis method can be used in the medical domain to rank the benefits of risk mitigation measures, in that case, mostly organizational. The third application is a model of seismic risk analysis and mitigation, with application to the San Francisco Bay area for the assessment of the costs and benefits of different seismic provisions of building codes. In all three cases, some aspects of the results were not intuitively obvious. The probabilistic risk analysis (PRA) method allowed identifying system weaknesses and the most cost-effective way to fix them.

Journal Article↗
PubMed1990

Classification of audiograms by sequential testing using a dynamic Bayesian procedure.

A new method for estimating audiograms using behavioral responses is presented. The method is based upon a modification of the Bayesian probability formula in which an outcome is predicted from a static set of events. In the new method, classification of audiograms by sequential testing (CAST), the probabilities of occurrence of audiogram patterns are dynamically updated according to the outcome of each test trial. Computer simulation using an infant response model suggests that the procedure is efficient, sensitive, and specific.

Algorithms↗
PubMed2025

The signed two-space proximity model for learning representations in protein-protein interaction networks.

MOTIVATION: Accurately predicting complex protein-protein interactions (PPIs) is crucial for decoding biological processes, from cellular functioning to disease mechanisms. However, experimental methods for determining PPIs are computationally expensive. Thus, attention has been recently drawn to machine learning approaches. Furthermore, insufficient effort has been made toward analyzing signed PPI networks, which capture both activating (positive) and inhibitory (negative) interactions. To accurately represent biological relationships, we present the Signed Two-Space Proximity Model (S2-SPM) for signed PPI networks, which explicitly incorporates both types of interactions, reflecting the complex regulatory mechanisms within biological systems. This is achieved by leveraging two independent latent spaces to differentiate between positive and negative interactions while representing protein similarity through proximity in these spaces. Our approach also enables the identification of archetypes representing extreme protein profiles. RESULTS: S2-SPM's superior performance in predicting the presence and sign of interactions in SPPI networks is demonstrated in link prediction tasks against relevant baseline methods. Additionally, the biological prevalence of the identified archetypes is confirmed by an enrichment analysis of Gene Ontology (GO) terms, which reveals that distinct biological tasks are associated with archetypal groups formed by both interactions. This study is also validated regarding statistical significance and sensitivity analysis, providing insights into the functional roles of different interaction types. Finally, the robustness and consistency of the extracted archetype structures are confirmed using the Bayesian Normalized Mutual Information (BNMI) metric, proving the model's reliability in capturing meaningful SPPI patterns. AVAILABILITY: S2-SPM is implemented and freely available under the MIT license at https://github.com/Nicknakis/S2SPM.

Protein Interaction Mapping↗
PubMed1999

Improving decisionmaking processes with the fuzzy logic approach in the epidemiology of sleep disorders.

Epidemiological studies can provide information not only on specific diagnostic entities but also on their underlying symptomatic constellations. For this purpose, an expert system was developed for the assessment of sleep disorders and endowed with the fuzzy logic capabilities necessary to determine the degree to which a given symptom corresponds to a specific diagnosis. Uncertainty is inherent in fields such as sleep medicine and psychiatry, and becomes evident in clinical practice at the stages of data collection and diagnostic formulation, when the clinician must determine whether a symptom is present and must choose from several diagnostic possibilities. The process involves a considerable degree of subjectivity on the part of the patient in trying to describe his or her symptoms, and of the clinician whose final diagnosis will depend on his or her clinical experience and interpretation of what is normal and what is pathological. Inferential models of the probabilistic or fuzzy logic type take into account such uncertainty. The Sleep-Eval system has been used in epidemiological and clinical studies involving 34,044 interviews collected by close to 300 interviewers. The diagnostic potential of these models is illustrated using data collected in an epidemiological study of the noninstitutionalized general population of Italy and underlines the advantages and limits of the binary, bayesian, and fuzzy logic methods and analyses.

Diagnosis, Computer-Assisted↗
PubMed2026

A Bayesian framework for multivariate differential analysis.

Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a hierarchical formulation with moderated-variance estimators for each analyte directly injected into the t-statistic. While standard hypothesis testing strategies are recognised for their low computational cost, allowing for quick extraction of the most differential among thousands of elements, they generally overlook key aspects such as handling missing values, inter-element correlations, and uncertainty quantification. The present paper proposes a fully Bayesian framework for differential analysis, leveraging a conjugate hierarchical formulation for both the mean and the variance. Inference is performed by computing the posterior distribution of compared experimental conditions and sampling from the distribution of differences. This approach provides well-calibrated uncertainty quantification at a similar computational cost as hypothesis testing by leveraging closed-form equations. Furthermore, a natural extension enables multivariate differential analysis that accounts for possible inter-element correlations. We also demonstrate that, in this Bayesian treatment, missing at random data should generally be ignored in univariate settings, and further derive a tailored approximation that handles multiple imputation for the multivariate setting. We argue that probabilistic statements in terms of effect size and associated uncertainty are better suited to practical decision-making. Therefore, we finally propose simple and intuitive inference criteria, such as the overlap coefficient, which express group similarity as a probability rather than traditional, and often misleading, p-values. The performance of this approach is evaluated through an extensive empirical study using both synthetic and controlled real-world proteomics datasets. Overall, we believe that this Bayesian framework for (multivariate) differential analysis provides a valuable and intuitive counterpart to standard methods at a comparable computational cost.

Bayes Theorem↗
PubMed1995

Theory and application of the maximum likelihood principle to NMR parameter estimation of multidimensional NMR data.

A general theory has been developed for the application of the maximum likelihood (ML) principle to the estimation of NMR parameters (frequency and amplitudes) from multidimensional time-domain NMR data. A computer program (ChiFit) has been written that carries out ML parameter estimation in the D-1 indirectly detected dimensions of a D-dimensional NMR data set. The performance of this algorithm has been tested with experimental three-dimensional (HNCO) and four-dimensional (HN(CO)-CAHA) data from a small protein labeled with 13C and 15N. These data sets, with different levels of digital resolution, were processed using ChiFit for ML analysis and employing conventional Fourier transform methods with prior extrapolation of the time-domain dimensions by linear prediction. Comparison of the results indicates that the ML approach provides superior frequency resolution compared to conventional methods, particularly under conditions of limited digital resolution in the time-domain input data, as is characteristic of D-dimensional NMR data of biomolecules. Close correspondence is demonstrated between the results of analyzing multidimensional time-domain NMR data by Fourier transformation, Bayesian probability theory [Chylla, R.A. and Markley, J.L. (1993) J. Biomol. NMR, 3, 515-533], and the ML principle.

Algorithms↗
PubMed1994

The hierarchical Bayesian approach to population pharmacokinetic modelling.

Compartmental models are widely used to model the profile of drug concentrations versus time from administration in an individual subject. Observed concentrations are then modelled as noisy departures from the underlying profile, the latter characterised for each individual by a small number of 'individual parameters'. When a population of individuals is studied, inter-individual variation is modelled by assuming that the individual profile parameters are drawn from a population distribution, the latter characterised by 'population parameters' describing, in effect, a mean population profile and individual variation around it. From a Bayesian statistical perspective, such models fit exactly into the so-called hierarchical modelling framework, which provides a coherent basis for individual and population inferences and prediction, as well as for decision-making (for example, the design of dosage regimens). This paper outlines the hierarchical model framework and describes how the required computations can be carried out in a straightforward manner by a Markov chain Monte Carlo technique known as Gibbs sampling, even when models involve mean-variance relationships and outliers.

Bayes Theorem↗
PubMed2000

Decision-support and intelligent tutoring systems in medical education.

One of the challenges in medical education is to teach the decision-making process. This learning process varies according to the experience of the student and can be supported by various tools. In this paper we present several approaches that can strengthen this mechanism, from decision-support tools, such as scoring systems, Bayesian models, neural networks, to cognitive models that can reproduce how the students progressively build their knowledge into memory and foster pedagogic methods.

Artificial Intelligence↗
PubMedDate not supplied

Qualitative probability versus quantitative probability in clinical diagnosis: a study using a computer simulation.

The use of Bayes' theorem as a diagnostic tool in clinical medicine normally requires an input of exact probability estimates. However, humans tend to think in categories ("likely," "unlikely," etc.) rather than in terms of exact probability. A computer simulation of the presenting features of a case of pelvic infection has been used to compare the effects of quantitative and qualitative probability estimates on the diagnostic accuracy of Bayes' theorem. For the commoner conditions (prior probability greater than or equal to 0.2) the use of a two- or three-category system is virtually equivalent to the use of exact probability. However, uncommon conditions (prior probability less than or equal to 0.03) are completely ignored by the qualitative system. It is concluded that the use of simple categories of probability is acceptable for a Bayesian diagnostic system provided that the target conditions have a relatively high prior probability.

Artificial Intelligence↗
PubMed2000

Validation of techniques for the prediction of carboplatin exposure: application of Bayesian methods.

OBJECTIVE: Several methods have been developed for the prediction of carboplatin exposure to facilitate pharmacokinetic guided dosing. The aim of this study was to develop and validate sparse data Bayesian methods for the estimation of carboplatin exposure and to validate other commonly applied techniques, such as the Chatelut formula, the Sorensen limited sampling model, and the Calvert formula, in which glomerular filtration rate was estimated with the Cockcroft-Gault, the Jelliffe, and the recently proposed Wright formulas. METHODS: Complete concentration-time curves were available for a total of 43 patients (45 courses) receiving carboplatin (265 or 400 mg/m2/day) in a 1-hour infusion for 4 consecutive days in combination with thiotepa and cyclophosphamide. A population two-compartment model was developed on an index set of 12 courses. The other 33 courses served as validation set. Bayesian estimates were generated with the population parameters by use of either one or two randomly timed samples or two samples at optimal time points determined with the D-optimality theory. RESULTS: The Bayesian methods provided an accurate and precise prediction of the area under the concentration-time curve (bias <4% and precision <18%). The other formulas (Sorensen model, Chatelut, and Calvert with Jelliffe, Cockcroft-Gault, and Wright) resulted in a precision >18%, whereas the Jelliffe formula and the Sorensen model resulted in a bias >12%. CONCLUSION: The applicability of a Bayesian method for the prediction of the carboplatin exposure by use of one or two samples without the necessity for exact timing of infusion duration and sampling was demonstrated. The Bayesian method may be very instrumental to execute pharmacokinetic guided dosing for carboplatin.

Adult↗
PubMedDate not supplied

Representation and analysis of medical decision problems with influence diagrams.

Influence diagrams are a powerful graphic representation for decision models, complementary to decision trees. Influence diagrams and decision trees are different graphic representations for the same underlying mathematical model and operations. This article describes the elements of an influence diagram, and shows several familiar decision problems represented as decision trees and as influence diagrams. The authors also contrast the information highlighted in each graphic representation, demonstrate how to calculate the expected utilities of decision alternatives modeled with an influence diagram, provide an overview of the conceptual basis of the solution algorithms that have been developed for influence diagrams, discuss the strengths and limitations of influence diagrams relative to decision trees, and describe the mathematical operations that are used to evaluate both decision trees and influence diagrams. They use clinical examples to illustrate the mathematical operations of the influence-diagram-evaluation algorithm; these operations are arc reversal, chance node removal by averaging, and decision node removal by policy determination. Influence diagrams may be helpful when problems have a high degree of conditional independence, when large models are needed, when communication of the probabilistic relationships is important, or when the analysis requires extensive Bayesian updating. The choice of graphic representation should be governed by convenience, and will depend on the problem being analyzed, on the experience of the analyst, and on the background of the consumers of the analysis.

AIDS-Related Opportunistic Infections↗
PubMed2001

Ideal observer approximation using Bayesian classification neural networks.

It is well understood that the optimal classification decision variable is the likelihood ratio or any monotonic transformation of the likelihood ratio. An automated classifier which maps from an input space to one of the likelihood ratio family of decision variables is an optimal classifier or "ideal observer." Artificial neural networks (ANNs) are frequently used as classifiers for many problems. In the limit of large training sample sizes, an ANN approximates a mapping function which is a monotonic transformation of the likelihood ratio, i.e., it estimates an ideal observer decision variable. A principal disadvantage of conventional ANNs is the potential over-parameterization of the mapping function which results in a poor approximation of an optimal mapping function for smaller training samples. Recently, Bayesian methods have been applied to ANNs in order to regularize training to improve the robustness of the classifier. The goal of training a Bayesian ANN with finite sample sizes is, as with unlimited data, to approximate the ideal observer. We have evaluated the accuracy of Bayesian ANN models of ideal observer decision variables as a function of the number of hidden units used, the signal-to-noise ratio of the data and the number of features or dimensionality of the data. We show that when enough training data are present, excess hidden units do not substantially degrade the accuracy of Bayesian ANNs. However, the minimum number of hidden units required to best model the optimal mapping function varies with the complexity of the data.

Bayes Theorem↗
PubMed2002

Disease transmission models for public health decision making: toward an approach for designing intervention strategies for Schistosomiasis japonica.

Mathematical models of disease transmission processes can serve as platforms for integration of diverse data, including site-specific information, for the purpose of designing strategies for minimizing transmission. A model describing the transmission of schistosomiasis is adapted to incorporate field data typically developed in disease control efforts in the mountainous regions of Sichuan Province in China, with the object of exploring the feasibility of model-based control strategies. The model is studied using computer simulation methods. Mechanistically based models of this sort typically have a large number of parameters that pose challenges in reducing parametric uncertainty to levels that will produce predictions sufficiently precise to discriminate among competing control options. We describe here an approach to parameter estimation that uses a recently developed statistical procedure called Bayesian melding to sequentially reduce parametric uncertainty as field data are accumulated over several seasons. Preliminary results of applying the approach to a historical data set in southwestern Sichuan are promising. Moreover, technologic advances using the global positioning system, remote sensing, and geographic information systems promise cost-effective improvements in the nature and quality of field data. This, in turn, suggests that the utility of the modeling approach will increase over time.

Bayes Theorem↗
PubMed1988

Evaluating diagnostic performance of clinical tests by spreadsheet modeling. Bayesian analysis using Ri/Cj ratio as a unifying concept.

We present a general spreadsheet model for evaluating diagnostic performance of clinical tests. Our model depicts test results as an r X c matrix, with r possible test results and c possible clinical states. Analysis of this matrix is based on the Ri/Cj ratio, calculated as a number of subjects having a specified result Ri within a given clinical state Cj, divided by total subjects within this clinical state. From this model, we can identify three special cases: (1) a 2 X c matrix, with two possible test results of T+ or T-, over c possible clinical states; (2) an r X 2 matrix, with r possible test results, over two possible clinical states of D+ or D-; and (3) a 2 X 2 matrix, with two possible test results over two possible clinical states. Application of the Ri/Cj ratio to the r X c matrix provides a useful approach to graphic analysis of multiple test results over multiple clinical states. The Ri/Cj ratio also provides a general approach to Bayesian analysis, in which likelihood ratio, relative operating characteristic analysis, sensitivity, and specificity represent special cases or special applications.

Bayes Theorem↗
PubMed1989

Computer-assisted optimization of aminophylline therapy in the emergency department.

The emergency department (ED) is a unique setting for pharmacokinetic-guided drug administration because of the need to rapidly optimize therapy. We compared outcomes in patients receiving intravenous aminophylline according to population-based ED guidelines (group 1) or Bayesian-derived pharmacokinetic estimates (group 2), we determined predictors for admission or discharge in our study group, and we assessed the ability of a Bayesian pharmacokinetic model to estimate theophylline requirements in the ED. The study population was composed of 82 patients (42 males, 40 females) with a mean age of 43 +/- 15.5 years. Fifteen patients were excluded because of protocol violations. Of the 67 cases studied, 30 were assigned to group 1, and 37 were assigned to group 2. Patient demographics, baseline theophylline concentration, and theophylline loading dose did not differ significantly between treatment groups. The aminophylline maintenance infusion was significantly (P less than .001) lower in group 1 (0.4 +/- 0.2 mg/kg/h) than in group 2 (0.6 +/- 0.2 mg/kg/h). Serum theophylline concentrations at one hour post-loading-dose did not differ significantly between treatment groups; however, significant differences were observed at two hours post-load (P less than .002) and four hours post-load (P less than .001). Baseline peak flow rate (PFR) was significantly (P less than .03) higher in group 1 (170 +/- 85 L/min) than in group 2 (132 +/- 62 L/min), but did not differ significantly at any other times throughout the study. The PFR one hour post-load (PFR-1) was the strongest (P less than .003) predictor of outcome.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗
PubMed2001

Predicting analysis times in randomized clinical trials.

Randomized clinical trial designs commonly include one or more planned interim analyses. At these times an external monitoring committee reviews the accumulated data and determines whether it is scientifically and ethically appropriate for the study to continue. With failure-time endpoints, it is common to schedule analyses at the times of occurrence of specified landmark events, such as the 50th event, the 100th event, and so on. Because interim analyses can impose considerable logistical burdens, it is worthwhile predicting their timing as accurately as possible. We describe two model-based methods for making such predictions during the course of a trial. First, we obtain a point prediction by extrapolating the cumulative mortality into the future and selecting the date when the expected number of deaths is equal to the landmark number. Second, we use a Bayesian simulation scheme to generate a predictive distribution of milestone times; prediction intervals are quantiles of this distribution. We illustrate our method with an analysis of data from a trial of immunotherapy in the treatment of chronic granulomatous disease.

Bayes Theorem↗
PubMedDate not supplied

Data-source effects on the sensitivities and specificities of clinical features in the diagnosis of rheumatoid arthritis: the relevance of multiple sources of knowledge for a decision-support system.

An experimental computer system was developed to support diagnosis of rheumatic disorders by computing diagnostic probabilities using modified likelihood ratios. The authors examined whether the performance of the model was affected by the settings in which the data used to derive the likelihood ratios were collected. The sensitivities and specificities of various clinical features for diagnosing rheumatoid arthritis (RA) were obtained from: 1) a study of 1,570 consecutive outpatients at a rheumatology clinic; 2) a review of the literature; 3) estimates by rheumatologists; and 4) a population study. Considerable variations in sensitivity and specificity but satisfactory agreement in likelihood ratios were found across the four data sets. The likelihood ratios were then used to compute the probabilities of RA in a test series of 570 of the rheumatology clinic outpatients. The model's diagnoses with likelihood ratios from the other sources were adequate. When the likelihood ratios from these sources were combined, discrimination came close to what could be achieved by using the likelihood ratios based on the data from the clinic. The method applied in the study, which makes use of variation of input data instead of variation of test series, and the results are relevant to assessing the external validity and transferability of Bayesian decision-support systems.

Adolescent↗
PubMed2002

Classical and Bayesian inference in neuroimaging: applications.

In Friston et al. ((2002) Neuroimage 16: 465-483) we introduced empirical Bayes as a potentially useful way to estimate and make inferences about effects in hierarchical models. In this paper we present a series of models that exemplify the diversity of problems that can be addressed within this framework. In hierarchical linear observation models, both classical and empirical Bayesian approaches can be framed in terms of covariance component estimation (e.g., variance partitioning). To illustrate the use of the expectation-maximization (EM) algorithm in covariance component estimation we focus first on two important problems in fMRI: nonsphericity induced by (i) serial or temporal correlations among errors and (ii) variance components caused by the hierarchical nature of multisubject studies. In hierarchical observation models, variance components at higher levels can be used as constraints on the parameter estimates of lower levels. This enables the use of parametric empirical Bayesian (PEB) estimators, as distinct from classical maximum likelihood (ML) estimates. We develop this distinction to address: (i) The difference between response estimates based on ML and the conditional means from a Bayesian approach and the implications for estimates of intersubject variability. (ii) The relationship between fixed- and random-effect analyses. (iii) The specificity and sensitivity of Bayesian inference and, finally, (iv) the relative importance of the number of scans and subjects. The forgoing is concerned with within- and between-subject variability in multisubject hierarchical fMRI studies. In the second half of this paper we turn to Bayesian inference at the first (within-voxel) level, using PET data to show how priors can be derived from the (between-voxel) distribution of activations over the brain. This application uses exactly the same ideas and formalism but, in this instance, the second level is provided by observations over voxels as opposed to subjects. The ensuing posterior probability maps (PPMs) have enhanced anatomical precision and greater face validity, in relation to underlying anatomy. Furthermore, in comparison to conventional SPMs they are not confounded by the multiple comparison problem that, in a classical context, dictates high thresholds and low sensitivity. We conclude with some general comments on Bayesian approaches to image analysis and on some unresolved issues.

Algorithms↗