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PubMed2006

Deterministic and statistical methods for reconstructing multidimensional NMR spectra.

Reconstruction of an image from a set of projections is a well-established science, successfully exploited in X-ray tomography and magnetic resonance imaging. This principle has been adapted to generate multidimensional NMR spectra, with the key difference that, instead of continuous density functions, high-resolution NMR spectra comprise discrete features, relatively sparsely distributed in space. For this reason, a reliable reconstruction can be made from a small number of projections. This speeds the measurements by orders of magnitude compared to the traditional methodology, which explores all evolution space on a Cartesian grid, one step at a time. Speed is of crucial importance for structural investigations of biomolecules such as proteins and for the investigation of time-dependent phenomena. Whereas the recording of a suitable set of projections is a straightforward process, the reconstruction stage can be more problematic. Several practical reconstruction schemes are explored. The deterministic methods-additive back-projection and the lowest-value algorithm-derive the multidimensional spectrum directly from the experimental projections. The statistical search methods include iterative least-squares fitting, maximum entropy, and model-fitting schemes based on Bayesian analysis, particularly the reversible-jump Markov chain Monte Carlo procedure. These competing reconstruction schemes are tested on a set of six projections derived from the three-dimensional 700-MHz HNCO spectrum of a 187-residue protein (HasA) and compared in terms of reliability, absence of artifacts, sensitivity to noise, and speed of computation.

Journal Article↗

PubMed2006

Modeling water diffusion anisotropy within fixed newborn primate brain using Bayesian probability theory.

An active area of research involves optimally modeling brain diffusion MRI data for various applications. In this study Bayesian analysis procedures were used to evaluate three models applied to phase-sensitive diffusion MRI data obtained from formalin-fixed perinatal primate brain tissue: conventional diffusion tensor imaging (DTI), a cumulant expansion, and a family of modified DTI expressions. In the latter two cases the optimum expression was selected from the model family for each voxel in the image. The ability of each model to represent the data was evaluated by comparing the magnitude of the residuals to the thermal noise. Consistent with previous findings from other laboratories, the DTI model poorly represented the experimental data. In contrast, the cumulant expansion and modified DTI expressions were both capable of modeling the data to within the noise using six to eight adjustable parameters per voxel. In these cases the model selection results provided a valuable form of image contrast. The successful modeling procedures differ from the conventional DTI model in that they allow the MRI signal to decay to a positive offset. Intuitively, the positive offset can be thought of as spins that are sufficiently restricted to appear immobile over the sampled range of b-values.

Animals↗

PubMed2003

Generalized monotonic regression using random change points.

We introduce a procedure for generalized monotonic curve fitting that is based on a Bayesian analysis of the isotonic regression model. Conventional isotonic regression fits monotonically increasing step functions to data. In our approach we treat the number and location of the steps as random. For each step level we adopt the conjugate prior to the sampling distribution of the data as if the curve was unconstrained. We then propose to use Markov chain Monte Carlo simulation to draw samples from the unconstrained model space and retain only those samples for which the monotonic constraint holds. The proportion of the samples collected for which the constraint holds can be used to provide a value for the weight of evidence in terms of Bayes factors for monotonicity given the data. Using the samples, probability statements can be made about other quantities of interest such as the number of change points in the data and posterior distributions on the location of the change points can be provided. The method is illustrated throughout by a reanalysis of the leukaemia data studied by Schell and Singh.

Bayes Theorem↗

PubMed2005

Bayesian non-response models for categorical data from small areas: an application to BMD and age.

We provide a Bayesian analysis of data categorized into two levels of age (younger than 50 years, at least 50 years) and three levels of bone mineral density (normal, osteopenia, osteoporosis) for white females at least 20 years old in the third National Health and Nutrition Examination Survey. For the sample, the age of each individual is known, but some individuals did not have their BMD measured. We use two types of models: In the ignorable non-response models the propensity to respond does not depend on BMD and age of an individual, while in the non-ignorable non-response models it does. These are the baseline models which are used to derive all models for testing. Our non-ignorable non-response models are 'close' to the ignorable non-response models, thereby reducing the effects of the assumptions about non-respondents that cannot be tested in non-response models. We have data from 35 counties, small areas, and therefore our models are hierarchical, a feature that allows a 'borrowing of strength' across the counties, and they provide a substantial reduction in variation. The non-ignorable non-response models are generalizations of the ignorable non-response models, and therefore, the non-ignorable non-response models allow broader inference. The joint posterior density of the parameters for each model is complex, and therefore, we fit each model using Markov chain Monte Carlo methods to obtain samples which are used to make inference about BMD and age. For each county we can estimate the proportion of individuals in each BMD and age cell of the categorical table, and we can assess the relation between BMD and age using the Bayes factor. A sensitivity analysis shows that there are differences (typically small) in inference that permits different levels of association between BMD and age. A simulation study shows that there is not much difference between the baseline ignorable and non-ignorable non-response models.

Adult↗

PubMed2005

A correlated frailty model for analysing risk factors in bilateral corneal graft rejection for Keratoconus: a Bayesian approach.

There are many unknown causes that increase the rate of corneal graft rejection. In bilateral cases, some of these unknown causes are common, and some are individual factors. In this paper, we use a correlated frailty model to analyse risk factors for bilateral corneal graft in Keratoconus. Applying the piecewise constant baseline hazard model, we have performed a Bayesian analysis of the correlated frailty model using the Markov chain Monte Carlo method. The correlated frailty model and the shared frailty model are compared by deviance information criterion. The results show more accurate and better fit for the correlated frailty model.

Bayes Theorem↗

PubMed2006

Non-linear random effects models with continuous time autoregressive errors: a Bayesian approach.

Measurements on subjects in longitudinal medical studies are often collected at several different times or under different experimental conditions. Such multiple observations on the same subject generally produce serially correlated outcomes. Traditional regression methods assume that observations within subjects are independent which is not true in longitudinal data. In this paper we develop a Bayesian analysis for the traditional non-linear random effects models with errors that follow a continuous time autoregressive process. In this way, unequally spaced observations do not present a problem in the analysis. Parameter estimation of this model is done via the Gibbs sampling algorithm. The method is illustrated with data coming from a study in pregnant women in Santiago, Chile, that involves the non-linear regression of plasma volume on gestational age.

Bayes Theorem↗

PubMed2007

Bayesian estimation of false-negative rate in a clinical trial of sentinel node biopsy.

Estimating the false-negative rate is a major issue in evaluating sentinel node biopsy (SNB) for staging cancer. In a large multicentre trial of SNB for intra-operative staging of clinically node-negative breast cancer, two sources of information on the false-negative rate are available.Direct information is available from a preliminary validation phase: all patients underwent SNB followed by axillary nodal clearance or sampling. Of 803 patients with successful sentinel node localization, 19 (2.4 per cent) were classed as false negatives. Indirect information is also available from the randomized phase. Ninety-seven (25.4 per cent) of 382 control patients undergoing axillary clearance had positive axillae. In the experimental group, 94/366 (25.7 per cent) were apparently node positive. Taking a simple difference of these proportions gives a point estimate of -0.3 per cent for the proportion of patients who had positive axillae but were missed by SNB. This estimate is clearly inadmissible. In this situation, a Bayesian analysis yields interpretable point and interval estimates. We consider the single proportion estimate from the validation phase; the difference between independent proportions from the randomized phase, both unconstrained and constrained to non-negativity; and combined information from the two parts of the study. As well as tail-based and highest posterior density interval estimates, we examine three obvious point estimates, the posterior mean, median and mode. Posterior means and medians are similar for the validation and randomized phases separately and combined, all between 2 and 3 per cent, indicating similarity rather than conflict between the two data sources.

Bayes Theorem↗

PubMedDate not supplied

The exclusion of patients from a clinical trial.

In designing a clinical trial, the investigator must often decide whether or not to exclude certain patients from randomization. Using Bayesian analysis this paper proposes a criterion for making this decision, based on an extension of Colton's model for the choice between two medical treatments.

Bayes Theorem↗

PubMed1991

Using empirical Bayes methods in biopharmaceutical research.

A compound sampling model, where a unit-specific parameter is sampled from a prior distribution and then observed are generated by a sampling distribution depending on the parameter, underlies a wide variety of biopharmaceutical data. For example, in a multi-centre clinical trial the true treatment effect varies from centre to centre. Observed treatment effects deviate from these true effects through sampling variation. Knowledge of the prior distribution allows use of Bayesian analysis to compute the posterior distribution of clinic-specific treatment effects (frequently summarized by the posterior mean and variance). More commonly, with the prior not completely specified, observed data can be used to estimate the prior and use it to produce the posterior distribution: an empirical Bayes (or variance component) analysis. In the empirical Bayes model the estimated prior mean gives the typical treatment effect and the estimated prior standard deviation indicates the heterogeneity of treatment effects. In both the Bayes and empirical Bayes approaches, estimated clinic effects are shrunken towards a common value from estimates based on single clinics. This shrinkage produces more efficient estimates. In addition, the compound model helps structure approaches to ranking and selection, provides adjustments for multiplicity, allows estimation of the histogram of clinic-specific effects, and structures incorporation of external information. This paper outlines the empirical Bayes approach. Coverage will include development and comparison of approaches based on parametric priors (for example, a Gaussian prior with unknown mean and variance) and non-parametric priors, discussion of the importance of accounting for uncertainty in the estimated prior, comparison of the output and interpretation of fixed and random effects approaches to estimating population values, estimating histograms, and identification of key considerations in the use and interpretation of empirical Bayes methods.

Bayes Theorem↗

PubMed1993

The value of randomization and control in clinical trials.

This paper examines the two principal justifications that have been offered for the standard conditions that clinical trials be randomized and controlled, with the conclusion that, strictly speaking, neither justification is valid. It is argued, on the other hand, that a Bayesian analysis of clinical trials affords a valid, intuitively plausible rationale for selective controls, and marks out a more limited role for randomization than it is generally accorded. The feasibility of retrospective trials is then considered in the light of these conclusions.

Bayes Theorem↗

PubMed2002

Non-linear hierarchical models for monitoring compliance.

As biomarkers transformable by specific drug agents increasingly become available, so their usefulness also increases for monitoring compliance in clinical and prevention trials, and for subsequent monitoring in the general population if a treatment is found successful. Marker levels measured over the course of a treatment yield a longitudinal trajectory that is typically non-linear, with varying velocities during the phase-in and steady-state periods of treatment, followed by decays back to normal in the presence of non-compliance. There is often considerable between-individual variability both in the mean parameters of the trajectory and the variability over time. An example is the biomarker mean corpuscular volume (MCV), which increases by 20 per cent from the drug zidovudine (AZT), and has been used to monitor compliance to AZT. Using MCV data from a previous AIDS clinical trial as an example, we describe a non-linear hierarchical growth model suitable for biomarkers that exhibit sigmoidal and/or asymptotic growth behaviour and show how such models can be supplemented with a change-point to identify potential times of non-compliance. We perform a fully Bayesian analysis to obtain a variety of posterior summaries for the behaviour of the longitudinal trajectory and the times of non-compliance, and describe how to obtain predictions of non-compliance for new individuals.

Acquired Immunodeficiency Syndrome↗

PubMed1998

A Bayes-optimal sequence-structure theory that unifies protein sequence-structure recognition and alignment.

A rigorous Bayesian analysis is presented that unifies protein sequence-structure alignment and recognition. Given a sequence, explicit formulae are derived to select (1) its globally most probable core structure from a structure library; (2) its globally most probable alignment to a given core structure; (3) its most probable joint core structure and alignment chosen globally across the entire library; and (4) its most probable individual segments, secondary structure, and super-secondary structures across the entire library. The computations involved are NP-hard in the general case (3D-3D). Fast exact recursions for the restricted sequence singleton-only (1D-3D) case are given. Conclusions include: (a) the most probable joint core structure and alignment is not necessarily the most probable alignment of the most probable core structure, but rather maximizes the product of core and alignment probabilities; (b) use of a sequence-independent linear or affine gap penalty may result in the highest-probability threading not having the lowest score; (c) selecting the most probable core structure from the library (core structure selection or fold recognition only) involves comparing probabilities summed over all possible alignments of the sequence to the core, and not comparing individual optimal (or near-optimal) sequence-structure alignments; and (d) assuming uninformative priors, core structure selection is equivalent to comparing the ratio of two global means.

Amino Acid Sequence↗

PubMed1984

Implications of intraindividual variability in bioavailability studies of furosemide.

Intrasubject variation in bioavailability (rate and extent) and disposition of furosemide 40 mg was investigated using a repeated, randomized, double-blind cross-over study in 8 healthy subjects. Two generic tablet formulations (Lasix and Furix) and intravenous furosemide were compared on 6 separate days. Extensive intrasubject variability after oral administration was observed in AUC, mean absorption time (MAT) and urinary excretion. The variability (error variance) within the dosage forms was as large as that between the two generics. These variations most probably depended on the absorption process, since the repeated i.v. doses showed only marginal intrasubject variability. Absolute bioavailability was 56% for Lasix and 55% for Furix (AUC). The range was 20 to 84% between individuals and the maximal range within one individual was 20 to 61%. Confidence interval and Bayesian analysis showed a high probability of non-equivalence not only between but also within the generics when the separate cross-over experiments were analyzed (8 observations). When extending the analysis to 16 observations, bioequivalence was demonstrated for the two generic tablets. Rate of absorption, quantified as MAT, was 128 min for Lasix and 98 min for Furix (16 observations). Since MAT was significantly longer (p less than 0.001) than the mean residence time after the i.v. dose (57 min), absorption was evidently the rate-limiting step in the overall kinetics of oral furosemide. Intraindividual variation in absorption is a confounding factor in bioavailability studies of furosemide using limited numbers of subjects. This is important to consider when designing and evaluating bioavailability studies for drugs showing these variations.

Administration, Oral↗

PubMedDate not supplied

Noninvasive testing of asymptomatic bilateral hilar adenopathy.

The diagnostic strategy for asymptomatic patients with persistent bilateral bilar adenopathy often involves invasive procedures. The authors used Bayesian analysis to: 1) estimate the relative prevalences of diseases causing bilateral bilar adenopathy; 2) assess changes in the prevalence of disease by race, the presence of other clinical symptoms, and geography; and 3) determine the value of relevant noninvasive tests, including the angiotensin-converting enzyme (ACE) assay, gallium scan, and purified protein derivative (PPD), in order to assess when a strategy of watchful waiting is appropriate. The analysis indicated that the ACE assay, particularly when paired with the PPD, can identify many patients who might safely be managed without immediate invasive biopsy. Patients who are ACE+ and PPD- have an estimated probability of sarcoidosis of 0.95 or greater; patients who are ACE- and PPD+ have a probability of tuberculosis of 0.86 if black, 0.79 if white. In contrast, gallium scanning has no diagnostic role in this clinical situation. Bronchoscopic or mediastinoscopic biopsy has a limited role for patients who are ACE+ PPD- or ACE- PPD+ because of limited sensitivity. Patients who are both ACE- and PPD-, particularly if white, may have a high enough risk of lymphoma to consider invasive biopsy.

Bayes Theorem↗

PubMed1995

Interpretation of the tuberculin skin test.

OBJECTIVE: To reinterpret epidemiologic information about the tuberculin test (purified protein derivative) in terms of modern approaches to test characteristics; to clarify why different cutpoints of induration should be used to define a positive test in different populations; and to calculate test characteristics of the intermediate-strength tuberculin skin test, the probability of Mycobacterium tuberculosis infection at various induration sizes, the area under the receiver operating characteristic (ROC) curve, and optimal cutpoints for positivity. METHODS: Standard epidemiologic assumptions were used to distinguish M. tuberculosis-infected from -uninfected persons; also used were data from the U.S. Navy recruit and World Health Organization tuberculosis surveys; and Bayesian analysis. RESULTS: In the general U.S. population, the test's sensitivity is 0.59 to 1.0, the specificity is 0.95 to 1.0, and the positive predictive value is 0.44 to 1.0, depending on the cutpoint. Among tuberculosis patients, the sensitivity is nearly the same as in the general population; the positive predictive value is 1.0. The area under the ROC curve is 0.997. The probability of M. tuberculosis infection at each induration size varies widely, depending on the prevalence. The optimal cutpoint varies from 2 mm to 16 mm and is dependent on prevalence and the purpose for testing. CONCLUSIONS: The operating characteristics of the tuberculin test are superior to those of nearly all commonly used screening and diagnostic tests. The tuberculin test has an excellent ability to distinguish M. tuberculosis-infected from -uninfected persons. Interpretation requires consideration of prevalence and the purpose for testing. These findings support the recommendation to use different cutpoints for various populations. Even more accurate information can be gotten by interpreting induration size as indicating a probability of M. tuberculosis infection.

Adolescent↗

PubMed2002

Frequency of alleles conferring resistance to Bt maize in French and US corn belt populations of the European corn borer, Ostrinia nubilalis.

Farmers, industry, governments and environmental groups agree that it would be useful to manage transgenic crops producing insecticidal proteins to delay the evolution of resistance in target pests. The main strategy proposed for delaying resistance to Bacillus thuringiensis ( Bt) toxins in transgenic crops is the high-dose/refuge strategy. This strategy is based on the unverified assumption that resistance alleles are initially rare (<10(-3)). We used an F(2) screen on >1,200 isofemale lines of Ostrinia nubilalis Hübner (Lepidoptera: Crambidae) collected in France and the US corn belt during 1999-2001. In none of the isofemale lines did we detect alleles conferring resistance to Bt maize producing the Cry1Ab toxin. A Bayesian analysis of the data indicates that the frequency of resistance alleles in France was <9.20 x 10(-4) with 95% probability, and a detection probability of >80%. In the northern US corn belt, the frequency of resistance to Bt maize was <4.23 x 10(-4) with 95% probability, and a detection probability of >90%. Only 95 lines have been screened from the southern US corn belt, so these data are still inconclusive. These results suggest that resistance is probably rare enough in France and the northern US corn belt for the high-dose plus refuge strategy to delay resistance to Bt maize.

Alleles↗

PubMed2000

Contribution of ultrasonography and cholescintigraphy to the diagnosis of acute acalculous cholecystitis in intensive care unit patients.

OBJECTIVES: To assess the respective value of ultrasonography (US) and morphine cholescintigraphy (MC) in the diagnosis of acute acalculous cholecystitis (AAC). DESIGN AND SETTING: Prospective study in an intensive care unit of a university hospital. PATIENTS AND INTERVENTION: Twenty-eight patients with clinically and biologically suspected of AAC. US was performed at the bedside and less than 12 h later MC. US was considered positive if three major criteria were present: wall thickness greater than 4 mm, hydrops, sludge; MC results were regarded as positive if the gallbladder could not be visualized. These latter patients underwent cholecystectomy and the diagnosis of AAC was confirmed through histopathological study. MEASUREMENTS AND MAIN RESULTS: Sensitivity of US and MC, respectively, was 50% and 67%, specificity 94% and 100%, positive predictive value 86% and 100%, negative predictive value 71% and 80%, and accuracy 75% and 86%. The correlation between US and MC findings was 71%, with chi = 0.31. By Bayesian analysis the probability of disease if the MC finding was positive was 100% regardless of US results. A positive US finding was associated with a 86% probability of disease, but with a probability of only 66% in case of negative MC results. MC is thus superior to US for confirming AAC in selected critically ill patients. Nevertheless, US is an easy, noninvasive, and effective method of bedside screening. The combination of the two imaging tests improves diagnostic accuracy and reduces false-positive and false-negative rates. Poor agreement between the two tests leads to better diagnostic complementarity.

Acute Disease↗

PubMed2001

Assessing the reliability of PBPK models using data from methyl chloride-exposed, non-conjugating human subjects.

Physiologically based pharmacokinetic (PBPK) models are often optimized by adjusting metabolic parameters so as to fit experimental toxicokinetic data. The estimates of the metabolic parameters are then conditional on the assumed values for all other parameters. Meanwhile, the reliability of other parameters, or the structural model, is usually not questioned. Inhalation exposures with human volunteers in our laboratory show that non-conjugators lack metabolic capacity for methyl chloride entirely, and that elimination in these subjects takes place via exhalation only. Therefore, data from these methyl chloride exposures provide an excellent opportunity to assess the general reliability of standard inhalation PBPK models for humans. A hierarchical population PBPK model for methyl chloride was developed. The model was fit to the experimental data in a Bayesian framework using Markov chain Monte Carlo (MCMC) simulation. In a Bayesian analysis, it is possible to merge a priori knowledge of the physiological, anatomical and physicochemical parameters with the information embedded in the experimental toxicokinetic data obtained in vivo. The resulting estimates are both statistically and physiologically plausible. Model deviations suggest that a pulmonary sub-compartment may be needed in order to describe the inhalation and exhalation of volatile adequately. The results also indicate that there may be significant intra-individual variability in the model parameters. To our knowledge, this is the first time that the toxicokinetics of a non-metabolized chemical is used to assess population PBPK parameters. This approach holds promise for more elaborate experiments in order to assess the reliability of PBPK models in general.

Adult↗