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PubMed2001

A case study on the choice, interpretation and checking of multilevel models for longitudinal binary outcomes.

Recent advances in statistical software have led to the rapid diffusion of new methods for modelling longitudinal data. Multilevel (also known as hierarchical or random effects) models for binary outcomes have generally been based on a logistic-normal specification, by analogy with earlier work for normally distributed data. The appropriate application and interpretation of these models remains somewhat unclear, especially when compared with the computationally more straightforward semiparametric or 'marginal' modelling (GEE) approaches. In this paper we pose two interrelated questions. First, what limits should be placed on the interpretation of the coefficients and inferences derived from random-effect models involving binary outcomes? Second, what diagnostic checks are appropriate for evaluating whether such random-effect models provide adequate fits to the data? We address these questions by means of an extended case study using data on adolescent smoking from a large cohort study. Bayesian estimation methods are used to fit a discrete-mixture alternative to the standard logistic-normal model, and posterior predictive checking is used to assess model fit. Surprising parallels in the parameter estimates from the logistic-normal and mixture models are described and used to question the interpretability of the so-called 'subject-specific' regression coefficients from the standard multilevel approach. Posterior predictive checks suggest a serious lack of fit of both multilevel models. The results do not provide final answers to the two questions posed, but we expect that lessons learned from the case study will provide general guidance for further investigation of these important issues.

Journal Article↗
PubMed2005

Frequentist performance of Bayesian confidence intervals for comparing proportions in 2 x 2 contingency tables.

This article investigates the performance, in a frequentist sense, of Bayesian confidence intervals (CIs) for the difference of proportions, relative risk, and odds ratio in 2 x 2 contingency tables. We consider beta priors, logit-normal priors, and related correlated priors for the two binomial parameters. The goal was to analyze whether certain settings for prior parameters tend to provide good coverage performance regardless of the true association parameter values. For the relative risk and odds ratio, we recommend tail intervals over highest posterior density (HPD) intervals, for invariance reasons. To protect against potentially very poor coverage probabilities when the effect is large, it is best to use a diffuse prior, and we recommend the Jeffreys prior. Otherwise, with relatively small samples, Bayesian CIs using more informative (even uniform) priors tend to have poorer performance than the frequentist CIs based on inverting score tests, which perform uniformly quite well for these parameters.

Bayes Theorem↗
PubMed2006

Longitudinal and repeated cross-sectional cluster-randomization designs using mixed effects regression for binary outcomes: bias and coverage of frequentist and Bayesian methods.

As medical applications for cluster randomization designs become more common, investigators look for guidance on optimal methods for estimating the effect of group-based interventions over time. This study examines two distinct cluster randomization designs: (1) the repeated cross-sectional design in which centres are followed over time but patients change, and (2) the longitudinal design in which individual patients are followed over time within treatment clusters. Simulations of each study design stipulated a multiplicative treatment effect (on the log odds scale), between 5 and 15 clusters in each of two treatment arms, and followed over two time periods. Estimation options included linear mixed effects models using restricted maximum likelihood (REML), generalized estimating equations (GEE), mixed effects logistic regression using both penalized quasi likelihood (PQL) and numerical integration, and Bayesian Monte Carlo analysis. For the repeated cross-sectional designs, most methods performed well in terms of bias and coverage when clusters were numerous (30) and variability across clusters of baseline risk and treatment effect was modest. With few clusters (two groups of five) and higher variability, only the Bayesian methods maintained coverage. In the longitudinal designs, the common methods of REML, GEE, or PQL performed poorly when compared to numerical integration, while Bayesian methods demonstrated less bias and better coverage for estimates of both log odds ratios and risk differences. The performance of common statistical tools for the analysis of cluster randomization designs depends heavily on the precise design, the number of clusters, and the variability of baseline outcomes and treatment effects across centres.

Bayes Theorem↗
PubMed2007

Bayesian reconstruction of nanodosimetric cluster distributions at 100% detection efficiency.

Ionisation spectra in nanometric volumes at a given distance from a charged particle track are obtained by using electron (or ion) gas detectors, having non-uniformly distributed detection efficiency. Therefore, such spectra should be properly processed in order to reconstruct the frequency distribution of clusters really produced in the detector gas. A Bayesian unfolding has been applied to ionisation distributions due to 5.4 MeV alpha particles in a 20-nm site obtained by Monte Carlo simulations, taking into account different detection efficiency conditions. It will be shown that Bayesian analysis provides a valid tool for reconstructing the true ionisation distributions, well beyond the maximum measured cluster size.

Bayes Theorem↗
PubMedDate not supplied

Bayesian segmentation of protein secondary structure.

We present a novel method for predicting the secondary structure of a protein from its amino acid sequence. Most existing methods predict each position in turn based on a local window of residues, sliding this window along the length of the sequence. In contrast, we develop a probabilistic model of protein sequence/structure relationships in terms of structural segments, and formulate secondary structure prediction as a general Bayesian inference problem. A distinctive feature of our approach is the ability to develop explicit probabilistic models for alpha-helices, beta-strands, and other classes of secondary structure, incorporating experimentally and empirically observed aspects of protein structure such as helical capping signals, side chain correlations, and segment length distributions. Our model is Markovian in the segments, permitting efficient exact calculation of the posterior probability distribution over all possible segmentations of the sequence using dynamic programming. The optimal segmentation is computed and compared to a predictor based on marginal posterior modes, and the latter is shown to provide significant improvement in predictive accuracy. The marginalization procedure provides exact secondary structure probabilities at each sequence position, which are shown to be reliable estimates of prediction uncertainty. We apply this model to a database of 452 nonhomologous structures, achieving accuracies as high as the best currently available methods. We conclude by discussing an extension of this framework to model nonlocal interactions in protein structures, providing a possible direction for future improvements in secondary structure prediction accuracy.

Algorithms↗
PubMed2006

A Bayesian mixture model for partitioning gene expression data.

In recent years there has been great interest in making inference for gene expression data collected over time. In this article, we describe a Bayesian hierarchical mixture model for partitioning such data. While conventional approaches cluster the observed data, we assume a nonparametric, random walk model, and partition on the basis of the parameters of this model. The model is flexible and can be tuned to the specific context, respects the order of observations within each curve, acknowledges measurement error, and allows prior knowledge on parameters to be incorporated. The number of partitions may also be treated as unknown, and inferred from the data, in which case computation is carried out via a birth-death Markov chain Monte Carlo algorithm. We first examine the behavior of the model on simulated data, along with a comparison with more conventional approaches, and then analyze meiotic expression data collected over time on fission yeast genes.

Bayes Theorem↗
PubMed2002

Bayesian model adequacy and choice in phylogenetics.

Bayesian inference is becoming a common statistical approach to phylogenetic estimation because, among other reasons, it allows for rapid analysis of large data sets with complex evolutionary models. Conveniently, Bayesian phylogenetic methods use currently available stochastic models of sequence evolution. However, as with other model-based approaches, the results of Bayesian inference are conditional on the assumed model of evolution: inadequate models (models that poorly fit the data) may result in erroneous inferences. In this article, I present a Bayesian phylogenetic method that evaluates the adequacy of evolutionary models using posterior predictive distributions. By evaluating a model's posterior predictive performance, an adequate model can be selected for a Bayesian phylogenetic study. Although I present a single test statistic that assesses the overall (global) performance of a phylogenetic model, a variety of test statistics can be tailored to evaluate specific features (local performance) of evolutionary models to identify sources failure. The method presented here, unlike the likelihood-ratio test and parametric bootstrap, accounts for uncertainty in the phylogeny and model parameters.

Animals↗
PubMed2004

Modelling blood-brain barrier partitioning using Bayesian neural nets.

We have employed three families of molecular molecular descriptors, together with Bayesian regularized neural nets, to model the partitioning of a diverse range of drugs and other small molecules across the blood-brain barrier (BBB). The relative efficacy of each descriptors class is compared, and the advantages of flexible, parsimonious, model free mapping methods, like Bayesian neural nets, illustrated. The relative importance of the molecular descriptors for the most predictive BBB model were determined by use of automatic relevance determination (ARD), and compared with the important descriptors from other literature models of BBB partitioning.

Bayes Theorem↗
PubMed2001

Bayesian source separation for reference function determination in fMRI.

In analyzing fMRI results, identification of significant activation in voxels is a crucial task. A standard method selects a "known" reference function and performs a regression of the time courses on it and a linear trend. Once the linear trend is found, the correlation between the assumed to be known reference function and the detrended observed time-course in each voxel is computed. But the most important question is: How does one choose the reference function? Here, a Bayesian source separation approach to determining the underlying reference function is described and applied to real fMRI data. This underlying reference function is the unobserved response due to the presentation of the experimental stimulus.

Bayes Theorem↗
PubMed2002

Hardy-Weinberg equilibrium diagnostics.

We propose two diagnostics for the statistical assessment of Hardy-Weinberg equilibrium. One diagnostic is the posterior probability of the complement of the smallest highest posterior density credible region that includes points in the parameter space consistent with the hypothesis of equilibrium. The null hypothesis of equilibrium is to be rejected if this probability is less than a pre-selected critical level. The second diagnostic is the proportion of the parameter space occupied by the highest posterior density credible region associated with the critical level. These Bayesian diagnostics can be interpreted as analogues of the classical types I and II error probabilities. They are broadly applicable: they can be computed for any hypothesis test, using samples of any size generated according to any distribution.

Alleles↗
PubMed2005

Efficient kernel density estimation of shape and intensity priors for level set segmentation.

We propose a nonlinear statistical shape model for level set segmentation which can be efficiently implemented. Given a set of training shapes, we perform a kernel density estimation in the low dimensional subspace spanned by the training shapes. In this way, we are able to combine an accurate model of the statistical shape distribution with efficient optimization in a finite-dimensional subspace. In a Bayesian inference framework, we integrate the nonlinear shape model with a nonparametric intensity model and a set of pose parameters which are estimated in a more direct data-driven manner than in previously proposed level set methods. Quantitative results show superior performance (regarding runtime and segmentation accuracy) of the proposed nonparametric shape prior over existing approaches.

Algorithms↗
PubMed2006

Humans ignore motion and stereo cues in favor of a fictional stable world.

As we move through the world, our eyes acquire a sequence of images. The information from this sequence is sufficient to determine the structure of a three-dimensional scene, up to a scale factor determined by the distance that the eyes have moved. Previous evidence shows that the human visual system accounts for the distance the observer has walked and the separation of the eyes when judging the scale, shape, and distance of objects. However, in an immersive virtual-reality environment, observers failed to notice when a scene expanded or contracted, despite having consistent information about scale from both distance walked and binocular vision. This failure led to large errors in judging the size of objects. The pattern of errors cannot be explained by assuming a visual reconstruction of the scene with an incorrect estimate of interocular separation or distance walked. Instead, it is consistent with a Bayesian model of cue integration in which the efficacy of motion and disparity cues is greater at near viewing distances. Our results imply that observers are more willing to adjust their estimate of interocular separation or distance walked than to accept that the scene has changed in size.

Computer Simulation↗
PubMed1998

Bayesian decision procedures based on logistic regression models for dose-finding studies.

Early-phase clinical trials, conducted to determine the appropriate dose of an experimental drug to take forward to later trials, are considered. The objective is to find the dose associated with some low probability of an adverse event. A Bayesian model is presented, and a decision-theoretic procedure for finding the optimal doses for each of a series of cohorts of subjects is derived. The procedure is flexible and can easily be conducted using standard statistical software. The results of simulations investigating the properties of the procedure are presented.

Bayes Theorem↗
PubMed1990

Probability modelling of a surgical probe for tumour detection.

Probability functions for the output counts from a radiation detector probe are needed to implement Bayesian detection strategies or to assess performance of the probe. This paper presents methods for simulating a surgical probe designed for tumour detection to obtain statistical information for modelling probability functions of output data. Statistical models of pharmaceutical uptake in normal organs and tumours were estimated from animal and human data, and these models were combined with a digitised human torso phantom to create a large set of simulated patients. With the simulated patients and with a spatial map of the probe response, computer simulations of intraoperative probe measurements provided a large set of simulated probe data. Probability models derived from these data using maximum-likelihood methods helped to formulate the detection strategy and to evaluate the performance of the surgical probe.

Computer Simulation↗
PubMed2000

Improved image quality in digital mammography with image processing.

PURPOSE: The effect of image processing, specifically Bayesian image estimation (BIE), on digital mammographic images is studied. BIE is an iterative, nonlinear statistical estimation technique that has previously been used in chest radiography to reduce image scatter content and improve the contrast-to-noise ratio (CNR). We adapt this technique to digital mammography and examine its effect. METHODS/MATERIALS: Images of the American College of Radiologists (ACR) breast phantom were acquired on a calibrated digital mammography system at a normal mammographic exposure both with and without a grid. An iterative Bayesian estimation algorithm was formulated and used to process the images acquired without a grid. Quantitative scatter fractions were measured and compared for the image acquired with the grid, the image acquired without the grid, and the image acquired without the grid and processed by the Bayesian algorithm. CNR values were also computed for the four visible masses in the ACR phantom before and after processing and compared to a grid. RESULTS: Initial images acquired without an antiscatter grid had scatter fractions of 0.46. Processing this image with BIE reduced the scatter content to under 0.04. In comparison, the image acquired with a grid had scatter of 0.19. BIE processing accounted for CNR improvements from 29% to 219% for the masses seen in the ACR phantom as compared to the unprocessed image. Visibility of the four masses in the phantom was improved. CONCLUSIONS: Bayesian image estimation can be used with digital mammography to reduce scatter fractions. This technique is very useful as it can reduce scatter content effectively without introducing any adverse effects, such as grid line aliasing. Bayesian processing can also increase image CNR, which may potentially increase the visualization of subtle masses. Preliminary work shows an improvement in CNR to values greater than that provided by a standard grid.

Algorithms↗
PubMed2000

Developmental dysplasia of the hip practice guideline: technical report. Committee on Quality Improvement, and Subcommittee on Developmental Dysplasia of the Hip.

OBJECTIVE: To create a recommendation for pediatricians and other primary care providers about their role as screeners for detecting developmental dysplasia of the hip (DDH) in children. PATIENTS: Theoretical cohorts of newborns. METHOD: Model-based approach using decision analysis as the foundation. Components of the approach include the following: PERSPECTIVE: Primary care provider. OUTCOMES: DDH, avascular necrosis of the hip (AVN). OPTIONS: Newborn screening by pediatric examination; orthopaedic examination; ultrasonographic examination; orthopaedic or ultrasonographic examination by risk factors. Intercurrent health supervision-based screening. PREFERENCES: 0 for bad outcomes, 1 for best outcomes. MODEL: Influence diagram assessed by the Subcommittee and by the methodology team, with critical feedback from the Subcommittee. EVIDENCE SOURCES: Medline and EMBASE search of the research literature through June 1996. Hand search of sentinel journals from June 1996 through March 1997. Ancestor search of accepted articles. EVIDENCE QUALITY: Assessed on a custom subjective scale, based primarily on the fit of the evidence to the decision model. RESULTS: After discussion, explicit modeling, and critique, an influence diagram of 31 nodes was created. The computer-based and the hand literature searches found 534 articles, 101 of which were reviewed by 2 or more readers. Ancestor searches of these yielded a further 17 articles for evidence abstraction. Articles came from around the globe, although primarily Europe, British Isles, Scandinavia, and their descendants. There were 5 controlled trials, each with a sample size less than 40. The remainder were case series. Evidence was available for 17 of the desired 30 probabilities. Evidence quality ranged primarily between one third and two thirds of the maximum attainable score (median: 10-21; interquartile range: 8-14). Based on the raw evidence and Bayesian hierarchical meta-analyses, our estimate for the incidence of DDH revealed by physical examination performed by pediatricians is 8.6 per 1000; for orthopaedic screening, 11.5; for ultrasonography, 25. The odds ratio for DDH, given breech delivery, is 5.5; for female sex, 4.1; for positive family history, 1.7, although this last factor is not statistically significant. Postneonatal cases of DDH were divided into mid-term (younger than 6 months of age) and late-term (older than 6 months of age). Our estimates for the mid-term rate for screening by pediatricians is 0.34/1000 children screened; for orthopaedists, 0.1; and for ultrasonography, 0.28. Our estimates for late-term DDH rates are 0.21/1000 newborns screened by pediatricians; 0.08, by orthopaedists; and 0.2 for ultrasonography. The rates of AVN for children referred before 6 months of age is estimated at 2.5/1000 infants referred. For those referred after 6 months of age, our estimate is 109/1000 referred infants. The decision model (reduced, based on available evidence) suggests that orthopaedic screening is optimal, but because orthopaedists in the published studies and in practice would differ, the supply of orthopaedists is relatively limited, and the difference between orthopaedists and pediatricians is statistically insignificant, we conclude that pediatric screening is to be recommended. The place of ultrasonography in the screening process remains to be defined because there are too few data about postneonatal diagnosis by ultrasonographic screening to permit definitive recommendations. These data could be used by others to refine the conclusions based on costs, parental preferences, or physician style. Areas for research are well defined by our model-based approach.

Decision Support Techniques↗
PubMed2005

Multiple imputation under Bayesianly smoothed pattern-mixture models for non-ignorable drop-out.

Conventional pattern-mixture models can be highly sensitive to model misspecification. In many longitudinal studies, where the nature of the drop-out and the form of the population model are unknown, interval estimates from any single pattern-mixture model may suffer from undercoverage, because uncertainty about model misspecification is not taken into account. In this article, a new class of Bayesian random coefficient pattern-mixture models is developed to address potentially non-ignorable drop-out. Instead of imposing hard equality constraints to overcome inherent inestimability problems in pattern-mixture models, we propose to smooth the polynomial coefficient estimates across patterns using a hierarchical Bayesian model that allows random variation across groups. Using real and simulated data, we show that multiple imputation under a three-level linear mixed-effects model which accommodates a random level due to drop-out groups can be an effective method to deal with non-ignorable drop-out by allowing model uncertainty to be incorporated into the imputation process.

Antipsychotic Agents↗
PubMed2003

Bayesian multimodality non-rigid image registration via conditional density estimation.

We present a Bayesian multimodality non-rigid image registration method. Since the likelihood is unknown in the general multimodality setting, we use a density estimator as a drop in replacement to the true likelihood. The prior is a standard small deformation penalty on the displacement field. Since mutual information-based methods are in widespread use for multimodality registration, we attempt to relate the Bayesian approach to mutual information-based approaches. To this end, we derive a new criterion which when satisfied, guarantees that the displacement field which minimizes the Bayesian maximum a posteriori (MAP) objective also maximizes the true mutual information (with a small deformation penalty) as the number of pixels tends to infinity. The criterion imposes an upper bound on the number of configurations of the displacement field. Finally, we compare the results of the Bayesian approach with mutual information, joint entropy and joint probability approaches on synthetic data and simulated T1 and T2 2D MR images.

Algorithms↗