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ScITree: Scalable Bayesian inference of transmission tree from epidemiological and genomic data.

Phylodynamic models capture joint epidemiological-evolutionary dynamics during an outbreak, providing a powerful tool to enhance understanding and management of disease transmission. Existing phylodynamic approaches, however, mostly rely on various non-mechanistic or semi-mechanistic approximations of the underlying epidemiological-evolutionary process. Previous work by Lau and colleagues has shown that full Bayesian mechanistic models, without relying on these approximations, can enable highly accurate joint inference of the epidemiological-evolutionary dynamics including the unobserved transmission tree. However, the Lau method faces major computational bottlenecks. As the volume of genomic data collected during outbreaks continues to grow, it is crucial to develop scalable yet accurate phylodynamic methods. Here we propose a new Bayesian phylodynamic model, overcoming the major scalability issue in the previous method and enabling a readily deployable, yet accurate, phylodynamic modeling framework. Specifically, we develop a scalable spatio-temporal phylodynamic framework for inferring the transmission tree (ScITree) and other key epidemiological parameters considering the infinite sites assumption in modeling mutation on the sequence level, in contrast to the Lau method in which mutation was modeled explicitly on the nucleotide level. Our approach features full Bayesian implementation utilizing an exact likelihood to mechanistically integrate epidemiological and evolutionary processes. We develop a computationally-efficient data-augmentation Markov Chain Monte Carlo algorithm, inferring key model parameters and unobserved dynamics including the transmission tree. We assess performance of our method using multiple simulated outbreak datasets. Our results indicate that our method can achieve high inference accuracy, comparable to the performance of the Lau method. Additionally, our method scales significantly more efficiently for large outbreaks, with computing time increasing linearly with outbreak size, compared to the exponential scaling of the Lau method. We also demonstrate our method's utility by applying our validated modeling framework to a dataset describing a foot-and-mouth disease outbreak in the UK. Our results show that our method is able to generate estimates of the transmission dynamics consistent with those from the prior method, further demonstrating the robustness of our new approach. In summary, our method provides a computationally-efficient, highly scalable, accurate modeling framework for inferring the joint spatio-temporal dynamics of epidemiological and evolutionary processes, facilitating timely and effective outbreak responses in space and time. Our method is implemented in our R package ScITree.

Bayes Theorem↗

Adaptive control of drug dosage regimens: basic foundations, relevant issues, and clinical examples.

In this paper we examine several of the fundamental foundations and relevant clinical issues in adaptive control of drug dosage regimens for patients. Truly individualized therapy with drugs having narrow margins of safety first requires a practical pharmacokinetic/dynamic model of the behavior of a drug. Past experience with a drug is stored in the form of a population model. Next, using the information in such a model and its relationship to the incidence of adverse reactions, a specific, explicit therapeutic goal must be selected by the responsible clinician, based on the patient's need for the drug and the risk of adverse reactions felt to be justified by each patient's need, small, moderate, or great. Individualized drug therapy thus begins with the selection of individualized therapeutic goals (low, moderate, or high) for each patient. Using subsequent feedback from the patient's serum drug levels, and using Bayesian fitting, the model is then linked to each patient as a patient-specific model. Control of the model by the dosage regimen increasingly controls the patient, to better obtain the desired explicit therapeutic goals. This process is essentially similar to that of a flight control or missile guidance system.

Bayes Theorem↗

Segregation of visceral and somatosensory afferents: an fMRI and cytoarchitectonic mapping study.

Ano-rectal stimulation provides an important model for the processing of somatosensory and visceral sensations in the human nervous system. In spite of their anatomical proximity, the anal canal is innervated by somatosensory afferents whereas the rectum is innervated by the visceral nervous system. In a functional magnetic resonance (fMRI) experiment, we examined the cerebral responses to pneumatic balloon distension of these two structures to test whether somatosensory and visceral stimulation elicited distinct brain activations in spite of their spinal convergence. The specificity of the identified activations was analyzed by Bayesian mixed effects modeling. Activations in the parietal operculum were also compared to the location of cytoarchitectonically defined areas OP 1-4, which are part of the secondary somatosensory cortex (SII), to analyze whether the SII region was activated by anal and/or rectal stimulation. The lowest segregation between visceral and somatosensory stimuli was in the insular cortex, which supports the interpretation of the insula as an integrative region, receiving input from different sensory modalities. The most distinct segregation was found in the fronto-parietal operculum. Here the activations following anal and rectal stimulation were not only functionally but also anatomically distinct. Anal sensations were processed similar to other somatosensory stimuli in the SII cortex (area OP 4). Rectal afferents on the other hand were not processed in SII. Rather, they evoked activation at a more anterior location on the precentral operculum. These results demonstrate a functionally and anatomically distinct processing of somatosensory and visceral afferents in the human cerebral cortex.

Adult↗

Modeling the effects of a bidirectional latent predictor from multivariate questionnaire data.

Researchers often measure stress using questionnaire data on the occurrence of potentially stress-inducing life events and the strength of reaction to these events, characterized as negative or positive and assigned an ordinal ranking. In studying the health effects of stress, one needs to obtain measures of an individual's negative and positive stress levels to be used as predictors. Motivated by data of this type, we propose a latent variable model, which is characterized by event-specific negative and positive reaction scores. If the positive reaction score dominates the negative reaction score for an event, then the individual's reported response to that event will be positive, with an ordinal ranking determined by the value of the score. Measures of overall positive and negative stress can be obtained by summing the reactivity scores across the events that occur for an individual. By incorporating these measures as predictors in a regression model and fitting the stress and outcome models jointly using Bayesian methods, inferences can be conducted without the need to assume known weights for the different events. We propose an MCMC algorithm for posterior computation and apply the approach to study the effects of stress on preterm delivery.

Algorithms↗

Constructing Bayesian formulations of sparse kernel learning methods.

We present here a simple technique that simplifies the construction of Bayesian treatments of a variety of sparse kernel learning algorithms. An incomplete Cholesky factorisation is employed to modify the dual parameter space, such that the Gaussian prior over the dual model parameters is whitened. The regularisation term then corresponds to the usual weight-decay regulariser, allowing the Bayesian analysis to proceed via the evidence framework of MacKay. There is in addition a useful by-product associated with the incomplete Cholesky factorisation algorithm, it also identifies a subset of the training data forming an approximate basis for the entire dataset in the kernel-induced feature space, resulting in a sparse model. Bayesian treatments of the kernel ridge regression (KRR) algorithm, with both constant and heteroscedastic (input dependent) variance structures, and kernel logistic regression (KLR) are provided as illustrative examples of the proposed method, which we hope will be more widely applicable.

Algorithms↗

Estimation in Bayesian disease mapping.

Recent work on Bayesian inference of disease mapping models discusses the advantages of the fully Bayesian (FB) approach over its empirical Bayes (EB) counterpart, suggesting that FB posterior standard deviations of small-area relative risks are more reflective of the uncertainty associated with the relative risk estimation than counterparts based on EB inference, since the latter fail to account for the variability in the estimation of the hyperparameters. In this article, an EB bootstrap methodology for relative risk inference with accurate parametric EB confidence intervals is developed, illustrated, and contrasted with the hyperprior Bayes. We elucidate the close connection between the EB bootstrap methodology and hyperprior Bayes, present a comparison between FB inference via hybrid Markov chain Monte Carlo and EB inference via penalized quasi-likelihood, and illustrate the ability of parametric bootstrap procedures to adjust for the undercoverage in the "naive" EB interval estimates. We discuss the important roles that FB and EB methods play in risk inference, map interpretation, and real-life applications. The work is motivated by a recent analysis of small-area infant mortality rates in the province of British Columbia in Canada.

Algorithms↗

Incorporation of splice site probability models for non-canonical introns improves gene structure prediction in plants.

MOTIVATION: The vast majority of introns in protein-coding genes of higher eukaryotes have a GT dinucleotide at their 5'-terminus and an AG dinucleotide at their 3' end. About 1-2% of introns are non-canonical, with the most abundant subtype of non-canonical introns being characterized by GC and AG dinucleotides at their 5'- and 3'-termini, respectively. Most current gene prediction software, whether based on ab initio or spliced alignment approaches, does not include explicit models for non-canonical introns or may exclude their prediction altogether. With present amounts of genome and transcript data, it is now possible to apply statistical methodology to non-canonical splice site prediction. We pursued one such approach and describe the training and implementation of GC-donor splice site models for Arabidopsis and rice, with the goal of exploring whether specific modeling of non-canonical introns can enhance gene structure prediction accuracy. RESULTS: Our results indicate that the incorporation of non-canonical splice site models yields dramatic improvements in annotating genes containing GC-AG and AT-AC non-canonical introns. Comparison of models shows differences between monocot and dicot species, but also suggests GC intron-specific biases independent of taxonomic clade. We also present evidence that GC-AG introns occur preferentially in genes with atypically high exon counts. AVAILABILITY: Source code for the updated versions of GeneSeqer and SplicePredictor (distributed with the GeneSeqer code) isavailable at http://bioinformatics.iastate.edu/bioinformatics2go/gs/download.html. Web servers for Arabidopsis, rice and other plant species are accessible at http://www.plantgdb.org/PlantGDB-cgi/GeneSeqer/AtGDBgs.cgi, http://www.plantgdb.org/PlantGDB-cgi/GeneSeqer/OsGDBgs.cgi and http://www.plantgdb.org/PlantGDB-cgi/GeneSeqer/PlantGDBgs.cgi, respectively. A SplicePredictor web server is available at http://bioinformatics.iastate.edu/cgi-bin/sp.cgi. Software to generate training data and parameterizations for Bayesian splice site models is available at http://gremlin1.gdcb.iastate.edu/~volker/SB05B/BSSM4GSQ/

Base Composition↗

Estimation of population pharmacokinetic parameters of saquinavir in HIV patients with the MONOLIX software.

In nonlinear mixed-effects models, estimation methods based on a linearization of the likelihood are widely used although they have several methodological drawbacks. Kuhn and Lavielle (Comput. Statist. Data Anal. 49:1020-1038 (2005)) developed an estimation method which combines the SAEM (Stochastic Approximation EM) algorithm, with a MCMC (Markov Chain Monte Carlo) procedure for maximum likelihood estimation in nonlinear mixed-effects models without linearization. This method is implemented in the Matlab software MONOLIX which is available at http://www.math.u-psud.fr/~lavielle/monolix/logiciels. In this paper we apply MONOLIX to the analysis of the pharmacokinetics of saquinavir, a protease inhibitor, from concentrations measured after single dose administration in 100 HIV patients, some with advance disease. We also illustrate how to use MONOLIX to build the covariate model using the Bayesian Information Criterion. Saquinavir oral clearance (CL/F) was estimated to be 1.26 L/h and to increase with body mass index, the inter-patient variability for CL/F being 120%. Several methodological developments are ongoing to extend SAEM which is a very promising estimation method for population pharmacockinetic/pharmacodynamic analyses.

Administration, Oral↗

A pattern-mixture model for the analysis of censored quality-of-life data.

We propose a pattern-mixture model for describing the joint distribution of incomplete repeated measurements of quality of life (QoL) and right-censored survival times. The model assumes that the survival times follow a multinomial distribution and that the quality of life outcome follows a multivariate normal distribution conditional on the survival time. We estimate the model using a Bayesian approach by importance sampling. We then use simulated parameters to create multiple imputations of the censored QoL outcomes, which can then be used to calculate individual values of quality-adjusted life-years (QALYs). We apply the method to data from the Randomized Evaluation of Mechanical Assistance in the Treatment of Congestive Heart Failure (REMATCH) clinical trial.

Bayes Theorem↗

A Bayesian approach to randomized controlled trials in children utilizing information from adults: the case of Guillain-Barré syndrome.

BACKGROUND: Guillain-Barré syndrome (GBS) is a rare neurologic disease that occurs at all ages, causing a progressive, ascending paralysis that usually resolves over weeks or months. The disease appears to be identical in children and adults, except that children recover more quickly, with fewer residua. For patients who lose the ability to walk independently, the main treatment options are plasmapheresis or intravenous immune globulin (IVIg), treatments that have shown to have identical effectiveness in adults in two large RCTs involving 388 patients. The effectiveness of the treatments in children has only been studied in small, poorly controlled studies. If one could capture all eligible patients in the United States, only about 100-300 children would be available for a trial annually. METHODS: The goal of this case was to demonstrate how Bayesian methods could be used to incorporate prior information on treatment efficacy from adults to design a randomized noninferiority trial of IVIg versus plasmapheresis in children. A Bayesian normal-normal model on the hazard ratio of time to independent walking was implemented. RESULTS: An evidence-based prior was constructed that was equivalent to 72 children showing exact equivalence between the therapies. A design was constructed based on a Bayesian normal-normal model on the hazard ratio, yielding a sample size of 160 children, with a preposterior analysis demonstrating a "Type I" error rate of 5% and a power of 77%. CONCLUSIONS: This case study illustrates a rational approach to constructing an evidence-based prior that would allow information from adults to formally augment data from children to minimize unnecessary pediatric experimentation. The frequentist properties of a Bayesian design can be evaluated and reported as they would be for a standard design. Discussion of the appropriate prior for such designs is both a necessary and desirable feature of Bayesian trials.

Adult↗

Reasoning requirements for diagnosis of heart disease.

Over the past dozen years, the Heart Disease Program (HDP) has been developed to assist physicians in reasoning about cardiovascular disorders. Driven by several evaluations, the inference mechanism has progressed from a logic based model, to a Bayesian Probability Network (BPN) and finally a pseudo-Bayesian network with temporal and severity reasoning. Though aspects of cardiovascular reasoning are handled well by BPNs, temporal reasoning, homeostatic feedback mechanisms and effects of disease severities require additional inference strategies. This article discusses how these reasoning problems are handled, and deals with closely linked issues in building the user interface to collect detailed cardiovascular data and provide clear explanations of diagnoses.

Artificial Intelligence↗

Contrasting patterns in the small-scale heterogeneity of human helminth infections in urban and rural environments in Brazil.

Marked heterogeneity exists in the patterns of parasitic infection between individuals, households and communities. Analysis of parasite distributions within populations is complicated by the fact that parasite distributions are highly aggregated and few studies have explicitly incorporated this distribution when investigating small-scale spatial heterogeneities. This study aimed to quantify the small-scale (within- and between-household) heterogeneity of helminth infection in an area of Minas Gerais State, Brazil, with rural and urban sectors. Parasitological data from a cross-sectional survey of 1,249 individuals aged 0-86 years from 242 households were analysed. Within-household clustering of infection was assessed using random effect logistic regression models and between-household spatial heterogeneity was assessed using a Bayesian negative binomial spatial model. The overall prevalence of hookworm (Necator americanus) was 66.9%, the prevalence of Schistosoma mansoni was 44.9% and the prevalence of Ascaris lumbricoides was 48.8%. Statistical analysis indicated significant (within) household and (between household) spatial clustering of hookworm in both rural and urban areas and of S. mansoni in rural areas. There was no evidence of either household or spatial clustering of S. mansoni in urban areas. The spatial correlation of S. mansoni was estimated to reduce by half over a distance of 700 m in the rural area. Rural hookworm had a much smaller half-distance (28 m) and urban hookworm showed an even smaller half-distance (12 m). We suggest that such species-specific differences in patterns of infection by environment are primarily due to variation in exposure and parasite life cycle, although host genetic factors cannot be ruled out.

Adolescent↗

The RIN: an RNA integrity number for assigning integrity values to RNA measurements.

BACKGROUND: The integrity of RNA molecules is of paramount importance for experiments that try to reflect the snapshot of gene expression at the moment of RNA extraction. Until recently, there has been no reliable standard for estimating the integrity of RNA samples and the ratio of 28S:18S ribosomal RNA, the common measure for this purpose, has been shown to be inconsistent. The advent of microcapillary electrophoretic RNA separation provides the basis for an automated high-throughput approach, in order to estimate the integrity of RNA samples in an unambiguous way. METHODS: A method is introduced that automatically selects features from signal measurements and constructs regression models based on a Bayesian learning technique. Feature spaces of different dimensionality are compared in the Bayesian framework, which allows selecting a final feature combination corresponding to models with high posterior probability. RESULTS: This approach is applied to a large collection of electrophoretic RNA measurements recorded with an Agilent 2100 bioanalyzer to extract an algorithm that describes RNA integrity. The resulting algorithm is a user-independent, automated and reliable procedure for standardization of RNA quality control that allows the calculation of an RNA integrity number (RIN). CONCLUSION: Our results show the importance of taking characteristics of several regions of the recorded electropherogram into account in order to get a robust and reliable prediction of RNA integrity, especially if compared to traditional methods.

Algorithms↗

A hierarchical Binomial-Poisson model for the analysis of a crossover design for correlated binary data when the number of trials is dose-dependent.

The differential reinforcement of a low-rate 72-seconds schedule (DRL-72) is a standard behavioral test procedure for screening a potential antidepressant compound. The data analyzed in the article are binary outcomes from a crossover design for such an experiment. Recently, Shkedy et al. (2004) proposed to estimate the treatments effect using either generalized linear mixed models (GLMM) or generalized estimating equations (GEE) for clustered binary data. The models proposed by Shkedy et al. (2004) assumed the number of responses at each binomial observation is fixed. This might be an unrealistic assumption for a behavioral experiment such as the DRL-72 because the number of responses (the number of trials in each binomial observation) is expected to be influenced by the administered dose level. In this article, we extend the model proposed by Shkedy et al. (2004) and propose a hierarchical Bayesian binomial-Poisson model, which assumes the number of responses to be a Poisson random variable. The results obtained from the GLMM and the binomial-Poisson models are comparable. However, the latter model allows estimating the correlation between the number of successes and number of trials.

Algorithms↗

Bayesian combination of ambiguous shape cues.

We investigate how different depth cues are combined when one cue is ambiguous. Convex and concave surfaces produce similar texture projections at large viewing distances. Our study considered unambiguous disparity information and its combination with ambiguous texture information. Specifically, we asked whether disparity and texture were processed separately, before linear combination of shape estimates, or jointly, such that disparity disambiguated the texture information. Vertical ridges of various depths were presented stereoscopically. Their texture was consistent (in terms of maximum likelihood) with both a convex and a concave ridge. Disparity was consistent with either a convex or concave ridge. In a separate experiment the stimuli were defined solely by texture (monocular viewing). Under monocular viewing observers consistently reported the convex interpretation of the texture cue. However, in stereoscopic stimuli, texture information modulated shape from disparity in a way inconsistent with simple linear combination. When disparity indicated a concave surface, a texture pattern perceived as highly convex when viewed monocularly caused the stimulus to appear more concave than a "flat" texture pattern. Our data confirm that different cues can disambiguate each other. Data from both experiments are well modeled by a Bayesian approach incorporating a prior for convexity.

Bayes Theorem↗

Bayesian analysis of a multivariate null intercept errors-in-variables regression model.

Longitudinal data are of great interest in analysis of clinical trials. In many practical situations the covariate can not be measured precisely and a natural alternative model is the errors-in-variables regression models. In this paper we study a null intercept errors-in-variables regression model with a structure of dependency between the response variables within the same group. We apply the model to real data presented in Hadgu and Koch (Hadgu, A., Koch, G. (1999). Application of generalized estimating equations to a dental randomized clinical trial. J. Biopharmaceutical Statistics 9(1):161-178). In that study volunteers with preexisting dental plaque were randomized to two experimental mouth rinses (A and B) or a control mouth rinse with double blinding. The dental plaque index was measured for each subject in the beginning of the study and at two follow-up times, which leads to the presence of an interclass correlation. We propose the use of a Bayesian approach to model a multivariate null intercept errors-in-variables regression model to the longitudinal data. The proposed Bayesian approach accommodates the correlated measurements and incorporates the restriction that the slopes must lie in the (0, 1) interval. A Gibbs sampler is used to perform the computations.

Bayes Theorem↗

Towards empirical description of malaria seasonality in southern Africa: the example of Zimbabwe.

BACKGROUND: Quantitative description and mapping of malaria seasonality is important for timely spatial targeting of interventions and for modelling malaria risk. There is a need for seasonality models that predict quantitative variation in transmission between months. METHODS: We use Zimbabwe as an example for developing an empirical map of malaria seasonality. We describe the relationship between seasonality in malaria and environmental covariates for the period 1988--1999, by fitting a spatial-temporal regression model within a Bayesian framework to provide smoothed maps of the seasonal trend. We adapt a seasonality concentration index used previously for rainfall to quantify malaria case load during the peak transmission season based on monthly values. RESULTS: Combinations of mean monthly temperature (range 28--32 degrees C), maximum temperature (24--28 degrees C) and high rainfall provide suitable conditions for seasonal transmission. High monthly maximum and mean monthly minimum temperatures limit months of high transmission. The intensity of seasonal transmission was highest in the north western part of the country from February to May with the peak in April and lowest in the whole country from July to December. The north western lowlands had the highest concentration of malaria cases (>25%) followed by some districts in the north central and eastern part with a moderate concentration of cases (20-25%). The central highlands and south eastern part of the country had the lowest concentration of malaria cases (<20%). This pattern was closely associated to the geographic variation in the seasonality of climatic covariates particularly rainfall and temperature. Conclusions Our modelling approach quantifies the geographical variation in seasonal trend and the concentration of cases during the peak transmission season and therefore has potential application in malaria control. The use of a covariate adjusted empirical model may prove useful for predicting the seasonal risk pattern across southern Africa.

Humans↗

Clinical efficacies of antihypertensive drugs.

OBJECTIVE: According to published data, the ability to prevent various hypertension-related events differs between the various antihypertensive drug groups. Although absolute drug effects differ among studies, relative drug effects could be considered constant. We therefore explored the possibility of drawing statistically valid conclusions about the differences in clinical efficacy between various drug groups by doing an overview of published data. DESIGN: We made a meta-analysis with a Bayesian fixed effect model in which we related the drug effects to the effects of placebo drugs. We selected 27 clinical trials from the literature according to specific criteria, including results from studies reporting the effects of the newer drugs when tested against diuretics and beta-blockers, and from studies in which diuretics and beta-blockers had been tested against placebo. We calculated the posterior probability distributions of the relative effects of angiotensin-converting enzyme (ACE) inhibitors vs calcium antagonists with three different endpoints: stroke, coronary disease and heart failure with point estimates of effects and with 95% credibility intervals. As an intermediate step in this procedure we obtained similar information about the effects of the three groups of active drugs, ACE inhibitors, calcium antagonists and diuretics or beta-blockers, tested against placebo. For coronary disease we also tested calcium antagonists against diuretics or beta-blockers. RESULTS: ACE inhibitors and calcium antagonists have an almost identical ability to prevent stroke in hypertensive individuals with a risk ratio (RR) of 1.04. On the other hand, calcium antagonists reduce coronary disease by only 8% relative to placebo. When ACE inhibitors and calcium antagonists are compared with the Bayesian method, the outcome is a 14% difference in favor of the ACE inhibitors to prevent coronary disease, with a credibility interval almost reaching identity. Nor do calcium antagonists do as well as diuretics or beta-blockers in this respect, RR = 1.12 with 95% credibility interval 1.01-1.24. All the tested drug groups have a profound preventive effect on the occurrence of heart failure when given to hypertensive patients, showing reductions of 42-54%. When ACE inhibitors are compared with calcium antagonists RR = 0.79, with a credibility interval 0.65-0.95. CONCLUSION: There is statistically an indisputable difference between ACE inhibitors and calcium antagonists in respect of effects on coronary disease and heart failure when treating hypertensive individuals, ACE inhibitors being more efficacious. There are no differences in the effect on stroke. Moreover, beta-blockers or diuretics are also superior to calcium antagonists in preventing coronary events.

Adrenergic beta-Antagonists↗