Mapping the number of female sex workers in countries across sub-Saharan Africa.

Female sex workers (FSW) are affected by individual, network, and structural risks, making them vulnerable to poor health and well-being. HIV prevention strategies and local community-based programs can rely on estimates of the number of FSW to plan and implement differentiated HIV prevention and treatment services. However, there are limited systematic assessments of the number of FSW in countries across sub-Saharan Africa to facilitate the identification of prevention and treatment gaps. Here we provide estimated population sizes of FSW and the corresponding uncertainties for almost all sub-national areas in sub-Saharan Africa. We first performed a literature review of FSW size estimates and then developed a Bayesian hierarchical model to synthesize these size estimates, resolving competing size estimates in the same area and producing estimates in areas without any data. We estimated that there are 2.5 million (95% uncertainty interval 1.9 to 3.1) FSW aged 15 to 49 in sub-Saharan Africa. This represents a proportion as percent of all women of childbearing age of 1.1% (95% uncertainty interval 0.8 to 1.3%). The analyses further revealed substantial differences between the proportions of FSW among adult females at the sub-national level and studied the relationship between these heterogeneities and many predictors. Ultimately, achieving the vision of no new HIV infections by 2030 necessitates dramatic improvements in our delivery of evidence-based services for sex workers across sub-Saharan Africa.

Dynamic models augmented by hierarchical data: an application of estimating HIV epidemics at sub-national level.

Dynamic models have been successfully used in producing estimates of HIV epidemics at the national level due to their epidemiological nature and their ability to estimate prevalence, incidence, and mortality rates simultaneously. Recently, HIV interventions and policies have required more information at sub-national levels to support local planning, decision-making and resource allocation. Unfortunately, many areas lack sufficient data for deriving stable and reliable results, and this is a critical technical barrier to more stratified estimates. One solution is to borrow information from other areas within the same country. However, directly assuming hierarchical structures within the HIV dynamic models is complicated and computationally time-consuming. In this article, we propose a simple and innovative way to incorporate hierarchical information into the dynamical systems by using auxiliary data. The proposed method efficiently uses information from multiple areas within each country without increasing the computational burden. As a result, the new model improves predictive ability and uncertainty assessment.

DifferentialRegulation: a Bayesian hierarchical approach to identify differentially regulated genes.

Although transcriptomics data is typically used to analyze mature spliced mRNA, recent attention has focused on jointly investigating spliced and unspliced (or precursor-) mRNA, which can be used to study gene regulation and changes in gene expression production. Nonetheless, most methods for spliced/unspliced inference (such as RNA velocity tools) focus on individual samples, and rarely allow comparisons between groups of samples (e.g. healthy vs. diseased). Furthermore, this kind of inference is challenging, because spliced and unspliced mRNA abundance is characterized by a high degree of quantification uncertainty, due to the prevalence of multi-mapping reads, ie reads compatible with multiple transcripts (or genes), and/or with both their spliced and unspliced versions. Here, we present DifferentialRegulation, a Bayesian hierarchical method to discover changes between experimental conditions with respect to the relative abundance of unspliced mRNA (over the total mRNA). We model the quantification uncertainty via a latent variable approach, where reads are allocated to their gene/transcript of origin, and to the respective splice version. We designed several benchmarks where our approach shows good performance, in terms of sensitivity and error control, vs. state-of-the-art competitors. Importantly, our tool is flexible, and works with both bulk and single-cell RNA-sequencing data. DifferentialRegulation is distributed as a Bioconductor R package.

A modeling framework for detecting and leveraging node-level information in Bayesian network inference.

Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected alongside the data of primary interest constitutes an opportunity to mitigate these difficulties by guiding the detection of dependence structures. For instance, gene network inference may be informed by the use of publicly available summary statistics on the regulation of genes by genetic variants. Here we present a novel Gaussian graphical modeling framework to identify and leverage information on the centrality of nodes in conditional independence graphs. Specifically, we consider a fully joint hierarchical model to simultaneously infer (i) sparse precision matrices and (ii) the relevance of node-level information for uncovering the sought-after network structure. We encode such information as candidate auxiliary variables using a spike-and-slab submodel on the propensity of nodes to be hubs, which allows hypothesis-free selection and interpretation of a sparse subset of relevant variables. As efficient exploration of large posterior spaces is needed for real-world applications, we develop a variational expectation conditional maximization algorithm that scales inference to hundreds of samples, nodes and auxiliary variables. We illustrate and exploit the advantages of our approach in simulations and in a gene network study which identifies hub genes involved in biological pathways relevant to immune-mediated diseases.

Robust knowledge-guided biclustering for multi-omics data.

Biclustering is a useful method for simultaneously grouping samples and features and has been applied across various biomedical data types. However, most existing biclustering methods lack the ability to integratively analyze multi-modal data such as multi-omics data such as genome, transcriptome and epigenome. Moreover, the potential of leveraging biological knowledge represented by graphs, which has been demonstrated to be beneficial in various statistical tasks such as variable selection and prediction, remains largely untapped in the context of biclustering. To address both, we propose a novel Bayesian biclustering method called Bayesian graph-guided biclustering (BGB). Specifically, we introduce a new hierarchical sparsity-inducing prior to effectively incorporate biological graph information and establish a unified framework to model multi-view data. We develop an efficient Markov chain Monte Carlo algorithm to conduct posterior sampling and inference. Extensive simulations and real data analysis show that BGB outperforms other popular biclustering methods. Notably, BGB is robust in terms of utilizing biological knowledge and has the capability to reveal biologically meaningful information from heterogeneous multi-modal data.

Baldur: Bayesian Hierarchical Modeling for Label-Free Proteomics with Gamma Regressing Mean-Variance Trends.

Label-free proteomics is a fast-growing methodology to infer abundances in mass spectrometry proteomics. Extensive research has focused on spectral quantification and peptide identification. However, research toward modeling and understanding quantitative proteomics data is scarce. Here we propose a Bayesian hierarchical decision model (Baldur) to test for differences in means between conditions for proteins, peptides, and post-translational modifications. We developed a Bayesian regression model to characterize local mean-variance trends in data, to estimate measurement uncertainty and hyperparameters for the decision model. A key contribution is the development of a new gamma regression model that describes the mean-variance dependency as a mixture of a common and a latent trend-allowing for localized trend estimates. We then evaluate the performance of Baldur, limma-trend, and t test on six benchmark datasets: five total proteomics and one post-translational modification dataset. We find that Baldur drastically improves the decision in noisier post-translational modification data over limma-trend and t test. In addition, we see significant improvements using Baldur over the other methods in the total proteomics datasets. Finally, we analyzed Baldur's performance when increasing the number of replicates and found that the method always increases precision with sample size, while showing robust control of the false positive rate. We conclude that our model vastly improves over popular data analysis methods (limma-trend and t test) in several spike-in datasets by achieving a high true positive detection rate, while greatly reducing the false-positive rate.

Probabilistic forecasts of international bilateral migration flows.

We propose a method for forecasting global human migration flows. A Bayesian hierarchical model is used to make probabilistic projections of the 39,800 bilateral migration flows among the 200 most populous countries. We generate out-of-sample forecasts for all bilateral flows for the 2015 to 2020 period, using models fitted to bilateral migration flows for five 5-y periods from 1990 to 1995 through 2010 to 2015. We find that the model produces well-calibrated out-of-sample forecasts of bilateral flows, as well as total country-level inflows, outflows, and net flows. The mean absolute error decreased by 61% using our method, compared to a leading model of international migration. Out-of-sample analysis indicated that simple methods for forecasting migration flows offered accurate projections of bilateral migration flows in the near term. Our method matched or improved on the out-of-sample performance using these simple deterministic alternatives, while also accurately assessing uncertainty. We integrate the migration flow forecasting model into a fully probabilistic population projection model to generate bilateral migration flow forecasts by age and sex for all flows from 2020 to 2025 through 2040 to 2045.

Modeling Risk Factors for Intraindividual Variability: A Mixed-Effects Beta-Binomial Model Applied to Cognitive Function in Older People in the English Longitudinal Study of Ageing.

Cognitive functioning in older age profoundly impacts quality of life and health. While most research on cognition in older age has focused on mean levels, intraindividual variability (IIV) around this may have risk factors and outcomes independent of the mean value. Investigating risk factors associated with IIV has typically involved deriving a summary statistic for each person from residual error around a fitted mean. However, this ignores uncertainty in the estimates, prohibits exploring associations with time-varying factors, and is biased by floor/ceiling effects. To address this, we propose a mixed-effects location scale beta-binomial model for estimating average probability and IIV in a word recall test in the English Longitudinal Study of Ageing. After adjusting for mean performance, an analysis of 9,873 individuals across 7 (mean = 3.4) waves (2002-2015) found IIV to be greater at older ages, with lower education, in females, with more difficulties in activities of daily living, in later birth cohorts, and when interviewers recorded issues potentially affecting test performance. Our study introduces a novel method for identifying groups with greater IIV in bounded discrete outcomes. Our findings have implications for daily functioning and care, and further work is needed to identify the impact for future health outcomes.

High-dimensional genomic feature selection with the ordered stereotype logit model.

For many high-dimensional genomic and epigenomic datasets, the outcome of interest is ordinal. While these ordinal outcomes are often thought of as the observed cutpoints of some latent continuous variable, some ordinal outcomes are truly discrete and are comprised of the subjective combination of several factors. The nonlinear stereotype logistic model, which does not assume proportional odds, was developed for these 'assessed' ordinal variables. It has previously been extended to the frequentist high-dimensional feature selection setting, but the Bayesian framework provides some distinct advantages in terms of simultaneous uncertainty quantification and variable selection. Here, we review the stereotype model and Bayesian variable selection methods and demonstrate how to combine them to select genomic features associated with discrete ordinal outcomes. We compared the Bayesian and frequentist methods in terms of variable selection performance. We additionally applied the Bayesian stereotype method to an acute myeloid leukemia RNA-sequencing dataset to further demonstrate its variable selection abilities by identifying features associated with the European LeukemiaNet prognostic risk score.

Flagging unusual clusters based on linear mixed models using weighted and self-calibrated predictors.

Statistical models incorporating cluster-specific intercepts are commonly used in hierarchical settings, for example, observations clustered within patients or patients clustered within hospitals. Predicted values of these intercepts are often used to identify or "flag" extreme or outlying clusters, such as poorly performing hospitals or patients with rapid declines in their health. We consider a variety of flagging rules, assessing different predictors, and using different accuracy measures. Using theoretical calculations and comprehensive numerical evaluation, we show that previously proposed rules based on the 2 most commonly used predictors, the usual best linear unbiased predictor and fixed effects predictor, perform extremely poorly: the incorrect flagging rates are either unacceptably high (approaching 0.5 in the limit) or overly conservative (eg, much <0.05 for reasonable parameter values, leading to very low correct flagging rates). We develop novel methods for flagging extreme clusters that can control the incorrect flagging rates, including very simple-to-use versions that we call "self-calibrated." The new methods have substantially higher correct flagging rates than previously proposed methods for flagging extreme values, while controlling the incorrect flagging rates. We illustrate their application using data on length of stay in pediatric hospitals for children admitted for asthma diagnoses.

Bayesian meta-analysis of penetrance for cancer risk.

Multi-gene panel testing allows many cancer susceptibility genes to be tested quickly at a lower cost making such testing accessible to a broader population. Thus, more patients carrying pathogenic germline mutations in various cancer-susceptibility genes are being identified. This creates a great opportunity, as well as an urgent need, to counsel these patients about appropriate risk-reducing management strategies. Counseling hinges on accurate estimates of age-specific risks of developing various cancers associated with mutations in a specific gene, ie, penetrance estimation. We propose a meta-analysis approach based on a Bayesian hierarchical random-effects model to obtain penetrance estimates by integrating studies reporting different types of risk measures (eg, penetrance, relative risk, odds ratio) while accounting for the associated uncertainties. After estimating posterior distributions of the parameters via a Markov chain Monte Carlo algorithm, we estimate penetrance and credible intervals. We investigate the proposed method and compare with an existing approach via simulations based on studies reporting risks for two moderate-risk breast cancer susceptibility genes, ATM and PALB2. Our proposed method is far superior in terms of coverage probability of credible intervals and mean square error of estimates. Finally, we apply our method to estimate the penetrance of breast cancer among carriers of pathogenic mutations in the ATM gene.

Bayesian inference for prediction of survival probability in prime-boost vaccination regimes.

We focus on Bayesian inference for survival probabilities in a prime-boost vaccination regime in the development of an Ebola vaccine. We are interested in the heterologous prime-boost regimen (unmatched vaccine deliverys using the same antigen) due to its demonstrated durable immunity, well-tolerated safety profile, and suitability as a population vaccination strategy. Our research is motivated by the need to estimate the survival probability given the administered dosage. To do so, we establish two key relationships. Firstly, we model the connection between the designed dose concentration and the induced antibody count using a Bayesian response surface model. Secondly, we model the association between the antibody count and the probability of survival when experimental subjects are exposed to the Ebola virus in a controlled setting using a Bayesian probability of survival model. Finally, we employ a combination of the two models with dose concentration as the predictor of the survival probability for a future vaccinated population. We implement our two-level Bayesian model in Stan, and illustrate its use with simulated and real-world data. Performance of this model is evaluated via simulation. Our work offers a new application of drug synergy models to examine prime-boost vaccine efficacy, and does so using a hierarchical Bayesian framework that allows us to use dose concentration to predict survival probability.

Exploiting relationship directionality to enhance statistical modeling of peer-influence across social networks.

Risky-prescribing is the excessive or inappropriate prescription of drugs that singly or in combination pose significant risks of adverse health outcomes. In the United States, prescribing of opioids and other "risky" drugs is a national public health concern. We use a novel data framework-a directed network connecting physicians who encounter the same patients in a sequence of visits-to investigate if risky-prescribing diffuses across physicians through a process of peer-influence. Using a shared-patient network of 10 661 Ohio-based physicians constructed from Medicare claims data over 2014-2015, we extract information on the order in which patients encountered physicians to derive a directed patient-sharing network. This enables the novel decomposition of peer-effects of a medical practice such as risky-prescribing into directional (outbound and inbound) and bidirectional (mutual) relationship components. Using this framework, we develop models of peer-effects for contagion in risky-prescribing behavior as well as spillover effects. The latter is measured in terms of adverse health events suspected to be related to risky-prescribing in patients of peer-physicians. Estimated peer-effects were strongest when the patient-sharing relationship was mutual as opposed to directional. Using simulations we confirmed that our modeling and estimation strategies allows simultaneous estimation of each type of peer-effect (mutual and directional) with accuracy and precision. We also show that failing to account for these distinct mechanisms (a form of model mis-specification) produces misleading results, demonstrating the importance of retaining directional information in the construction of physician shared-patient networks. These findings suggest network-based interventions for reducing risky-prescribing.

A domain-general frontoparietal network interacts with domain-preferential intermediate pathways to support working memory task.

Working memory (WM) is essential for cognition, but the underlying neural mechanisms remain elusive. From a hierarchical processing perspective, this paper proposed and tested a hypothesis that a domain-general network at the top of the WM hierarchy can interact with distinct domain-preferential intermediate circuits to support WM. Employing a novel N-back task, we first identified the posterior superior temporal gyrus (pSTG), middle temporal area (MT), and postcentral gyrus (PoCG) as intermediate regions for biological motion and shape motion processing, respectively. Using further psychophysiological interaction analyses, we delineated a frontal-parietal network (FPN) as the domain-general network. These results were further verified and extended by a delayed match to sample (DMS) task. Although the WM load-dependent and stimulus-free activations during the DMS delay phase confirm the role of FPN as a domain-general network to maintain information, the stimulus-dependent activations within this network during the DMS encoding phase suggest its involvement in the final stage of the hierarchical processing chains. In contrast, the load-dependent activations of intermediate regions in the N-back task highlight their further roles beyond perception in WM tasks. These results provide empirical evidence for a hierarchical processing model of WM and may have significant implications for WM training.

Variable Selection in Bayesian Multiple Instance Regression using Shotgun Stochastic Search.

In multiple instance learning (MIL), a bag represents a sample that has a set of instances, each of which is described by a vector of explanatory variables, but the entire bag only has one label/response. Though many methods for MIL have been developed to date, few have paid attention to interpretability of models and results. The proposed Bayesian regression model stands on two levels of hierarchy, which transparently show how explanatory variables explain and instances contribute to bag responses. Moreover, two selection problems are simultaneously addressed; the instance selection to find out the instances in each bag responsible for the bag response, and the variable selection to search for the important covariates. To explore a joint discrete space of indicator variables created for selection of both explanatory variables and instances, the shotgun stochastic search algorithm is modified to fit in the MIL context. Also, the proposed model offers a natural and rigorous way to quantify uncertainty in coefficient estimation and outcome prediction, which many modern MIL applications call for. The simulation study shows the proposed regression model can select variables and instances with high performance (AUC greater than 0.86), thus predicting responses well. The proposed method is applied to the musk data for prediction of binding strengths (labels) between molecules (bags) with different conformations (instances) and target receptors. It outperforms all existing methods, and can identify variables relevant in modeling responses.

Bayesian Hierarchical Models for Subgroup Analysis.

In conventional subgroup analyses, subgroup treatment effects are estimated using data from each subgroup separately without considering data from other subgroups in the same study. The subgroup treatment effects estimated this way may be heterogenous with high variability due to small sample sizes in some subgroups and much different from the treatment effect in the overall population. A Bayesian hierarchical model (BHM) can be used to derive more precise, and less heterogenous estimates of subgroup treatment effects that are closer to the treatment effect in the overall population. BHM assumes exchangeability in treatment effect across subgroups after adjusting for effect modifiers and other relevant covariates. In this article, we will discuss the technical details for applying one-way and multi-way BHM using summary-level statistics, and patient-level data for subgroup analysis. Four case studies based on four new drug applications are used to illustrate the application of these models in subgroup analyses for continuous, dichotomous, time-to-event, and count endpoints.

A Hierarchical Low-Rank Denoising Model for Remote Sensing Images Based on Deep Unfolding.

Recently, the low-rank representation (LRR) model has been widely used in the field of remote sensing image denoising due to its excellent noise suppression capability. However, those low-rank-based methods always discard important edge details as residuals, leading to a common issue of blurred edges in denoised results. To address this problem, we take a new look at low-rank residuals and try to extract edge information from them. Therefore, a hierarchical denoising framework was combined with a low-rank model to extract edge information from low-rank residuals within the edge subspace. A prior knowledge matrix was designed to enable the model to learn necessary structural information rather than noise. Also, such traditional model-driven approaches require multiple iterations, and the solutions may be very complex and computationally intensive. To further enhance the noise suppression performance and computing efficiency, a hierarchical low-rank denoising model based on deep unrolling (HLR-DUR) was proposed, integrating deep neural networks into the hierarchical low-rank denoising framework to expand the information capture and representation capabilities of the proposed shallow model. Sufficient experiments on optical images, hyperspectral images (HSI), and synthetic aperture radar (SAR) images showed that HLR-DUR achieved state-of-the-art (SOTA) denoising results.

A generalized calibrated Bayesian hierarchical modeling approach to basket trials with multiple endpoints.

A basket trial simultaneously evaluates a treatment in multiple cancer subtypes, offering an effective way to accelerate drug development in multiple indications. Many basket trials are designed and monitored based on a single efficacy endpoint, primarily the tumor response. For molecular targeted or immunotherapy agents, however, a single efficacy endpoint cannot adequately characterize the treatment effect. It is increasingly important to use more complex endpoints to comprehensively assess the risk-benefit profile of such targeted therapies. We extend the calibrated Bayesian hierarchical modeling approach to monitor phase II basket trials with multiple endpoints. We propose two generalizations, one based on the latent variable approach and the other based on the multinomial-normal hierarchical model, to accommodate different types of endpoints and dependence assumptions regarding information sharing. We introduce shrinkage parameters as functions of statistics measuring homogeneity among subgroups and propose a general calibration approach to determine the functional forms. Theoretical properties of the generalized hierarchical models are investigated. Simulation studies demonstrate that the monitoring procedure based on the generalized approach yields desirable operating characteristics.

Spatiotemporal joint analysis of PM2.5 and Ozone in California with INLA approach.

The substantial threat of concurrent air pollutants to public health is increasingly severe under climate change. To identify the common drivers and extent of spatiotemporal similarity of PM2.5 and ozone (O3), this paper proposed a log Gaussian-Gumbel Bayesian hierarchical model allowing for sharing a stochastic partial differential equation and autoregressive model of order one (SPDE-AR(1)) spatiotemporal interaction structure. The proposed model, implemented by the approach of integrated nested Laplace approximation (INLA), outperforms in terms of estimation accuracy and prediction capacity for its increased parsimony and reduced uncertainty, especially for the shared O3 sub-model. Besides the consistently significant influence of temperature (positive), extreme drought (positive), fire burnt area (positive), gross domestic product (GDP) per capita (positive), and wind speed (negative) on both PM2.5 and O3, surface pressure and precipitation demonstrate positive associations with PM2.5 and O3, respectively. While population density relates to neither. In addition, our results demonstrate similar spatiotemporal interactions between PM2.5 and O3, indicating that the spatial and temporal variations of these pollutants show relatively considerable consistency in California. Finally, with the aid of the excursion function, we see that the areas around the intersection of San Luis Obispo and Santa Barbara counties are likely to exceed the unhealthy O3 level for USG simultaneously with other areas throughout the year. Our findings provide new insights for regional and seasonal strategies in the co-control of PM2.5 and O3. Our methodology is expected to be utilized when interest lies in multiple interrelated processes in the fields of environment and epidemiology.

A review towards developing a hierarchical model for sustainable hospital solid waste management in rural areas of Zimbabwe.

Management of solid waste from rural hospitals is amongst problems affecting Zimbabwe due to diseases, population, and hospital increase. Solid waste from rural hospitals is receiving little attention translating to environmental health problems. Therefore, 101 secondary sources were used to write a paper aiming to proffer a hierarchical model to achieve sustainable solid waste management at rural hospitals. Rural hospitals' solid waste encompasses electronic waste, sharps, pharmaceutical, pathological, radioactive, chemical, infectious, and general waste. General solid waste from rural hospitals is between 77.35 and 79% whilst hazardous waste is between 21 and 22.65%. Solid waste increase add burden to nearly incapacitated rural hospitals. Rural hospital solid waste management processes include storage, transportation, treatment methods like autoclaving and chlorination, waste reduction alternatives, and disposal. Disposal strategies involve open pits, open burning, dumping, and incineration. Rural hospital solid waste management is guided by legislation, policies, guidelines, and conventions. Effectiveness of legal framework is limited by economic and socio-political problems. Rural hospital solid waste management remain inappropriate causing environmental health risks. Developed hierarchical model can narrow the route to attain sustainable management of rural hospitals' solid waste. Proposed hierarchical model consists of five-layered strategies and acted as a guide for identifying and ranking approaches to manage rural hospitals' solid waste. Additionally, Zimbabwean government, Environmental Management Agency and Ministry of Health is recommended to collaborate to provide sufficient resources to rural hospitals whilst enforcing legal framework. Integration of all hierarchical model's elements is essential whereas all-stakeholder involvement and solid waste minimisation approaches are significant at rural hospitals.