Hierarchical Bayesian model for joint prediction of runway pavement metrics considering measurement uncertainty

A Bayesian hierarchical model for the inference between metal grade with reduced variance: Case studies in porphyry Cu deposits

BACKGROUND AND AIM: Mixtures analysis methods are increasingly being applied in environmental epidemiology, but current methods are often limited by either only providing a group effect or independent exposure effects without a group effect. We investigate Bayesian Hierarchical Regression Modelling (BHRM) and show how it can be adapted to handle highly correlated exposures to estimate: 1) independent exposure effects; 2) interactions between exposures; and 3) combined effects for a mixture exposure. METHODS: BHRM is a flexible framework that can provide robust estimation for highly correlated exposures (via g-prior specification), yield conditional exposure-specific estimates, and include interactions effects. We demonstrate how these general regression models can provide additional inference on the combined effect for a multi-pollutant exposure. To demonstrate potential advantages of certain specifications, we applied BHRM to an analysis of liver injury and exposure to perfluoroalkyl substances (PFAS), including PFOS, PFOA, PFHxS, PFNA, and PFUnDA, in 1105 children from the Human Early Life Exposome (HELIX) project. Liver injury was defined as 90th percentile for any serum liver injury biomarker (ALT, AST, GGT). We used BHRM to estimate the mixture effect and pollutant-specific effects. For comparison, we also applied Bayesian Weighted Quantile Sum regression (BWQS)—an alternative specification within Bayesian Hierarchical Modeling. RESULTS:PFAS mixture was associated with childhood liver injury: OR=1.64 (95%CI:1.34-2.00) per increased exposure equivalent to one standard deviation for all PFAS. Within this mixture effect, PFNA was the predominant exposure driving the association with OR=1.62 (95%CI:1.11-1.97) and a posterior inclusion probability of 0.969 (Bayes factor, BF=125). No strong evidence of interactions. Although BWQS estimated a mixture effect of OR=1.85 (95%CI:1.50-2.25) and indicated PFNA had the most substantial estimated weight of 0.513 (BF=4.21), the approach lacks pollutant-specific effects. CONCLUSIONS:BHRM is an efficient method for mixtures analysis. Estimation of pollutant-specific effects with group effects provide critical data for identifying causal agents in mixtures of environmental contaminants. KEYWORDS: mixtures, methods, Bayesian Hierarchical Regression Modelling, multi-pollutant

There have been few investigations of cancer prognosis models based on Bayesian hierarchical models. In this study, we used a novel Bayesian method to screen mRNAs and estimate the effects of mRNAs on the prognosis of patients with lung adenocarcinoma. Based on the identified mRNAs, we can build a prognostic model combining mRNAs and clinical features, allowing us to explore new molecules with the potential to predict the prognosis of lung adenocarcinoma. The mRNA data (n = 594) and clinical data (n = 470) for lung adenocarcinoma were obtained from the TCGA database. Gene set enrichment analysis (GSEA), univariate Cox proportional hazards regression, and the Bayesian hierarchical Cox proportional hazards model were used to explore the mRNAs related to the prognosis of lung adenocarcinoma. Multivariate Cox proportional hazard regression was used to identify independent markers. The prediction performance of the prognostic model was evaluated not only by the internal cross-validation but also by the external validation based on the GEO dataset (n = 437). With the Bayesian hierarchical Cox proportional hazards model, a 14-gene signature that included CPS1, CTPS2, DARS2, IGFBP3, MCM5, MCM7, NME4, NT5E, PLK1, POLR3G, PTTG1, SERPINB5, TXNRD1, and TYMS was established to predict overall survival in lung adenocarcinoma. Multivariate analysis demonstrated that the 14-gene signature (HR 3.960, 95% CI 2.710–5.786), T classification (T1, reference; T3, HR 1.925, 95% CI 1.104–3.355) and N classification (N0, reference; N1, HR 2.212, 95% CI 1.520–3.220; N2, HR 2.260, 95% CI 1.499–3.409) were independent predictors. The C-index of the model was 0.733 and 0.735, respectively, after performing cross-validation and external validation, a nomogram was provided for better prediction in clinical application. Bayesian hierarchical Cox proportional hazards models can be used to integrate high-dimensional omics information into a prediction model for lung adenocarcinoma to improve the prognostic prediction and discover potential targets. This approach may be a powerful predictive tool for clinicians treating malignant tumours.

For effectively predicting the tank failure time and analyzing the key elements influencing the reliability of corroded bottom plates, this article presents a model for calculating the reliability of corroded tank bottom plates based on a hierarchical Bayesian corrosion growth model. Firstly, the growth of corrosion defect depth is expressed by the gamma process, and the hierarchical Bayesian model is used to calculate the corrosion depth growth. After that, the reliability calculation model of the corroded tank base plate is established by combining the results of the hierarchical Bayesian model with the stress-strength interference theory, and the three uncertain factors of the base plate thickness, radius, and yield strength are considered in the model. Finally, the reliability assessment and sensitivity analysis of corroded bottom plate are carried out. The results show that the proposed reliability calculation model can provide more accurate failure state prediction results than the reliability calculation model which only considers the influence of corrosion depth, and can provide reference for reducing the failure rate of tank floor and reasonably formulating the maintenance plan of tank floor.

Chapter 4 - Bayesian hierarchical modeling for the linkages between air pollution and population health

Ecosystems are undergoing continuous degradation due to the dual perturbation of global climate change and human activities, posing unprecedented threats and challenges to the ecosystem services they provide. To gain a deeper understanding of the spatio-temporal evolution of ecosystem service value (ESV), it is essential to accurately capture the characteristics of its spatial and temporal changes and its influencing factors. However, traditional spatio-temporal statistical methods are limited to analyzing the heterogeneity of ESV in a single temporal or spatial dimension, which fails to meet the comprehensive analysis needs for spatio-temporal heterogeneity over an extended continuum. Therefore, this paper constructs a Bayesian spatio-temporal hierarchical model to analyze the ESV heterogeneity in both temporal and spatial dimensions in Northeast China from 2000 to 2020 to accurately identify the regions with unstable fluctuations in ESV and analyze the influencing factors behind them. It aims to comprehensively and systematically reveal the intrinsic laws of spatio-temporal evolution of ESV, and provide a scientific basis for relevant decision-making. The study found a continuous fluctuating downward trend of ESV in Northeast China from 2000 to 2020, with significant spatial and temporal heterogeneity. Notably, the distribution of hot and cold spots is regularly concentrated, especially in the transition zone from low hills to plains, which forms an “unstable zone” of spatial and temporal fluctuations of ESV. Natural factors such as NDVI and NPP exhibit a significant positive correlation with ESV, while social factors like population density and GDP show a strong negative correlation. Compared to traditional statistical methods, the Bayesian spatio-temporal hierarchical model, with its outstanding flexibility and accuracy, provides a new perspective and way of thinking for analyzing classical spatio-temporal problems. Firstly, the model examines time and space as a whole and fully accounts for the influence of spatio-temporal interactions on ESV. Secondly, the Bayesian spatio-temporal hierarchical model meets the needs of long-term continuous ESV outcome detection, which provides us with solid support for a deeper understanding of the evolution of ESV.

Introduction: Despite the traffic barriers effectiveness in reduction of the severity of run-off road crashes, the severity of barrier crashes still accounts for a significant fraction of road fatalities. Although extensive research has already been conducted in studying traffic barrier crashes, those studies mostly either consider the severity or frequency of crashes. Here, the equivalent property damage only (EPDO) was used to account for both aspects of crashes. While modeling EPDO crashes, there are challenges associated with that type of dataset including its sparse distribution, and the presence of heterogeneity in the dataset due to aggregation of various crash types. Methods: Ignoring the sparse nature of the data might result in biased or even erroneous results. Thus, in this study we identify factors to barriers EPDO crashes while considering the discussed challenges. Those consideration are especially important as in the next step we will employ the modeling results for conducting the cost-benefit analysis. Two main methods were considered in this study to address the discussed challenges including parametric and non-parametric Bayesian hierarchical models. A semiparametric Bayesian approach was used to relax the normality assumption by using a mixture of multivariate Dirichlet prior, defining a flexible nonparametric model for the random effects’ distribution, and using grouping to account for the heterogeneity due to the structure of the dataset. On the other hand, Bayesian hierarchical models with two distributions of Poisson and negative binomial with similar levels of hierarchy were considered. These models were chosen as closest models to the Bayesian semiparametric model. The incorporated models were compared in terms of deviance information criterion (DIC). Results and Discussion: The results highlighted that although the semi-parametric method outperforms the Bayesian hierarchical model with Poisson distribution, the Bayesian hierarchical model with negative binomial (NB) distribution outperform the semi-parametric model. The findings might be related to the severe sparse nature of the EPDO, which cannot optimally be accounted by semiparametric approach, and the model needs more flexibility. Conclusion: It was found that being unrestrained, driving in interstate system, driving in clear weather, light conditions, and driving in a higher traffic all increase the likelihood of EPDO crashes. Also, while some predictors were significant in less accommodative models of semi-parametric or Poisson models, they were not for Negative binomial model.

The Canadian Wildlife Service (CWS) requires reliable estimates of the harvest of migratory game birds, including waterfowl, to effectively manage populations of these hunted species. The National Harvest Survey is an annual survey of hunters who purchase Canada's mandatory migratory game bird hunting permit, integrating information from a survey of hunting activity with information from a separate survey of species composition in the harvest. We used these survey data to estimate the number of birds harvested for each species and hunting activity metrics (e.g., number of active hunters, days spent hunting). The analytical methods used to generate these estimates have not changed since the survey was first designed in the early 1970s. We describe a new hierarchical Bayesian integrated model, which replaces the series of ratio estimators that comprised the old model. We are using this new model to generate estimates for migratory bird harvests as of the 2019–2020 hunting season, and to generate updated estimates for all earlier years. The hierarchical Bayesian model uses over‐dispersed Poisson distributions to model mean hunter activity and harvest (zero‐inflated Poisson and zero‐truncated Poisson, respectively). It also includes multinomial distributions to model some key components (e.g., variation in harvest across periods of the hunting season, the species composition of the harvest within each of those periods, the age and sex composition in the harvests of a given species). We estimated the parameters of the Poisson and the multinomial distributions for each year as random effects using first‐difference time‐series. This time‐series component allows the model to share information across years and reduces the sensitivity of the estimates to annual sampling noise. The new model estimates are generally very similar to those from the old model, particularly for the species that occur most commonly in the harvest, so the results do not suggest any major changes to harvest management decisions and regulations. Estimates for all species from the new model are more precise and less susceptible to annual sampling error, particularly for species that occur less commonly in the harvest (e.g., sea ducks, other species of conservation concern). This new model, with its hierarchical Bayesian framework, will also facilitate future improvements and elaborations, allowing the incorporation of prior information from the rich literature and knowledge in game bird management and biology.

Identifying and controlling the emergence of antimicrobial resistance (AMR) is a high priority for researchers and public health officials. One critical component of this control effort is timely detection of emerging or increasing resistance using surveillance programs. Currently, detection of temporal changes in AMR relies mainly on analysis of the proportion of resistant isolates based on the dichotomization of minimum inhibitory concentration (MIC) values. In our work, we developed a hierarchical Bayesian latent class mixture model that incorporates a linear trend for the mean log2MIC of the non-resistant population. By introducing latent variables, our model addressed the challenges associated with the AMR MIC values, compensating for the censored nature of the MIC observations as well as the mixed components indicated by the censored MIC distributions. Inclusion of linear regression with time as a covariate in the hierarchical structure allowed modelling of the linear creep of the mean log2MIC in the non-resistant population. The hierarchical Bayesian model was accurate and robust as assessed in simulation studies. The proposed approach was illustrated using Salmonella enterica I,4,[5],12:i:- treated with chloramphenicol and ceftiofur in human and veterinary samples, revealing some significant linearly increasing patterns from the applications. Implementation of our approach to the analysis of an AMR MIC dataset would provide surveillance programs with a more complete picture of the changes in AMR over years by exploring the patterns of the mean resistance level in the non-resistant population. Our model could therefore serve as a timely indicator of a need for antibiotic intervention before an outbreak of resistance, highlighting the relevance of this work for public health. Currently, however, due to extreme right censoring on the MIC data, this approach has limited utility for tracking changes in the resistant population.

My dissertation is motivated by the need for improved statistical approaches for understanding differences in cancer risk in rural vs. urban areas. To accomplish this goal, we develop three statistical methods that can be used to model and explain differences in age-adjusted rates between small areas with differing characteristics. These methods allow researchers to draw meaningful inferences from sparse spatial or spatio-temporal datasets at the ZIP code or county levels. Furthermore, they can be used to identify regions that might require public health interventions and to motivate costly data collection efforts at the individual level. The statistical methods we propose in this dissertation can be classified into two categories: estimation and mediation. Chapter 2 focuses on precisely estimating age-adjusted cancer mortality rates for small areas from spatio-temporal datasets with an excessive number of zeros. A large proportion of zeros are often present in datasets involving low-prevalence diseases and in datasets that include rural regions with small population sizes. When stratifying counts for each region and year by age group in the process of estimating age-adjusted rates, the proportion of zeros in the dataset is further inflated. We propose a novel Bayesian hierarchical hurdle model with spatial and temporal random effects for estimating age-adjusted rates in these settings. Via a simulation study and two data examples, we study the performance of this model and make recommendations as to when it should be used over a Bayesian hierarchical Poisson regression model for age-adjusted rates. Chapters 3 and 4 address the goal of mediation. Specifically, Chapter 3 focuses on a method for performing a mediation analysis and Chapter 4 introduces a method for performing a decomposition analysis. Both chapters aim to explain a difference in age-adjusted rates at the ZIP code level based on either a ZIP code-level exposure (mediation) or a fixed characteristic (decomposition). We develop flexible statistical methods that use Bayesian hierarchical models with spatial random effects and a Bayesian version of the g-computation technique from causal inference. Both methods were designed to create counterfactual small area estimates of age-adjusted rates within the analysis and consequently stable estimates of the effects of interest. Through a simulation study, we illustrate a high level of precision and minimal bias in the total, direct, and indirect effects when using our proposed mediation analysis method. We also compare our proposed mediation method to two methods used in the medical literature and show that our method exhibits the best trade-off of bias and variance. To demonstrate the performance of our decomposition method, we perform a data analysis to understand whether park access explains the disparity in age-adjusted colorectal cancer incidence rates in rural vs. urban ZIP codes in Iowa. We illustrate that precise inferences can be made from sparse ZIP code-level datasets when incorporating small area estimation techniques into each analysis.

When using Bayesian hierarchical modeling, a popular approach for Item Response Theory (IRT) models, researchers typically face a tradeoff between the precision and accuracy of the item parameter estimates. Given the pooling principle and variance-dependent shrinkage, the expected behavior of Bayesian hierarchical IRT models is to deliver more precise but biased item parameter estimates, compared to those obtained in nonhierarchical models. Previous research, however, points out the possibility that, in the context of the two-parameter logistic IRT model, the aforementioned tradeoff has not to be made. With a comprehensive simulation study, we provide an in-depth investigation into this possibility. The results show a superior performance, in terms of bias, RMSE and precision, of the hierarchical specifications compared to the nonhierarchical counterpart. Under certain conditions, the bias in the item parameter estimates is independent of the bias in the variance components. Moreover, we provide a bias correction procedure for item discrimination parameter estimates. In sum, we show that IRT models create a unique situation where the Bayesian hierarchical approach indeed yields parameter estimates that are not only more precise, but also more accurate, compared to nonhierarchical approaches. We discuss this beneficial behavior from both theoretical and applied point of views.

Examining driver injury severity in intersection-related crashes using cluster analysis and hierarchical Bayesian models

Appropriate inference for stocks or species with low-quality data (poor data) or limited data (data poor) is extremely important. Hierarchical Bayesian methods are especially applicable to small-area, small-sample-size estimation problems because they allow poor-data species to borrow strength from species with good-quality data. We used a hammerhead shark complex as an example to investigate the advantages of using hierarchical Bayesian models in assessing the status of poor-data and data-poor exploited species. The hammerhead shark complex (Sphyrna spp.) along the Atlantic and Gulf of Mexico coasts of the United States is composed of three species: the scalloped hammerhead (S. lewini), the great hammerhead (S. mokarran), and the smooth hammerhead (S. zygaena) sharks. The scalloped hammerhead comprises 70-80% of the catch and has catch and relative abundance data of good quality, whereas great and smooth hammerheads have relative abundance indices that are both limited and of low quality presumably because of low stock density and limited sampling. Four hierarchical Bayesian state-space surplus production models were developed to simulate variability in population growth rates, carrying capacity, and catchability of the species. The results from the hierarchical Bayesian models were considerably more robust than those of the nonhierarchical models. The hierarchical Bayesian approach represents an intermediate strategy between traditional models that assume different population parameters for each species and those that assume all species share identical parameters. Use of the hierarchical Bayesian approach is suggested for future hammerhead shark stock assessments and for modeling fish complexes with species-specific data, because the poor-data species can borrow strength from the species with good data, making the estimation more stable and robust.

<p>Contaminants that cause water pollution are generated from large areas and flow into rivers. It becomes difficult to obtain an accurate prediction of water quality due to the large spatio-temporal variability in a changing climate which in turn leads to considerable uncertainty in the estimation of water quality. Water quality over South Korea highly depends on hydrometeorological conditions due to distinct seasonality. In this context, we explored the use of hydrometeorological variables (i.e., precipitation and temperature) and the autocorrelation structure of water quality parameters in the water quality prediction model within a Bayesian modeling framework. More specifically, we analyzed explored the interdepedencies and correlations between hydrometeorological factors and the water quality parameters for the Mangyeong River basin, and built a hierarchical Bayesian regression model for the TN and TP which are main water quality paramters in South Korea. The result shows that the proposed modeling framework can capture the key aspects of the water quality paramters in terms of seasonality and their uncertainty.</p><p> </p><p>KEYWORDS: Hierarchical Bayesian Model, Meteorological factors, Water Quality prediction</p><p> </p><p>Acknowledgement</p><p>This work was funded by the Korea Meteorological Administration Research and Development Program under Grant KMI(KMI2018-01215)</p>

Detection of safety signals based on multiple comparisons of adverse events (AEs) between two treatments in a clinical trial involves evaluations requiring multiplicity adjustment. A Bayesian hierarchical mixture model is a good solution to this problem as it borrows information across AEs within the same System Organ Class (SOC) and modulates extremes due merely to chance. However, the hierarchical model compares only the incidence rates of AEs, regardless of severity. In this article, we propose a three-level Bayesian hierarchical non-proportional odds cumulative logit model. Our model allows for testing the equality of incidence rate and severity for AEs between the control arm and the treatment arm while addressing multiplicities. We conduct simulation study to investigate the operating characteristics of the proposed hierarchical model. The simulation study demonstrates that the proposed method could be implemented as an extension of the Bayesian hierarchical mixture model in detecting AEs with elevated incidence rate and/or elevated severity. To illustrate, we apply our proposed method using the safety data from a phase III, two-arm randomized trial.