Integrative Modeling of 3D Genome Organization by Bayesian Molecular Dynamics Simulations with Hi-C Metainference.

Polymer modeling has been playing an increasingly important role in complementing 3D genome experiments, both to aid their interpretation and to reveal the underlying molecular mechanisms. This chapter illustrates an application of Hi-C metainference, a Bayesian approach to explore the 3D organization of a target genomic region by integrating experimental contact frequencies into a prior model of chromatin. The method reconstructs the conformational ensemble of the target locus by combining molecular dynamics simulation and Monte Carlo sampling from the posterior probability distribution given the data. Using prior chromatin models at both 1 kb and nucleosome resolution, we apply this approach to a 30 kb locus of mouse embryonic stem cells consisting of two well-defined domains linking several gene promoters together. Retaining the advantages of both physics-based and data-driven strategies, Hi-C metainference can provide an experimentally consistent representation of the system while at the same time retaining molecular details necessary to derive physical insights.

Novel prediction model of early screening lung adenocarcinoma with pulmonary fibrosis based on haematological index.

BACKGROUND: Lung cancer (LC), a paramount global life-threatening condition causing significant mortality, is most commonly characterized by its subtype, lung adenocarcinoma (LUAD). Concomitant with LC, pulmonary fibrosis (PF) and interstitial lung disease (ILD) contribute to an intricate landscape of respiratory diseases. Idiopathic pulmonary fibrosis (IPF) in association with LC has been explored. However, other fibrotic interrelations remain underrepresented, especially for LUAD-PF and LUAD-ILD. METHODS: We analysed data with statistical analysis from 7,137 healthy individuals, 7,762 LUAD patients, 7,955 ILD patients, and 2,124 complex PF patients collected over ten years. Furthermore, to identify blood indicators related to lung disease and its complications and compare the relationships between different indicators and lung diseases, we successfully applied the naive Bayes model for a biomarker-based prediction of diagnosis and development into complex PF. RESULTS: Males predominantly marked their presence in all categories, save for complex PF where females took precedence. Biomarkers, specifically AGR, MLR, NLR, and PLR emerged as pivotal in discerning lung diseases. A machine-learning-driven predictive model underscored the efficacy of these markers in early detection and diagnosis, with NLR exhibiting unparalleled accuracy. CONCLUSIONS: Our study elucidates the gender disparities in lung diseases and illuminates the profound potential of serum biomarkers, including AGR, MLR, NLR, and PLR in early lung cancer detection. With NLR as a standout, therefore, this study advances the exploration of indicator changes and predictions in patients with pulmonary disease and fibrosis, thereby improving early diagnosis, treatment, survival rate, and patient prognosis.

GlyCompute: towards the automated analysis of protein N-linked glycosylation kinetics via an open-source computational framework.

Understanding the complex biosynthetic pathways of glycosylation is crucial for the expanding field of glycosciences. Computer-aided glycosylation analysis has greatly benefited in recent years from the development of tools found in web-based portals and open-source libraries. However, the in silico analysis of cellular glycosylation kinetics is underrepresented in current glycoscience-related tools and databases. This could be partly attributed to the limited accessibility of kinetic models developed using proprietary software and the difficulty in reliably parameterising such models. This work aims to address these challenges by proposing GlyCompute, an open-source framework demonstrating a novel, streamlined approach for the assembly, simulation, and parameterisation of kinetic models of protein N-linked glycosylation. Specifically, given one or more sets of experimentally observed N-glycan structures and their relative abundances, minimum representations of a glycosylation reaction network are generated. The topology of the resulting networks is then used to automatically assemble the material balances and kinetic mechanisms underpinning the mathematical model. To match the experimentally observed relative abundances, a sequential parameter estimation strategy using Bayesian inference is proposed, with stages determined automatically based on the underlying network topology. The proposed framework was tested on a case study involving the simultaneous fitting of the kinetic model to two protein N-linked glycoprofiles produced by the same CHO cell culture, showing good agreement with experimental observations. We envision that GlyCompute could help glycoscientists gain quantitative insights into the effect of enzyme kinetics and their perturbations on experimentally observed glycoprofiles in biomanufacturing and clinical settings.

Genetic evaluation of early reproductive traits of Harnali sheep.

The aim of this study is to examine early reproductive traits and assess genetic parameters associated with them in Harnali crossbred ewes through Bayesian inference. The dataset encompasses 555 reproduction records spanning 24 years from 1998 to 2021. The traits under investigation include age at first lambing (AFL), weight at first lambing (WFL), and first lambing interval (FLI). First, least-squares modeling was conducted, incorporating fixed effects such as the period of birth and the dam's weight at lambing for the targeted traits. Subsequently, Bayesian estimation involved a series of animal models that accounted for direct additive effects, with or without maternal effects, along with significant fixed effects. The overall least-squares mean for AFL, WFL and FLI was observed as 851.49 ± 12.20 days, 27.5 ± 0.16 kg, 455.04 ± 10.66 days, respectively. The period of birth significantly influenced AFL and WFL, while the dam's weight at lambing showed a significant association with WFL only. Bayesian estimates revealed low direct heritability for AFL, WFL, and FLI, ranging from 0.12, 0.16 and 0.04, suggesting limited potential for improvement through selection. However, maternal effects accounted for a proportion of phenotypic variance ranging from 0.04 to 0.14 across these traits. It was concluded that enhancing reproductive efficiency in Harnali ewes would require a greater focus on management aspects, particularly feeding and breeding practices, while also considering maternal influences within the existing breeding plan.

Optimizing Piperacillin Dosing in Pediatric Liver Transplant Recipients: A Case Series.

BACKGROUND: Pathophysiological changes post-liver transplantation impact the pharmacokinetics and pharmacodynamics of antibiotics. Piperacillin, often used in combination with tazobactam, is a key antibiotic after transplantation to its broad-spectrum activity, but there is a lack of specific pharmacokinetic data in this population. This study aims to describe the pharmacokinetic parameters and target attainment of piperacillin in pediatric liver transplant recipients. METHODS: Patients with preserved renal function (estimated glomerular filtration rate > 50 mL/min/1.73 m2) receiving intravenous piperacillin-tazobactam at 112.5 mg/kg every 8 h (100 mg piperacillin/12.5 mg tazobactam), with a rapid infusion (0.5-1 h), were included. Two blood samples per child were collected during the same interval within 48 h of starting therapy. A Bayesian approach was applied to estimate individual pharmacokinetic parameters and perform dosing recommendations against Enterococcus spp., Enterobacterales and Pseudomonas aeruginosa. RESULTS: Eight patients with median age of 8 months were included. Median piperacillin clearance and central volume of distribution for the cohort were 11.11 L/h/70 kg and 9.80 L/70 kg, respectively. Seven patients (87.5%) presented with concentrations below the target of 100% fT > MIC. Simulations suggested that these patients required more frequent dosing and extended duration of infusion to ensure target attainment. One patient (12.5%) had trough concentrations that exceed 16 mg/L and could receive a lower daily dose. CONCLUSIONS: This case series highlights the importance of personalized therapy in pediatric liver transplant recipients due to the unpredictable and highly variable piperacillin pharmacokinetics in this population.

Ensemble for evaluating diagnostic efficacy of non-invasive indices in predicting liver fibrosis in untreated hepatitis C virus population.

BACKGROUND: Hepatitis C virus (HCV) infection progresses through various phases, starting with inflammation and ending with hepatocellular carcinoma. There are several invasive and non-invasive methods to diagnose chronic HCV infection. The invasive methods have their benefits but are linked to morbidity and complications. Thus, it is important to analyze the potential of non-invasive methods as an alternative. Shear wave elastography (SWE) is a non-invasive imaging tool widely validated in clinical and research studies as a surrogate marker of liver fibrosis. Liver fibrosis determination by invasive liver biopsy and non-invasive SWE agree closely in clinical studies and therefore both are gold standards. AIM: To analyzed the diagnostic efficacy of non-invasive indices [serum fibronectin, aspartate aminotransferase to platelet ratio index (APRI), alanine aminotransferase ratio (AAR), and fibrosis-4 (FIB-4)] in relation to SWE. We have used an Artificial Intelligence method to predict the severity of liver fibrosis and uncover the complex relationship between non-invasive indices and fibrosis severity. METHODS: We have conducted a hospital-based study considering 100 untreated patients detected as HCV positive using a quantitative Real-Time Polymerase Chain Reaction assay. We performed statistical and probabilistic analyses to determine the relationship between non-invasive indices and the severity of fibrosis. We also used standard diagnostic methods to measure the diagnostic accuracy for all the subjects. RESULTS: The results of our study showed that fibronectin is a highly accurate diagnostic tool for predicting fibrosis stages (mild, moderate, and severe). This was based on its sensitivity (100%, 92.2%, 96.2%), specificity (96%, 100%, 98.6%), Youden's index (0.960, 0.922, 0.948), area under receiver operating characteristic curve (0.999, 0.993, 0.922), and Likelihood test (LR+ > 10 and LR- < 0.1). Additionally, our Bayesian Network analysis revealed that fibronectin (> 200), AAR (> 1), APRI (> 3), and FIB-4 (> 4) were all strongly associated with patients who had severe fibrosis, with a 100% probability. CONCLUSION: We have found a strong correlation between fibronectin and liver fibrosis progression in HCV patients. Additionally, we observed that the severity of liver fibrosis increases with an increase in the non-invasive indices that we investigated.

Adjustability of gait speed in clinics and free-living environments in people with Parkinson's disease.

Objective: Gait speed is regulated by varying gait parameters depending on the diverse contexts of the environment. People with Parkinson's disease (PwPD) have difficulty in adapting to gait control in their environment; however, the relationship between gait speed and spatiotemporal parameters in free-living environments has not been clarified. This study aimed to compare gait parameters according to gait speed in clinics and free-living environments. Methods: PwPD were assessed at the clinic and in a free-living environment using an accelerometer on the lower back. By fitting a bimodal Gaussian model to the gait speed distribution, gait speed was divided into lower and higher speeds. We compared the spatiotemporal gait parameters using a 22 (environment [clinic/free-living]  speed [lower/higher]) repeated-measures analysis of variance. Associations between Parkinson's disease symptoms and gait parameters were evaluated using Bayesian Pearson's correlation coefficients. Results: In the 41 PwPD included in this study, spatiotemporal gait parameters were significantly worse in free-living environments than in clinics and at lower speeds than at higher speeds. The fit of the walking speed distribution to the bimodal Gaussian model (adjustability of gait speed) in free-living environments was related to spatiotemporal gait parameters, severity of Parkinson's disease, number of falls, and quality of life. Conclusions: The findings suggest that gait control, which involves adjusting gait speed according to context, differs between clinics and free-living environments in PwPD. Gait assessment for PwPD in both clinical and free-living environments should interpret gait impairments in a complementary manner.

Application of compound poisson model to estimate underreported risk of non-communicable diseases in underdeveloped areas.

Background: Hypertension and diabetes are major components of non-communicable diseases (NCDs), with a substantial number of patients residing in underdeveloped areas. Limited medical resources in these areas often results in underreporting of disease prevalence, masking the true extent of diseases. Taking the underdeveloped Liangshan Yi Autonomous Prefecture in China as an example, this study aimed to correct the underreported prevalence of hypertension and type 2 diabetes so as to provide inspiration for the allocation of medical resources in such areas. Methods: Assuming the true number of patients in each area follows a Poisson distribution, we applied a Compound Poisson Model based on Clustering of Data Quality (CPM-CDQ) to estimate the potential true prevalence of hypertension and diabetes, as well as the registration rate of existing patients. Specifically, a hierarchical clustering approach was utilized to group the counties based on the data quality, and then the registration rate of the cluster with the best data quality was used as a priori information for the model. The model parameters were estimated by the maximum likelihood method. Sensitivity analyses were performed to test the robustness of the model. Results: The estimated prevalence of hypertension in the entire Liangshan Prefecture from 2018 to 2020 ranged from 24.59 % to 25.28 %, and for diabetes, it ranged from 4.95 % to 8.42 %. The registration rates for hypertension and diabetes were 14.10 % to 24.59 % and 15.98 % to 29.12 %, respectively. Additionally, the accuracy of clustering the counties with the best data quality had a significant impact on the performance of the model. Conclusion: Liangshan Prefecture is experiencing a significant high prevalence of hypertension and diabetes, accompanied by a concerningly low registration rate. The CPM-CDQ proved useful for assessing underreporting risks and facilitating targeted interventions for NCDs control and prevention, particularly in underdeveloped areas.

Maintenance of zilucoplan efficacy in patients with generalised myasthenia gravis up to 24 weeks: a model-informed analysis.

Background: Clinical efficacy of zilucoplan has been demonstrated in a 12-week, placebo-controlled, phase III study in patients with acetylcholine receptor autoantibody-positive generalised myasthenia gravis (gMG). However, placebo-controlled zilucoplan data past 12 weeks are not available. Objectives: Predict the treatment effect of zilucoplan versus control (placebo or standard of care) in patients with gMG up to 24 weeks. Design: A model-informed analysis (MIA) within a Bayesian framework. Methods: Part 1 of the MIA comprised a control meta-regression using aggregate data on control response over time from randomised studies and a national myasthenia gravis (MG) registry. In Part 2, a combined Bayesian analysis of individual patient-level data from the phase II (NCT03315130), RAISE (NCT04115293) and RAISE-XT (NCT04225871) studies of zilucoplan was conducted using posterior distributions from Part 1 as informative priors. Population mean treatment effect in the change from baseline (CFB) at week 24 in MG-Activities of Daily Living (MG-ADL) and quantitative MG (QMG) scores for zilucoplan versus control were assessed. Results: At week 24, the predicted mean CFB in MG-ADL score was -4.55 (95% credible interval: -6.04, -3.13) with zilucoplan versus -2.00 (-3.35, -0.64) with control (difference: -2.55 [-3.76, -1.40]). The probability of a favourable treatment effect as measured by MG-ADL score at week 24 with zilucoplan versus control was >99.9%. There was an 82.8% probability that the difference in the predicted mean CFB in MG-ADL score at week 24 was greater than the clinically meaningful threshold (⩾2.0-point improvement). Comparable results were observed with QMG. Conclusion: This MIA demonstrates the maintenance of efficacy with zilucoplan versus control up to 24 weeks. Through combining real-world evidence with data from randomised studies, this novel method to estimate long-term treatment efficacy facilitated reduced exposure to placebo in the phase III RAISE study. This methodology could be used to reduce the length of future placebo-controlled studies.

Indulgent Parenting and Adolescents' Maladjustments: The Roles of Cultural Context and Parental Gender.

Background/Objectives. Adolescence is a critical developmental stage marked by the exploration of independence and self-identity. In this study, we aimed to examine the association between indulgent parenting (characterized by high responsiveness and low demandingness) and adolescents' maladjustments across emotional, behavioral, and social domains. Methods. Using a cross-cultural sample of high school students from the U.S. (n = 268) and China (n = 189), we tested the hypotheses that indulgent parenting was associated with adolescents' maladjustments, and that such association varied by cultural context (U.S. vs. China) and parental gender. Results. The results from Bayesian structural equation modeling supported the hypotheses, showing significant associations between indulgent parenting and adolescents' maladjustments and differences in the associations across cultures and parental gender. Conclusions. The findings highlighted the need for culturally informed parenting programs to foster healthy adolescent development.

DRpred: A Novel Deep Learning-Based Predictor for Multi-Label mRNA Subcellular Localization Prediction by Incorporating Bayesian Inferred Prior Label Relationships.

The subcellular localization of messenger RNA (mRNA) not only helps us to understand the localization regulation of gene expression but also helps to understand the relationship between RNA localization pattern and human disease mechanism, which has profound biological and medical significance. Several predictors have been proposed for predicting the subcellular localization of mRNA. However, there is still considerable room for improvement in their predictive performance, especially regarding multi-label prediction. This study proposes a novel multi-label predictor, DRpred, for mRNA subcellular localization prediction. This predictor first utilizes Bayesian networks to capture the dependencies among labels. Subsequently, it combines these dependencies with features extracted from mRNA sequences using Word2vec, forming the input for the predictor. Finally, it employs a neural network combining BiLSTM and an attention mechanism to capture the internal relationships of the input features for mRNA subcellular localization. The experimental validation on an independent test set demonstrated that DRpred obtained a competitive predictive performance in multi-label prediction and outperformed state-of-the-art predictors in predicting single subcellular localizations, obtaining accuracies of 82.14%, 93.02%, 80.37%, 94.00%, 90.58%, 84.53%, 82.01%, 79.71%, and 85.67% for the chromatin, cytoplasm, cytosol, exosome, membrane, nucleolus, nucleoplasm, nucleus, and ribosome, respectively. It is anticipated to offer profound insights for biological and medical research.

MCMC Methods for Parameter Estimation in ODE Systems for CAR-T Cell Cancer Therapy.

Chimeric antigen receptor (CAR)-T cell therapy represents a breakthrough in treating resistant hematologic cancers. It is based on genetically modifying T cells transferred from the patient or a donor. Although its implementation has increased over the last few years, CAR-T has many challenges to be addressed, for instance, the associated severe toxicities, such as cytokine release syndrome. To model CAR-T cell dynamics, focusing on their proliferation and cytotoxic activity, we developed a mathematical framework using ordinary differential equations (ODEs) with Bayesian parameter estimation. Bayesian statistics were used to estimate model parameters through Monte Carlo integration, Bayesian inference, and Markov chain Monte Carlo (MCMC) methods. This paper explores MCMC methods, including the Metropolis-Hastings algorithm and DEMetropolis and DEMetropolisZ algorithms, which integrate differential evolution to enhance convergence rates. The theoretical findings and algorithms were validated using Python and Jupyter Notebooks. A real medical dataset of CAR-T cell therapy was analyzed, employing optimization algorithms to fit the mathematical model to the data, with the PyMC library facilitating Bayesian analysis. The results demonstrated that our model accurately captured the key dynamics of CAR-T cell therapy. This conclusion underscores the potential of parameter estimation to improve the understanding and effectiveness of CAR-T cell therapy in clinical settings.

The Application of Machine Learning Algorithms to Bond Strength between Steel Rebars and Concrete Using Bayesian Optimization.

The purpose of this study is to estimate the bond strength between steel rebars and concrete using machine learning (ML) algorithms with Bayesian optimization (BO). It is important to conduct beam tests to determine the bond strength since it is affected by stress fields. A machine learning approach for bond strength based on 401 beam tests with six impact factors is presented in this paper. The model is composed of three standard algorithms, including random forest (RF), support vector regression (SVR), and extreme gradient boosting (XGBoost), combined with the BO technique. Compared to empirical models, BO-XGB`oost was found to be the most accurate method, with values of R2, MAE, and RMSE of 0.87, 0.897 MPa, and 1.516 MPa for the test set. The development of a simplified model that contains three input variables (diameter of the rebar, yield strength of reinforcement, concrete compressive strength) has been proposed to make it more convenient to apply. According to this prediction, the Shapley additive explanation (SHAP) can help explain why the ML-based model predicts the particular outcome it does. By utilizing machine learning algorithms to predict complex interfacial mechanical behavior, it is possible to improve the accuracy of the model.

Is the Current Systematic Subdivision of the Subfamily Neanurinae (Collembola, Neanuridae) Still Valid? Testing the Monophyly and Phylogenetic Relationships of Currently Established Tribes of the Neanurinae.

The subfamily Neanurinae is the largest in the family, with almost 800 described species. These springtails differ significantly from all other Collembola in their morphology, behaviour, and natural habitats. A systematic division of the Neanurinae into tribes was proposed more than 30 years ago by Cassagnau (1989), but it has not yet been tested using cladistic methods. Recent studies, both phylogenetic analyses of individual tribes or genera and descriptions of new taxa, suggest that the currently recognised tribes may not be monophyletic. The phylogenetic relationships among major lineages of the Neanurinae were explored by analysing a dataset of 101 discrete morphological characters. Bayesian and maximum parsimony analyses yielded similar tree topologies. The relationships among the Neanurinae were not resolved in any of the analyses, except for the support for the monophyly of the tribe Lobellini. The results indicate that the taxonomic characters used in the classification of Neanurinae are shared among members of the different tribes, which may have resulted in a classification with little phylogenetic basis. The article discusses the phylogenetic significance of morphological characters, including those recognised as key to the evolution and history of Neanurinae.

Nitrate sources and transformation in surface water and groundwater in Huazhou District, Shaanxi, China: Integrated research using hydrochemistry, isotopes and MixSIAR model.

Global water resources affected by excessive nitrate (NO3-) have caused a series of human health and ecological problems. Therefore, identification of NO3- sources and transformations is of pivotal significance in the strategic governance of widespread NO3- contaminant. In this investigation, a combination of statistical analysis, chemical indicators, isotopes, and MixSIAR model approaches was adopted to reveal the hydrochemical factors affecting NO3- concentrations and quantify the contribution of each source to NO3- concentrations in surface water and groundwater. The findings revealed that high groundwater NO3- concentration is concentrated in the southwestern region, peaking at 271 mg/L. NO3- concentration in the Wei River and Yuxian River exhibited an increase from upstream to downstream, but in the Shidi River and Luowen River, its concentration was highest in the upstream. Groundwater NO3- has noticeable correlation with Na+, Ca2+, Mg2+, Cl-, HCO3-, TDS, EC, and ORP. In surface water, NO3- level is significantly correlated with NH4+ and ORP. Major sources of NO3- in surface and groundwater comprise manure & sewage and soil nitrogen. Source contribution for surface water was calculated by MixSIAR model to obtain soil nitrogen (57.7%), manure & sewage (23.8%), chemical fertilizer (12%), and atmospheric deposition (6.4%). In groundwater, soil nitrogen and manure & sewage accounted for 19% and 63.8% of nitrate sources, respectively. Both surface water and groundwater exhibited strong oxidation, with nitrification the primary process. It is expected that this study will provide insights into the dynamics of NO3- and contribute to the development of effective strategies for mitigating NO3- contaminant, leading to sustainable management of water resources.

A BAYESIAN HIERARCHICAL SMALL AREA POPULATION MODEL ACCOUNTING FOR DATA SOURCE SPECIFIC METHODOLOGIES FROM AMERICAN COMMUNITY SURVEY, POPULATION ESTIMATES PROGRAM, AND DECENNIAL CENSUS DATA.

Small area population counts are necessary for many epidemiological studies, yet their quality and accuracy are often not assessed. In the United States, small area population counts are published by the United States Census Bureau (USCB) in the form of the decennial census counts, intercensal population projections (PEP), and American Community Survey (ACS) estimates. Although there are significant relationships between these three data sources, there are important contrasts in data collection, data availability, and processing methodologies such that each set of reported population counts may be subject to different sources and magnitudes of error. Additionally, these data sources do not report identical small area population counts due to post-survey adjustments specific to each data source. Consequently, in public health studies, small area disease/mortality rates may differ depending on which data source is used for denominator data. To accurately estimate annual small area population counts and their associated uncertainties, we present a Bayesian population (BPop) model, which fuses information from all three USCB sources, accounting for data source specific methodologies and associated errors. We produce comprehensive small area race-stratified estimates of the true population, and associated uncertainties, given the observed trends in all three USCB population estimates. The main features of our framework are: (1) a single model integrating multiple data sources, (2) accounting for data source specific data generating mechanisms and specifically accounting for data source specific errors, and (3) prediction of population counts for years without USCB reported data. We focus our study on the Black and White only populations for 159 counties of Georgia and produce estimates for years 2006-2023. We compare BPop population estimates to decennial census counts, PEP annual counts, and ACS multi-year estimates. Additionally, we illustrate and explain the different types of data source specific errors. Lastly, we compare model performance using simulations and validation exercises. Our Bayesian population model can be extended to other applications at smaller spatial granularity and for demographic subpopulations defined further by race, age, and sex, and/or for other geographical regions.

Flexible Regularized Estimation in High-Dimensional Mixed Membership Models.

Mixed membership models are an extension of finite mixture models, where each observation can partially belong to more than one mixture component. A probabilistic framework for mixed membership models of high-dimensional continuous data is proposed with a focus on scalability and interpretability. The novel probabilistic representation of mixed membership is based on convex combinations of dependent multivariate Gaussian random vectors. In this setting, scalability is ensured through approximations of a tensor covariance structure through multivariate eigen-approximations with adaptive regularization imposed through shrinkage priors. Conditional weak posterior consistency is established on an unconstrained model, allowing for a simple posterior sampling scheme while keeping many of the desired theoretical properties of our model. The model is motivated by two biomedical case studies: a case study on functional brain imaging of children with autism spectrum disorder (ASD) and a case study on gene expression data from breast cancer tissue. These applications highlight how the typical assumption made in cluster analysis, that each observation comes from one homogeneous subgroup, may often be restrictive in several applications, leading to unnatural interpretations of data features.

Rejoinder to the discussion on "LEAP: the latent exchangeability prior for borrowing information from historical data".

The discussions of our paper provide insights into the practical considerations of the latent exchangeability prior while also highlighting further extensions. In this rejoinder, we briefly summarize the discussions and provide comments.

Discussion on "LEAP: the latent exchangeability prior for borrowing information from historical data" by Ethan M. Alt, Xiuya Chang, Xun Jiang, Qing Liu, May Mo, H. Amy Xia, and Joseph G. Ibrahim.

We commend Alt et al.'s innovative approach for analysis with a hybrid control arm while offering insights into two key considerations: the necessity for extrapolation and the potential benefits of curating historical control data before analysis.

Discussion on "LEAP: the latent exchangeability prior for borrowing information from historical data" by Ethan M. Alt, Xiuya Chang, Xun Jiang, Qing Liu, May Mo, H. Amy Xia, and Joseph G. Ibrahim.

In the following discussion, we describe the various assumptions of exchangeability that have been made in the context of Bayesian borrowing and related models. In this context, we are able to highlight the difficulty of dynamic Bayesian borrowing under the assumption of individuals in the historical data being exchangeable with the current data and thus the strengths and novel features of the latent exchangeability prior. As borrowing methods are popular within clinical trials to augment the control arm, some potential challenges are identified with the application of the approach in this setting.