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.

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 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.

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 review and comparison of arm-based versus contrast-based network meta-analysis for binary outcomes-Understanding their differences and limitations.

Network meta-analysis (NMA) is a statistical procedure to simultaneously compare multiple interventions. Despite the added complexity of performing an NMA compared with the traditional pairwise meta-analysis, under proper assumptions the NMA can lead to more efficient estimates on the comparisons of interventions by combining and contrasting the direct and indirect evidence into a form of evidence that can be used to underpin treatment guidelines. Two broad classes of NMA methods are commonly used in practice: the contrast-based (CB-NMA) and the arm-based (AB-NMA) models. While CB-NMA only focuses on the relative effects by assuming fixed intercepts, the AB-NMA offers greater flexibility on the estimands, including both the absolute and relative effects by assuming random intercepts. A major criticism of the AB-NMA, on which we aim to elaborate in this paper, is that it does not retain randomization within trials, which may introduce bias in the estimated relative effects in some scenarios. This criticism was drawn under the implicit assumption that a given relative effect is transportable, in which case the data generating mechanism favors the inference based on CB-NMA, which models the relative effect. In this article, we aim to review, summarize, and elaborate on the underlying assumptions, similarities and differences, and also the advantages and disadvantages, between CB-NMA and AB-NMA methods. As indirect treatment comparison is susceptible to risk of bias no matter which approach is taken, it is important to consider both approaches in practice as complementary sensitivity analyses and to provide the totality of evidence from the data.

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.

Impact of Indoor Radon Exposure on Lung Cancer Incidence in Slovenia.

Indoor radon is an important risk factor for lung cancer, as 3-14% of lung cancer cases can be attributed to radon. The aim of our study was to estimate the impact of indoor radon exposure on lung cancer incidence over the last 40 years in Slovenia. We analyzed the distribution of lung cancer incidence across 212 municipalities and 6032 settlements in Slovenia. The standardized incidence ratios were smoothed with the Besag-York-Mollie model and fitted with the integrated nested Laplace approximation. A categorical explanatory variable, the risk of indoor radon exposure with low, moderate and high risk values, was added to the models. We also calculated the population attributable fraction. Between 2.8% and 6.5% of the lung cancer cases in Slovenia were attributable to indoor radon exposure, with values varying by time period. The relative risk of developing lung cancer was significantly higher among the residents of areas with a moderate and high risk of radon exposure. Indoor radon exposure is an important risk factor for lung cancer in Slovenia in areas with high natural radon radiation (especially in the southern and south-eastern parts of the country).

HBCR_DMR: A Hybrid Method Based on Beta-Binomial Bayesian Hierarchical Model and Combination of Ranking Method to Detect Differential Methylation Regions in Bisulfite Sequencing Data.

DNA methylation is a key epigenetic modification involved in gene regulation, contributing to both physiological and pathological conditions. For a more profound comprehension, it is essential to conduct a precise comparison of DNA methylation patterns between sample groups that represent distinct statuses. Analysis of differentially methylated regions (DMRs) using computational approaches can help uncover the precise relationships between these phenomena. This paper describes a hybrid model that combines the beta-binomial Bayesian hierarchical model with a combination of ranking methods known as HBCR_DMR. During the initial phase, we model the actual methylation proportions of the CpG sites (CpGs) within the replicates. This modeling is achieved through beta-binomial distribution, with parameters set by a group mean and a dispersion parameter. During the second stage, we establish the selection of distinguishing CpG sites based on their methylation status, employing multiple ranking techniques. Finally, we combine the ranking lists of differentially methylated CpG sites through a voting system. Our analyses, encompassing simulations and real data, reveal outstanding performance metrics, including a sensitivity of 0.72, specificity of 0.89, and an F1 score of 0.76, yielding an overall accuracy of 0.82 and an AUC of 0.94. These findings underscore HBCR_DMR's robust capacity to distinguish methylated regions, confirming its utility as a valuable tool for DNA methylation analysis.

An easily implemented single-visit survey method for intermittently available and imperfectly detectable wildlife applied to the Florida east coast diamondback terrapin (Malaclemys terrapin tequesta).

Single-visit surveys of plots are often used for estimating the abundance of species of conservation concern. Less-than-perfect availability and detection of individuals can bias estimates if not properly accounted for. We developed field methods and a Bayesian model that accounts for availability and detection bias during single-visit visual plot surveys. We used simulated data to test the accuracy of the method under a realistic range of generating parameters and applied the method to Florida's east coast diamondback terrapin in the Indian River Lagoon system, where they were formerly common but have declined in recent decades. Simulations demonstrated that the method produces unbiased abundance estimates under a wide range of conditions that can be expected to occur in such surveys. Using terrapins as an example we show how to include covariates and random effects to improve estimates and learn about species-habitat relationships. Our method requires only counting individuals during short replicate surveys rather than keeping track of individual identity and is simple to implement in a variety of point count settings when individuals may be temporarily unavailable for observation. We provide examples in R and JAGS for implementing the model and to simulate and evaluate data to validate the application of the method under other study conditions.

Revisiting the complex time-varying effect of non-pharmaceutical interventions on COVID-19 transmission in the United States.

Introduction: Although the global COVID-19 emergency ended, the real-world effects of multiple non-pharmaceutical interventions (NPIs) and the relative contribution of individual NPIs over time were poorly understood, limiting the mitigation of future potential epidemics. Methods: Based on four large-scale datasets including epidemic parameters, virus variants, vaccines, and meteorological factors across 51 states in the United States from August 2020 to July 2022, we established a Bayesian hierarchical model with a spike-and-slab prior to assessing the time-varying effect of NPIs and vaccination on mitigating COVID-19 transmission and identifying important NPIs in the context of different variants pandemic. Results: We found that (i) the empirical reduction in reproduction number attributable to integrated NPIs was 52.0% (95%CI: 44.4, 58.5%) by August and September 2020, whereas the reduction continuously decreased due to the relaxation of NPIs in following months; (ii) international travel restrictions, stay-at-home requirements, and restrictions on gathering size were important NPIs with the relative contribution higher than 12.5%; (iii) vaccination alone could not mitigate transmission when the fully vaccination coverage was less than 60%, but it could effectively synergize with NPIs; (iv) even with fully vaccination coverage >60%, combined use of NPIs and vaccination failed to reduce the reproduction number below 1 in many states by February 2022 because of elimination of above NPIs, following with a resurgence of COVID-19 after March 2022. Conclusion: Our results suggest that NPIs and vaccination had a high synergy effect and eliminating NPIs should consider their relative effectiveness, vaccination coverage, and emerging variants.

Miss it like Messi: Extracting value from off-target shots in soccer.

Measuring soccer shooting skill is a challenging analytics problem due to the scarcity and highly contextual nature of scoring events. The introduction of more advanced data surrounding soccer shots has given rise to model-based metrics which better cope with these challenges. Specifically, metrics such as expected goals added, goals above expectation, and post-shot expected goals all use advanced data to offer an improvement over the classical conversion rate. However, all metrics developed to date assign a value of zero to off-target shots, which account for almost two-thirds of all shots, since these shots have no probability of scoring. We posit that there is non-negligible shooting skill signal contained in the trajectories of off-target shots and propose two shooting skill metrics that incorporate the signal contained in off-target shots. Specifically, we develop a player-specific generative model for shot trajectories based on a mixture of truncated bivariate Gaussian distributions. We use this generative model to compute metrics that allow us to attach non-zero value to off-target shots. We demonstrate that our proposed metrics are more stable than current state-of-the-art metrics and have increased predictive power.

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.

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.

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.

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.

Reconstructing Spatial Transcriptomics at the Single-cell Resolution with BayesDeep.

Spatially resolved transcriptomics (SRT) techniques have revolutionized the characterization of molecular profiles while preserving spatial and morphological context. However, most next-generation sequencing-based SRT techniques are limited to measuring gene expression in a confined array of spots, capturing only a fraction of the spatial domain. Typically, these spots encompass gene expression from a few to hundreds of cells, underscoring a critical need for more detailed, single-cell resolution SRT data to enhance our understanding of biological functions within the tissue context. Addressing this challenge, we introduce BayesDeep, a novel Bayesian hierarchical model that leverages cellular morphological data from histology images, commonly paired with SRT data, to reconstruct SRT data at the single-cell resolution. BayesDeep effectively model count data from SRT studies via a negative binomial regression model. This model incorporates explanatory variables such as cell types and nuclei-shape information for each cell extracted from the paired histology image. A feature selection scheme is integrated to examine the association between the morphological and molecular profiles, thereby improving the model robustness. We applied BayesDeep to two real SRT datasets, successfully demonstrating its capability to reconstruct SRT data at the single-cell resolution. This advancement not only yields new biological insights but also significantly enhances various downstream analyses, such as pseudotime and cell-cell communication.

A novel Bayesian model for assessing intratumor heterogeneity of tumor infiltrating leukocytes with multi-region gene expression sequencing.

Intratumor heterogeneity (ITH) of tumor-infiltrated leukocytes (TILs) is an important phenomenon of cancer biology with potentially profound clinical impacts. Multi-region gene expression sequencing data provide a promising opportunity that allows for explorations of TILs and their intratumor heterogeneity for each subject. Although several existing methods are available to infer the proportions of TILs, considerable methodological gaps exist for evaluating intratumor heterogeneity of TILs with multi-region gene expression data. Here, we develop ICeITH, immune cell estimation reveals intratumor heterogeneity, a Bayesian hierarchical model that borrows cell type profiles as prior knowledge to decompose mixed bulk data while accounting for the within-subject correlations among tumor samples. ICeITH quantifies intratumor heterogeneity by the variability of targeted cellular compositions. Through extensive simulation studies, we demonstrate that ICeITH is more accurate in measuring relative cellular abundance and evaluating intratumor heterogeneity compared with existing methods. We also assess the ability of ICeITH to stratify patients by their intratumor heterogeneity score and associate the estimations with the survival outcomes. Finally, we apply ICeITH to two multi-region gene expression datasets from lung cancer studies to classify patients into different risk groups according to the ITH estimations of targeted TILs that shape either pro- or anti-tumor processes. In conclusion, ICeITH is a useful tool to evaluate intratumor heterogeneity of TILs from multi-region gene expression data.

Individual participant data from digital sources informed and improved precision in the evaluation of predictive biomarkers in Bayesian network meta-analysis.

OBJECTIVES: We aimed to develop a network meta-analytic model for the evaluation of treatment effectiveness within predictive biomarker subgroups, by combining evidence from individual participant data (IPD) from digital sources (in the absence of randomized controlled trials) and aggregate data (AD). STUDY DESIGN AND SETTING: A Bayesian framework was developed for modeling time-to-event data to evaluate predictive biomarkers. IPD were sourced from electronic health records, using a target trial emulation approach, or digitized Kaplan-Meier curves. The model is illustrated using two examples: breast cancer with a hormone receptor biomarker, and metastatic colorectal cancer with the Kirsten Rat Sarcoma (KRAS) biomarker. RESULTS: The model allowed for the estimation of treatment effects in two subgroups of patients defined by their biomarker status. Effectiveness of taxanes did not differ in hormone receptor positive and negative breast cancer patients. Epidermal growth factor receptor inhibitors were more effective than chemotherapy in KRAS wild type colorectal cancer patients but not in patients with KRAS mutant status. Use of IPD reduced uncertainty of the subgroup-specific treatment effect estimates by up to 49%. CONCLUSION: Utilization of IPD allowed for more detailed evaluation of predictive biomarkers and cancer therapies and improved precision of the estimates compared to use of AD alone.

Development of a Predictive Statistical Pharmacological Model for Local Anesthetic Agent Effects with Bayesian Hierarchical Model Parameter Estimation.

As an alternative to animal use, computer simulations are useful for predicting pharmacokinetics and cardiovascular activities. For this purpose, we constructed a statistical model to simulate the effects of local anesthetic agents. To train the model, animal experiments were performed on 6-week-old male Hartley guinea pigs. Firstly, the guinea pigs' backs were shaved, then local anesthetic agents were subcutaneously injected, with subsequent stimulation of the anesthetized site with a needle six times at regular intervals. The number of reactions (score value) was counted. In this statistical model, the probability of reacting to needle stimulation was calculated using the elapsed time, type of local anesthetic agent, and presence or absence of adrenaline. Score values were assumed to follow a binomial distribution at the calculated probability. Parameters were estimated using the Bayesian hierarchical model and Hamiltonian Monte Carlo method. The predicted curves using the estimated parameters fitted well the observed animal values. When score values were predicted using randomly generated parameters, the median of duration was similar between animal experiments and simulations (Procaine: 55 min vs. 50 min, Lidocaine: both 60 min, and Mepivacaine: both 85 min). This approach effectively modeled the effects of local anesthetic agents. It is possible to create the simulator using the parameter values estimated in this study.

Age-Specific Demographic Response of a Long-Lived Scavenger Species to Reduction of Organic Matter in a Landfill.

Food availability shapes demographic parameters and population dynamics. Certain species have adapted to predictable anthropogenic food resources like landfills. However, abrupt shifts in food availability can negatively impact such populations. While changes in survival are expected, the age-related effects remain poorly understood, particularly in long-lived scavenger species. We investigated the age-specific demographic response of a Griffon vulture (Gyps fulvus) population to a reduction in organic matter in a landfill and analyzed apparent survival and the probability of transience after initial capture using a Bayesian Cormack-Jolly-Seber model on data from 2012-2022. The proportion of transients among newly captured immatures and adults increased after the reduction in food. Juvenile apparent survival declined, increased in immature residents, and decreased in adult residents. These results suggest that there was a greater likelihood of permanent emigration due to intensified intraspecific competition following the reduction in food. Interestingly, resident immatures showed the opposite trend, suggesting the persistence of high-quality individuals despite the food scarcity. Although the reasons behind the reduced apparent survival of resident adults in the final four years of the study remain unclear, non-natural mortality potentially plays a part. In Europe landfill closure regulations are being implemented and pose a threat to avian scavenger populations, which underlines the need for research on food scarcity scenarios and proper conservation measures.