Pair-based likelihood approximations for stochastic epidemic models.

Fitting stochastic epidemic models to data is a non-standard problem because data on the infection processes defined in such models are rarely observed directly. This in turn means that the likelihood of the observed data is intractable in the sense that it is very computationally expensive to obtain. Although data-augmented Markov chain Monte Carlo (MCMC) methods provide a solution to this problem, employing a tractable augmented likelihood, such methods typically deteriorate in large populations due to poor mixing and increased computation time. Here, we describe a new approach that seeks to approximate the likelihood by exploiting the underlying structure of the epidemic model. Simulation study results show that this approach can be a serious competitor to data-augmented MCMC methods. Our approach can be applied to a wide variety of disease transmission models, and we provide examples with applications to the common cold, Ebola, and foot-and-mouth disease.

Damage Diagnosis of Single-Layer Latticed Shell Based on Temperature-Induced Strain under Bayesian Framework.

Under the framework of Bayesian theory, a probabilistic method for damage diagnosis of latticed shell structures based on temperature-induced strain is proposed. First, a new damage diagnosis index is proposed based on the correlation between temperature-induced strain and structural parameters. Then, Markov Chain Monte Carlo is adopted to analyze the newly proposed diagnosis index, based on which the frequency distribution histogram for the posterior probability of the diagnosis index is obtained. Finally, the confidence interval of the damage diagnosis is determined by the posterior distribution of the initial state (baseline condition). The damage probability of the unknown state is also calculated. The proposed method was validated by applying it to a latticed shell structure with finite element developed, where the rod damage and bearing failure were diagnosed based on importance analysis and temperature sensitivity analysis of the rod. The analysis results show that the proposed method can successfully consider uncertainties in the strain response monitoring process and effectively diagnose the failure of important rods in radial and annular directions, as well as horizontal (x- and y-direction) bearings of the latticed shell structure.

Bayesian splines versus fractional polynomials in network meta-analysis.

BACKGROUND: Network meta-analysis (NMA) provides a powerful tool for the simultaneous evaluation of multiple treatments by combining evidence from different studies, allowing for direct and indirect comparisons between treatments. In recent years, NMA is becoming increasingly popular in the medical literature and underlying statistical methodologies are evolving both in the frequentist and Bayesian framework. Traditional NMA models are often based on the comparison of two treatment arms per study. These individual studies may measure outcomes at multiple time points that are not necessarily homogeneous across studies. METHODS: In this article we present a Bayesian model based on B-splines for the simultaneous analysis of outcomes across time points, that allows for indirect comparison of treatments across different longitudinal studies. RESULTS: We illustrate the proposed approach in simulations as well as on real data examples available in the literature and compare it with a model based on P-splines and one based on fractional polynomials, showing that our approach is flexible and overcomes the limitations of the latter. CONCLUSIONS: The proposed approach is computationally efficient and able to accommodate a large class of temporal treatment effect patterns, allowing for direct and indirect comparisons of widely varying shapes of longitudinal profiles.

Comparing hierarchical models via the marginalized deviance information criterion.

Hierarchical models are extensively used in pharmacokinetics and longitudinal studies. When the estimation is performed from a Bayesian approach, model comparison is often based on the deviance information criterion (DIC). In hierarchical models with latent variables, there are several versions of this statistic: the conditional DIC (cDIC) that incorporates the latent variables in the focus of the analysis and the marginalized DIC (mDIC) that integrates them out. Regardless of the asymptotic and coherency difficulties of cDIC, this alternative is usually used in Markov chain Monte Carlo (MCMC) methods for hierarchical models because of practical convenience. The mDIC criterion is more appropriate in most cases but requires integration of the likelihood, which is computationally demanding and not implemented in Bayesian software. Therefore, we consider a method to compute mDIC by generating replicate samples of the latent variables that need to be integrated out. This alternative can be easily conducted from the MCMC output of Bayesian packages and is widely applicable to hierarchical models in general. Additionally, we propose some approximations in order to reduce the computational complexity for large-sample situations. The method is illustrated with simulated data sets and 2 medical studies, evidencing that cDIC may be misleading whilst mDIC appears pertinent.

Determinants of new drugs prescription in the Swiss healthcare market.

BACKGROUND: Drug markets are very complex and, while many new drugs are registered each year, little is known about what drives the prescription of these new drugs. This study attempts to lift the veil from this important subject by analyzing simultaneously the impact of several variables on the prescription of novelty. METHODS: Data provided by four Swiss sickness funds were analyzed. These data included information about more than 470,000 insured, notably their drug intake. Outcome variable that captured novelty was the age of the drug prescribed. The overall variance in novelty was partitioned across five levels (substitutable drug market, patient, physician, region, and prescription) and the influence of several variables measured at each of these levels was assessed using a non-hierarchical multilevel model estimated by Bayesian Markov Chain Monte Carlo methods. RESULTS: More than 92% of the variation in novelty was explained at the substitutable drug market-level and at the prescription-level. Newer drugs were prescribed in markets that were costlier, less concentrated, included more insured, provided more drugs and included more active substances. Over-the-counter drugs were on average 12.5 years older while generic drugs were more than 15 years older than non-generics. Regional disparities in terms of age of prescribed drugs could reach 2.8 years. CONCLUSIONS: Regulation of the demand has low impact, with little variation explained at the patient-level and physician-level. In contrary, the market structure (e.g. end of patent with generic apparition, concurrence among producers) had a strong contribution to the variation of drugs ages.

A Bayesian approach to sequential meta-analysis.

As evidence accumulates within a meta-analysis, it is desirable to determine when the results could be considered conclusive to guide systematic review updates and future trial designs. Adapting sequential testing methodology from clinical trials for application to pooled meta-analytic effect size estimates appears well suited for this objective. In this paper, we describe a Bayesian sequential meta-analysis method, in which an informative heterogeneity prior is employed and stopping rule criteria are applied directly to the posterior distribution for the treatment effect parameter. Using simulation studies, we examine how well this approach performs under different parameter combinations by monitoring the proportion of sequential meta-analyses that reach incorrect conclusions (to yield error rates), the number of studies required to reach conclusion, and the resulting parameter estimates. By adjusting the stopping rule thresholds, the overall error rates can be controlled within the target levels and are no higher than those of alternative frequentist and semi-Bayes methods for the majority of the simulation scenarios. To illustrate the potential application of this method, we consider two contrasting meta-analyses using data from the Cochrane Library and compare the results of employing different sequential methods while examining the effect of the heterogeneity prior in the proposed Bayesian approach. Copyright © 2016 John Wiley & Sons, Ltd.

Dynamics of shigellosis epidemics: estimating individual-level transmission and reporting rates from national epidemiologic data sets.

Shigellosis, a diarrheal disease, is endemic worldwide and is responsible for approximately 15,000 laboratory-confirmed cases in the United States every year. However, patients with shigellosis often do not seek medical care. To estimate the burden of shigellosis, we extended time-series susceptible-infected-recovered models to infer epidemiologic parameters from underreported case data. We applied the time-series susceptible-infected-recovered-based inference schemes to analyze the largest surveillance data set of Shigella sonnei in the United States from 1967 to 2007 with county-level resolution. The dynamics of shigellosis transmission show strong annual and multiyear cycles, as well as seasonality. By using the schemes, we inferred individual-level parameters of shigellosis infection, including seasonal transmissibilities and basic reproductive number (R0). In addition, this study provides quantitative estimates of the reporting rate, suggesting that the shigellosis burden in the United States may be more than 10 times the number of laboratory-confirmed cases. Although the estimated reporting rate is generally under 20%, and R0 is generally under 1.5, there is a strong negative correlation between estimates of the reporting rate and R0. Such negative correlations are likely to pose identifiability problems in underreported diseases. We discuss complementary approaches that might further disentangle the true reporting rate and R0.

A Bayesian spatial voting model to characterize the legislative behavior of the Colombian Senate 2010-2014.

This paper characterizes the legislators voting behavior in the Colombian Senate 2010-2014, by implementing a one-dimensional standard Bayesian ideal point estimator via Markov chain Monte Carlo algorithms. Our main goal is to retrieve the political preferences of legislators from their roll-call voting records, which individualizes the electoral behavior of the legislative chamber. Furthermore, we conclude about the nature of the latent trait underlying the deputies voting decisions and the legislators locations in political space. Finally, we also offer several methodological and theoretical tools to guide the analysis of nominal voting data in the context of unbalanced parliaments (multi-party systems), taking as reference the particular case of the Colombian Senate.

Investigating emergent nested geographic structure in consumer purchases: a Bayesian dynamic multi-scale spatiotemporal modeling approach.

Spatial modeling of consumer response data has gained increased interest recently in the marketing literature. In this paper, we extend the (spatial) multi-scale model by incorporating both spatial and temporal dimensions in the dynamic multi-scale spatiotemporal modeling approach. Our empirical application with a US company's catalog purchase data for the period 1997-2001 reveals a nested geographic market structure that spans geopolitical boundaries such as state borders. This structure identifies spatial clusters of consumers who exhibit similar spatiotemporal behavior, thus pointing to the importance of emergent geographic structure, emergent nested structure and dynamic patterns in multi-resolution methods. The multi-scale model also has better performance in estimation and prediction compared with several spatial and spatiotemporal models and uses a scalable and computationally efficient Markov chain Monte Carlo method that makes it suitable for analyzing large spatiotemporal consumer purchase datasets.

Evolutionary analysis of human respiratory syncytial virus collected in Myanmar between 2015 and 2018.

We studied genetic variation in the second hypervariable region (HVR) of the G gene of human respiratory syncytial virus (HRSV) from 1701 nasal swab samples collected from outpatients with acute respiratory infections at two general hospitals in the cities Yangon and Pyinmana in Myanmar from 2015 to 2018. HRSV genotypes were characterized using phylogenetic trees constructed using the maximum likelihood method. Time-scale phylogenetic tree analyses were performed using the Bayesian Markov chain Monte Carlo method. In total, 244 (14.3%) samples were HRSV-positive and were classified as HRSV-A (n = 84, 34.4%), HRSV-B (n = 158, 64.8%), and co-detection of HRSV-A/HRSV-B (n = 2, 0.8%). HRSV epidemics occurred seasonally between July (1.9%, 15/785) and August (10.5%, 108/1028), with peak infections in September (35.8%, 149/416) and October (58.2%, 89/153). HRSV infection rate was higher in children ≥1 year of age than in those <1 year of age (70.5% vs. 29.5%). The most common HRSV symptoms in children were cough (80%-90%) and rhinorrhea (70%-100%). The predominant genotypes were ON1for HRSV-A (78%) and BA9 for HRSV-B (64%). Time to the most recent common ancestor was 2014 (95% highest posterior density [HPD], 2012-2015) for HRSV-A ON1 and 2009 (95% HPD, 2004-2012) for HRSV-B BA9. The mean evolutionary rate (substitutions/site/year) for HRSV-B (2.12 × 10-2, 95% HPD, 8.53 × 10-3-3.63 × 10-2) was slightly higher than that for HRSV-A (1.39 × 10-2, 95% HPD, 6.03 × 10-3-2.12 × 10-2). The estimated effective population size (diversity) for HRSV-A increased from 2015 to 2016 and declined in mid-2018, whereas HRSV-B diversity was constant in 2015 and 2016 and increased in mid-2017. In conclusion, the dominant HRSV-A and HRSV-B genotypes in Myanmar were ON1 and BA9, respectively, between 2015 and 2018. HRSV-B evolved slightly faster than HRSV-A and exhibited unique phylogenetic characteristics.

Scalable Bayesian Inference for Coupled Hidden Markov and Semi-Markov Models.

Bayesian inference for coupled hidden Markov models frequently relies on data augmentation techniques for imputation of the hidden state processes. Considerable progress has been made on developing such techniques, mainly using Markov chain Monte Carlo (MCMC) methods. However, as the dimensionality and complexity of the hidden processes increase some of these methods become inefficient, either because they produce MCMC chains with high autocorrelation or because they become computationally intractable. Motivated by this fact we developed a novel MCMC algorithm, which is a modification of the forward filtering backward sampling algorithm, that achieves a good balance between computation and mixing properties, and thus can be used to analyze models with large numbers of hidden chains. Even though our approach is developed under the assumption of a Markovian model, we show how this assumption can be relaxed leading to minor modifications in the algorithm. Our approach is particularly well suited to epidemic models, where the hidden Markov chains represent the infection status of an individual through time. The performance of our method is assessed on simulated data on epidemic models for the spread of Escherichia coli O157:H7 in cattle. Supplementary materials for this article are available online.

Estimating densities with non-linear support by using Fisher-Gaussian kernels.

Current tools for multivariate density estimation struggle when the density is concentrated near a non-linear subspace or manifold. Most approaches require the choice of a kernel, with the multivariate Gaussian kernel by far the most commonly used. Although heavy-tailed and skewed extensions have been proposed, such kernels cannot capture curvature in the support of the data. This leads to poor performance unless the sample size is very large relative to the dimension of the data. The paper proposes a novel generalization of the Gaussian distribution, which includes an additional curvature parameter. We refer to the proposed class as Fisher-Gaussian kernels, since they arise by sampling from a von Mises-Fisher density on the sphere and adding Gaussian noise. The Fisher-Gaussian density has an analytic form and is amenable to straightforward implementation within Bayesian mixture models by using Markov chain Monte Carlo sampling. We provide theory on large support and illustrate gains relative to competitors in simulated and real data applications.

Joint longitudinal and time-to-event cure models for the assessment of being cured.

Medical time-to-event studies frequently include two groups of patients: those who will not experience the event of interest and are said to be "cured" and those who will develop the event and are said to be "susceptible". However, the cure status is unobserved in (right-)censored patients. While most of the work on cure models focuses on the time-to-event for the uncured patients (latency) or on the baseline probability of being cured or not (incidence), we focus in this research on the conditional probability of being cured after a medical intervention given survival until a certain time. Assuming the availability of longitudinal measurements collected over time and being informative on the risk to develop the event, we consider joint models for longitudinal and survival data given a cure fraction. These models include a linear mixed model to fit the trajectory of longitudinal measurements and a mixture cure model. In simulation studies, different shared latent structures linking both submodels are compared in order to assess their predictive performance. Finally, an illustration on HIV patient data completes the comparison.

Modeling outbreak data: Analysis of a 2012 Ebola virus disease epidemic in DRC.

We describe two approaches to modeling data from a small to moderate-sized epidemic outbreak. The first approach is based on a branching process approximation and direct analysis of the transmission network, whereas the second one is based on a survival model derived from the classical SIR equations with no explicit transmission information. We compare these approaches using data from a 2012 outbreak of Ebola virus disease caused by Bundibugyo ebolavirus in city of Isiro, Democratic Republic of the Congo. The branching process model allows for a direct comparison of disease transmission across different environments, such as the general community or the Ebola treatment unit. However, the survival model appears to yield parameter estimates with more accuracy and better precision in some circumstances.

Spatiotemporal trends in teen birth rates in the USA, 2003-2012.

The objective of this analysis was to explore temporal and spatial variation in teen birth rates TBRs across counties in the USA, from 2003 to 2012, by using hierarchical Bayesian models. Prior examination of spatiotemporal variation in TBRs has been limited by the reliance on large-scale geographies such as states, because of the potential instability in TBRs at smaller geographical scales such as counties. We implemented hierarchical Bayesian models with space-time interaction terms and spatially structured and unstructured random effects to produce smoothed county level TBR estimates, allowing for examination of spatiotemporal patterns and trends in TBRs at a smaller geographic scale across the USA. The results may help to highlight US counties where TBRs are higher or lower and to inform efforts to reduce birth rates to adolescents in the USA further.

Bayesian analysis of transformation latent variable models with multivariate censored data.

Transformation latent variable models are proposed in this study to analyze multivariate censored data. The proposed models generalize conventional linear transformation models to semiparametric transformation models that accommodate latent variables. The characteristics of the latent variables were assessed based on several correlated observed indicators through measurement equations. A Bayesian approach was developed with Bayesian P-splines technique and the Markov chain Monte Carlo algorithm to estimate the unknown parameters and transformation functions. Simulation shows that the performance of the proposed methodology is satisfactory. The proposed method was applied to analyze a cardiovascular disease data set.

A Bayesian approach to estimate changes in condom use from limited human immunodeficiency virus prevalence data.

Evaluation of large-scale intervention programmes against human immunodeficiency virus (HIV) is becoming increasingly important, but impact estimates frequently hinge on knowledge of changes in behaviour such as the frequency of condom use over time, or other self-reported behaviour changes, for which we generally have limited or potentially biased data. We employ a Bayesian inference methodology that incorporates an HIV transmission dynamics model to estimate condom use time trends from HIV prevalence data. Estimation is implemented via particle Markov chain Monte Carlo methods, applied for the first time in this context. The preliminary choice of the formulation for the time varying parameter reflecting the proportion of condom use is critical in the context studied, because of the very limited amount of condom use and HIV data available. We consider various novel formulations to explore the trajectory of condom use over time, based on diffusion-driven trajectories and smooth sigmoid curves. Numerical simulations indicate that informative results can be obtained regarding the amplitude of the increase in condom use during an intervention, with good levels of sensitivity and specificity performance in effectively detecting changes. The application of this method to a real life problem demonstrates how it can help in evaluating HIV interventions based on a small number of prevalence estimates, and it opens the way to similar applications in different contexts.

Bayesian Approach to Assessing Uncertainty and Calculating a Reference Value in Key Comparison Experiments.

International experiments called Key Comparisons pose an interesting statistical problem, the estimation of a quantity called a Reference Value. There are many possible forms that this estimator can take. Recently, this topic has received much international attention. In this paper, it is argued that a fully Bayesian approach to this problem is compatible with the current practice of metrology, and can easily be used to create statistical models which satisfy the varied properties and assumptions of these experiments.

Monte Carlo methods for light propagation in biological tissues.

Light propagation in turbid media is driven by the equation of radiative transfer. We give a formal probabilistic representation of its solution in the framework of biological tissues and we implement algorithms based on Monte Carlo methods in order to estimate the quantity of light that is received by a homogeneous tissue when emitted by an optic fiber. A variance reduction method is studied and implemented, as well as a Markov chain Monte Carlo method based on the Metropolis-Hastings algorithm. The resulting estimating methods are then compared to the so-called Wang-Prahl (or Wang) method. Finally, the formal representation allows to derive a non-linear optimization algorithm close to Levenberg-Marquardt that is used for the estimation of the scattering and absorption coefficients of the tissue from measurements.