A Bayesian hierarchical diffusion model decomposition of performance in Approach–Avoidance Tasks

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.

A hierarchical Bayesian model is proposed to quantify the magnitude of extreme surges on the Atlantic coast of Canada with limited data. Generalized extreme value distributions are fitted to surges derived from water levels measured at 21 buoys along the coast. The parameters of these distributions are linked together through a Gaussian field whose mean and variance are driven by atmospheric sea‐level pressure and the distance between stations, respectively. This allows for information sharing across the original stations and for interpolation anywhere along the coast. The use of a copula at the data level of the hierarchy further accounts for the dependence between locations, allowing for inference beyond a site‐by‐site basis. It is shown how the extreme surges derived from the model can be combined with the tidal process to predict potentially catastrophic water levels.

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.

PurposeDevelop a hierarchical longitudinal regression model for estimating local rates of change of macular ganglion cell complex (GCC) measurements with optical coherence tomography (OCT).MethodsWe enrolled 112 eyes with four or more macular OCT images and ≥2 years of follow-up. GCC thickness measurements within central 6 × 6 superpixels were extracted from macular volume scans. We fit data from each superpixel separately with several hierarchical Bayesian random-effects models. Models were compared with the Watanabe–Akaike information criterion. For our preferred model, we estimated population and individual slopes and intercepts (baseline thickness) and their correlation.ResultsMean (SD) follow-up time and median (interquartile range) baseline 24-2 visual field mean deviation were 3.6 (0.4) years and −6.8 (−12.2 to −4.3) dB, respectively. The random intercepts and slopes model with random residual variance was the preferred model. While more individual and population negative slopes were observed in the paracentral and papillomacular superpixels, superpixels in the superotemporal and inferior regions displayed the highest correlation between baseline thickness and rates of change (r = –0.43 to –0.50 for the top five correlations).ConclusionsA Bayesian linear hierarchical model with random intercepts/slopes and random variances is an optimal initial model for estimating GCC slopes at population and individual levels. This novel model is an efficient method for estimating macular rates of change and probability of glaucoma progression locally.Translational RelevanceThe proposed Bayesian hierarchical model can be applied to various macular outcomes from different OCT devices and to superpixels of variable sizes to estimate local rates of change and progression probability.

A Bayesian approach to model the trends and variability in urban stormwater quality associated with catchment and hydrologic parameters

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.

Meta-analyses are frequently performed on adverse event data and are primarily used for improving statistical power to detect safety signals. However, in the evaluation of drug safety for New Drug Applications, simple pooling of adverse event data from multiple clinical trials is still commonly used. We sought to propose a new Bayesian hierarchical meta-analytic approach based on consideration of a hierarchical structure of reported individual adverse event data from multiple randomized clinical trials. To develop our meta-analysis model, we extended an existing three-stage Bayesian hierarchical model by including an additional stage of the clinical trial level in the hierarchical model; this generated a four-stage Bayesian hierarchical model. We applied the proposed Bayesian meta-analysis models to published adverse event data from three premarketing randomized clinical trials of tadalafil and to a simulation study motivated by the case example to evaluate the characteristics of three alternative models. Comparison of the results from the Bayesian meta-analysis model with those from Fisher's exact test after simple pooling showed that 6 out of 10 adverse events were the same within a top 10 ranking of individual adverse events with regard to association with treatment. However, more individual adverse events were detected in the Bayesian meta-analysis model than in Fisher's exact test under the body system "Musculoskeletal and connective tissue disorders." Moreover, comparison of the overall trend of estimates between the Bayesian model and the standard approach (odds ratios after simple pooling methods) revealed that the posterior median odds ratios for the Bayesian model for most adverse events shrank toward values for no association. Based on the simulation results, the Bayesian meta-analysis model could balance the false detection rate and power to a better extent than Fisher's exact test. For example, when the threshold value of the posterior probability for signal detection was set to 0.8, the false detection rate was 41% and power was 88% in the Bayesian meta-analysis model, whereas the false detection rate was 56% and power was 86% in Fisher's exact test. Adverse events under the same body system were not necessarily positively related when we used "system organ class" and "preferred term" in the Medical Dictionary for Regulatory Activities as a hierarchical structure of adverse events. For the Bayesian meta-analysis models to be effective, the validity of the hierarchical structure of adverse events and the grouping of adverse events are critical. Our proposed meta-analysis models considered trial effects to avoid confounding by trial and borrowed strength from both within and across body systems to obtain reasonable and stable estimates of an effect measure by considering a hierarchical structure of adverse events.

Multivariate Bayesian hierarchical modeling of the non-stationary traffic conflict extremes for crash estimation

We present a novel source term estimation and SO2 ground concentration forecasting system for the Reykjanes peninsula, developed as a Digital Twin Component for the DT-GEO project. The joint distribution over the source term and ground concentrations is estimated by drawing samples from the posterior specified by a Bayesian hierarchical model, using Hamiltonian Monte Carlo. The Bayesian model consists of a physics based forward model that gives ground concentrations as a function of the source term, and an empirical model that describes the influence of the atmosphere on the source term. The forward model has to be (1) fast and (2) differentiable for the sampling procedure, so we replace the forward model (Fall3D) with an emulator. We can use simple linear emulators by taking advantage of the linearity of ground concentration with flux for basic scenarios, while neural network based emulators are being developed for more complicated model physics. Observations of SO2 flux, plume height, and ground concentration constrain the hierarchical model parameters that determine the forecast ground concentrations. Application to the recent basaltic fissure eruptions on Reykjanes, Iceland, will be presented.

Exploring the temporal structure of time series data for hazardous liquid pipeline incidents based on complex network theory

BackgroundIdentification of differentially expressed genes is a typical objective when analyzing gene expression data. Recently, Bayesian hierarchical models have become increasingly popular to solve this type of problems. These models show good performance in accommodating noise, variability and low replication of microarray data. However, the correlation between different fluorescent signals measured from a gene spot is ignored, which can diversely affect the data analysis step. In fact, the intensities of the two signals are significantly correlated across samples. The larger the log-transformed intensities are, the smaller the correlation is.ResultsMotivated by the complicated error relations in microarray data, we propose a multivariate hierarchical Bayesian framework for data analysis in the replicated microarray experiments. Gene expression data are modelled by a multivariate normal distribution, parameterized by the corresponding mean vectors and covariance matrixes with a conjugate prior distribution. Within the Bayesian framework, a generalized likelihood ratio test (GLRT) is also developed to infer the gene expression patterns. Simulation studies show that the proposed approach presents better operating characteristics and lower false discovery rate (FDR) than existing methods, especially when the correlation coefficient is large. The approach is illustrated with two examples of microarray analysis. The proposed method successfully detects significant genes closely related to the experimental states, which are verified by the biological information.ConclusionsThe multivariate Bayesian model, compatible with the dependence between mean and variance in the univariate Bayesian model, relaxes the constant coefficient of variation assumption between measurements by adding a covariance structure. This model improves the identification of differentially expressed genes significantly since the Bayesian model fit well with the microarray data.

BackgroundVaccines constitute a fundamental component of public health interventions, preventing the transmission of numerous diseases. Nevertheless, vaccines remain underutilized in various regions globally, particularly in East African nations, where high mortality rates among children under 5 years of age are predominantly attributable to vaccine‐preventable diseases. Consequently, this investigation is aimed at evaluating children′s vaccination coverage and its associated determinants in East Africa utilizing Bayesian hierarchical modeling based on Demographic and Health Survey (DHS) data (2019–2022).MethodsThis study analyzed nationally representative data from the DHS, a standardized cross‐sectional household survey program that collects health and population data using stratified two‐stage cluster sampling. Data were drawn from surveys conducted between 2019 and 2022 in five East African countries: Ethiopia (2019), Kenya (2022), Mozambique (2022), Rwanda (2019/20), and Tanzania (2022). A Bayesian hierarchical regression model was applied to identify factors influencing vaccination coverage, evaluating four candidate models using leave‐one‐out cross‐validation to select the best fit. Statistical significance was assessed using 95% posterior credible intervals (CrIs) after confirming model convergence.ResultsA total of 15,703 weighted children aged 12–23 months were included, with an overall survey response rate of 97.2%. A substantial proportion of children (73.81%) were only partially immunized, highlighting a critical gap in achieving full vaccination coverage. The Bayesian hierarchical ordinal logistic regression showed that several factors were significantly associated with the odds of being in a higher vaccination category versus a lower one. Children residing in Kenya had 3.10 times higher odds of being in a higher vaccination category compared with those in Ethiopia (AOR = 3.10; 95% CrI: 2.49–3.86). Maternal media exposure (AOR = 1.25, 95% CrI: 1.15, 1.38), maternal education (secondary or above) (AOR = 1.42, 95% CrI: 1.21, 1.67), health facility delivery (AOR = 1.53, 95% CrI: 1.19, 1.96), postnatal care visit (AOR = 1.28, 95% CrI: 1.15, 1.43), skilled birth attendance (AOR = 1.61, 95% CrI: 1.24, 2.079), and antenatal care (ANC) visits (four and above) (AOR = 4.08, 95% CrI: 3.44, 4.84) were all positively associated with higher odds of being in a higher vaccination category.ConclusionsVaccination coverage remains low across East Africa, with significant regional disparities. These results highlight the need for focused interventions in high‐risk areas and addressing key determinants to improve childhood vaccination rates.

Modeling player engagement is a key challenge in games. However, the gameplay signatures of engaged players can be highly context-sensitive, varying based on where the game is used or what population of players is using it. Traditionally, models of player engagement are investigated in a particular context, and it is unclear how effectively these models generalize to other settings and populations. In this work, we investigate a Bayesian hierarchical linear model for multi-task learning to devise a model of player engagement from a pair of datasets that were gathered in two complementary contexts: a Classroom Study with middle school students and a Laboratory Study with undergraduate students. Both groups of players used similar versions of Crystal Island, an educational interactive narrative game for science learning. Results indicate that the Bayesian hierarchical model outperforms both pooled and context-specific models in cross-validation measures of predicting player motivation from in-game behaviors, particularly for the smaller Classroom Study group. Further, we find that the posterior distributions of model parameters indicate that the coefficient for a measure of gameplay performance significantly differs between groups. Drawing upon their capacity to share information across groups, hierarchical Bayesian methods provide an effective approach for modeling player engagement with data from similar, but different, contexts.

Tourism development: Principles, processes, and policies: by William C. Gartner, Van Nostrand Reinhold, 115 Fifth Avenue, New York, NY 10003, 1996, $44.95, ISBN 0-442-00893-7.

When rejecting and accepting hypotheses, it is important to determine the risk of false positive conclusions. Hierarchical Bayesian models are frequently applied in cognitive science, psychology, cognitive neuroscience, and psychiatry to reduce the variability of low-level parameters through partial pooling, and to obtain more robust parameter estimates for complex models using limited data. This may lower the risk of false positive inferences from lower-level estimates. In contrast, higher-level (e.g. group-level) estimates may be more affected by modeling choices (e.g. prior distributions), population-level variances in effects, and inference methods, which may in turn affect false positive rates for group-level effects. Here we used simulation and computational modeling to systematically examine false positive rates and effects of specific modeling choices on inferences in a simple hierarchical Bayesian temporal discounting model. To this end, 600 data sets of a temporal discounting task with two conditions were simulated, drawing individual condition effect parameters from a null distribution with varying standard deviations. For each simulated data set, the group-level mean change in the discount rate was modeled with eight different prior variances of the condition effect. Results were subsequently evaluated using several commonly applied Bayesian inference methods: the Savage-Dickey Bayes factor (BF), the directional Bayes factor (dBF), P(effect > 0), and the highest density interval (HDI) against zero decision rule. Results confirm that inference methods that directly depend on the posterior distribution can be used regardless of prior variances, whereas the Savage-Dickey BF should only be used with sufficiently informative priors. Based on the simulation work, decision thresholds that ensure false positive rates below 5% are provided for each inference method. Results are discussed in the context of computational modeling approaches in cognitive (neuro-)science and psychology.