Visual Field Outcomes in the Primary Tube Versus Trabeculectomy Study.

PURPOSE: To describe visual field outcomes in the Primary Tube Versus Trabeculectomy (PTVT) Study. DESIGN: Cohort analysis of a prospective multicenter randomized clinical trial. SUBJECTS: A total of 155 eyes from 155 subjects randomly assigned to treatment with tube shunt surgery (n=84) or trabeculectomy with mitomycin C (n=71). METHODS: The PTVT Study was a multicenter randomized clinical trial comparing the safety and efficacy of trabeculectomy and tube shunt surgery in eyes without prior intraocular surgery. Subjects underwent standard automated perimetry (SAP) at baseline and annually for five years. SAP tests were deemed reliable if the false positive rate was ≤15%. Tests were excluded if visual acuity was ≤20/400 or loss of ≥2 Snellen lines from baseline were attributed to a non-glaucomatous etiology. Linear mixed-effects models were used to compare rates of change in SAP mean deviation (MD) between the two treatment groups. Intraocular pressure (IOP) control was assessed by percentage of visits with IOP <18 mmHg and mean IOP. OUTCOME MEASURES: Rate of change in SAP MD during follow-up. RESULTS: A total of 730 SAP tests were evaluated, with an average of 4.7 tests per eye. The average SAP MD at baseline was -12.8±8.3 dB in the tube group and -12.0±8.4 dB in the trabeculectomy group (p=0.57). The mean rate of change in SAP MD was -0.32±0.39 dB/year in the trabeculectomy group and -0.47±0.43 dB/year in the tube group (p=0.23). Eyes with mean IOP 14-17.5 mmHg had significantly faster rates of SAP MD loss compared to eyes with mean IOP <14 mmHg (-0.59±0.13 vs. -0.27±0.08 dB/year, p=0.012) and eyes with only 50-75% of visits with IOP <18 mmHg had faster rates than those with 100% of visits with IOP <18 mmHg (-0.90±0.16 vs. -0.29±0.08 dB/year, p<0.001). Multivariable analysis identified older age and worse IOP control as risk factors for faster progression in both treatment groups. CONCLUSIONS: No statistically significant difference in mean rates of visual field change was observed between trabeculectomy and tube shunt surgery in the PTVT Study. Worse IOP control was significantly associated with faster rates of SAP MD loss during follow-up. Older patients were also at risk for faster progression.

MUSSEL: Enhanced Bayesian polygenic risk prediction leveraging information across multiple ancestry groups.

Polygenic risk scores (PRSs) are now showing promising predictive performance on a wide variety of complex traits and diseases, but there exists a substantial performance gap across populations. We propose MUSSEL, a method for ancestry-specific polygenic prediction that borrows information in summary statistics from genome-wide association studies (GWASs) across multiple ancestry groups via Bayesian hierarchical modeling and ensemble learning. In our simulation studies and data analyses across four distinct studies, totaling 5.7 million participants with a substantial ancestral diversity, MUSSEL shows promising performance compared to alternatives. For example, MUSSEL has an average gain in prediction R2 across 11 continuous traits of 40.2% and 49.3% compared to PRS-CSx and CT-SLEB, respectively, in the African ancestry population. The best-performing method, however, varies by GWAS sample size, target ancestry, trait architecture, and linkage disequilibrium reference samples; thus, ultimately a combination of methods may be needed to generate the most robust PRSs across diverse populations.

Structured testing of genetic association with mixed clinical outcomes.

Genetic factors play a fundamental role in disease development. Studying the genetic association with clinical outcomes is critical for understanding disease biology and devising novel treatment targets. However, the frequencies of genetic variations are often low, making it difficult to examine the variants one-by-one. Moreover, the clinical outcomes are complex, including patients' survival time and other binary or continuous outcomes such as recurrences and lymph node count, and how to effectively analyze genetic association with these outcomes remains unclear. In this article, we proposed a structured test statistic for testing genetic association with mixed types of survival, binary, and continuous outcomes. The structured testing incorporates known biological information of variants while allowing for their heterogeneous effects and is a powerful strategy for analyzing infrequent genetic factors. Simulation studies show that the proposed test statistic has correct type I error and is highly effective in detecting significant genetic variants. We applied our approach to a uterine corpus endometrial carcinoma study and identified several genetic pathways associated with the clinical outcomes.

Incorporating genetic similarity of auxiliary samples into eGene identification under the transfer learning framework.

BACKGROUND: The term eGene has been applied to define a gene whose expression level is affected by at least one independent expression quantitative trait locus (eQTL). It is both theoretically and empirically important to identify eQTLs and eGenes in genomic studies. However, standard eGene detection methods generally focus on individual cis-variants and cannot efficiently leverage useful knowledge acquired from auxiliary samples into target studies. METHODS: We propose a multilocus-based eGene identification method called TLegene by integrating shared genetic similarity information available from auxiliary studies under the statistical framework of transfer learning. We apply TLegene to eGene identification in ten TCGA cancers which have an explicit relevant tissue in the GTEx project, and learn genetic effect of variant in TCGA from GTEx. We also adopt TLegene to the Geuvadis project to evaluate its usefulness in non-cancer studies. RESULTS: We observed substantial genetic effect correlation of cis-variants between TCGA and GTEx for a larger number of genes. Furthermore, consistent with the results of our simulations, we found that TLegene was more powerful than existing methods and thus identified 169 distinct candidate eGenes, which was much larger than the approach that did not consider knowledge transfer across target and auxiliary studies. Previous studies and functional enrichment analyses provided empirical evidence supporting the associations of discovered eGenes, and it also showed evidence of allelic heterogeneity of gene expression. Furthermore, TLegene identified more eGenes in Geuvadis and revealed that these eGenes were mainly enriched in cells EBV transformed lymphocytes tissue. CONCLUSION: Overall, TLegene represents a flexible and powerful statistical method for eGene identification through transfer learning of genetic similarity shared across auxiliary and target studies.

A scalar-on-quantile-function approach for estimating short-term health effects of environmental exposures.

Environmental epidemiologic studies routinely utilize aggregate health outcomes to estimate effects of short-term (eg, daily) exposures that are available at increasingly fine spatial resolutions. However, areal averages are typically used to derive population-level exposure, which cannot capture the spatial variation and individual heterogeneity in exposures that may occur within the spatial and temporal unit of interest (eg, within a day or ZIP code). We propose a general modeling approach to incorporate within-unit exposure heterogeneity in health analyses via exposure quantile functions. Furthermore, by viewing the exposure quantile function as a functional covariate, our approach provides additional flexibility in characterizing associations at different quantile levels. We apply the proposed approach to an analysis of air pollution and emergency department (ED) visits in Atlanta over 4 years. The analysis utilizes daily ZIP code-level distributions of personal exposures to 4 traffic-related ambient air pollutants simulated from the Stochastic Human Exposure and Dose Simulator. Our analyses find that effects of carbon monoxide on respiratory and cardiovascular disease ED visits are more pronounced with changes in lower quantiles of the population's exposure. Software for implement is provided in the R package nbRegQF.

Comparing Bayesian hierarchical meta-regression methods and evaluating the influence of priors for evaluations of surrogate endpoints on heterogeneous collections of clinical trials.

BACKGROUND: Surrogate endpoints, such as those of interest in chronic kidney disease (CKD), are often evaluated using Bayesian meta-regression. Trials used for the analysis can evaluate a variety of interventions for different sub-classifications of disease, which can introduce two additional goals in the analysis. The first is to infer the quality of the surrogate within specific trial subgroups defined by disease or intervention classes. The second is to generate more targeted subgroup-specific predictions of treatment effects on the clinical endpoint. METHODS: Using real data from a collection of CKD trials and a simulation study, we contrasted surrogate endpoint evaluations under different hierarchical Bayesian approaches. Each approach we considered induces different assumptions regarding the relatedness (exchangeability) of trials within and between subgroups. These include partial-pooling approaches, which allow subgroup-specific meta-regressions and, yet, facilitate data adaptive information sharing across subgroups to potentially improve inferential precision. Because partial-pooling models come with additional parameters relative to a standard approach assuming one meta-regression for the entire set of studies, we performed analyses to understand the impact of the parameterization and priors with the overall goals of comparing precision in estimates of subgroup-specific meta-regression parameters and predictive performance. RESULTS: In the analyses considered, partial-pooling approaches to surrogate endpoint evaluation improved accuracy of estimation of subgroup-specific meta-regression parameters relative to fitting separate models within subgroups. A random rather than fixed effects approach led to reduced bias in estimation of meta-regression parameters and in prediction in subgroups where the surrogate was strong. Finally, we found that subgroup-specific meta-regression posteriors were robust to use of constrained priors under the partial-pooling approach, and that use of constrained priors could facilitate more precise prediction for clinical effects in trials of a subgroup not available for the initial surrogacy evaluation. CONCLUSION: Partial-pooling modeling strategies should be considered for surrogate endpoint evaluation on collections of heterogeneous studies. Fitting these models comes with additional complexity related to choosing priors. Constrained priors should be considered when using partial-pooling models when the goal is to predict the treatment effect on the clinical endpoint.

Performance of Linear Mixed Models in Estimating Structural Rates of Glaucoma Progression Using Varied Random Effect Distributions.

Purpose: To compare how linear mixed models (LMMs) using Gaussian, Student t, and log-gamma (LG) random effect distributions estimate rates of structural loss in a glaucomatous population using OCT and to compare model performance to ordinary least squares (OLS) regression. Design: Retrospective cohort study. Subjects: Patients in the Bascom Palmer Glaucoma Repository (BPGR). Methods: Eyes with ≥ 5 reliable peripapillary retinal nerve fiber layer (RNFL) OCT tests over ≥ 2 years were identified from the BPGR. Retinal nerve fiber layer thickness values from each reliable test (signal strength ≥ 7/10) and associated time points were collected. Data were modeled using OLS regression as well as LMMs using different random effect distributions. Predictive modeling involved constructing LMMs with (n - 1) tests to predict the RNFL thickness of subsequent tests. A total of 1200 simulated eyes of different baseline RNFL thickness values and progression rates were developed to evaluate the likelihood of declared progression and predicted rates. Main Outcome Measures: Model fit assessed by Watanabe-Akaike information criterion (WAIC) and mean absolute error (MAE) when predicting future RNFL thickness values; log-rank test and median time to progression with simulated eyes. Results: A total of 35 862 OCT scans from 5766 eyes of 3491 subjects were included. The mean follow-up period was 7.0 ± 2.3 years, with an average of 6.2 ± 1.4 tests per eye. The Student t model produced the lowest WAIC. In predictive models, all LMMs demonstrated a significant reduction in MAE when estimating future RNFL thickness values compared with OLS (P < 0.001). Gaussian and Student t models were similar and significantly better than the LG model in estimating future RNFL thickness values (P < 0.001). Simulated eyes confirmed LMM performance in declaring progression sooner than OLS regression among moderate and fast progressors (P < 0.01). Conclusions: LMMs outperformed conventional approaches for estimating rates of OCT RNFL thickness loss in a glaucomatous population. The Student t model provides the best model fit for estimating rates of change in RNFL thickness, although the use of the Gaussian or Student t distribution in models led to similar improvements in accurately estimating RNFL loss. Financial Disclosures: Proprietary or commercial disclosure may be found in the Footnotes and Disclosures at the end of this article.

Benefits of the Curious Behavior of Bayesian Hierarchical Item Response Theory Models-An in-Depth Investigation and Bias Correction.

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.

Harnessing the power of regional baselines for broad-scale genetic stock identification: A multistage, integrated, and cost-effective approach.

In mixed-stock fishery analyses, genetic stock identification (GSI) estimates the contribution of each population to a mixture and is typically conducted at a regional scale using genetic baselines specific to the stocks expected in that region. Often these regional baselines cannot be combined to produce broader geographical baselines due to non-overlapping populations and genetic markers. In cases where the mixture contains stocks spanning across a wide area, a broad-scale baseline is created, but often at the cost of resolution. Here, we introduce a new GSI method to harness the resolution capabilities of baselines developed for regional applications in the analysis of mixtures containing individuals from a broad geographic range. This method employs a multistage framework that allows disparate baselines to be used in a single integrated process that produces estimates along with the propagated errors from each stage. All individuals in the mixture sample are required to be genotyped for all genetic markers in the baselines used by this model, but the baselines do not require overlap in genetic markers or populations representing the broad-scale or regional baselines. We demonstrate the utility of our integrated multistage model using a synthesized data set made up of Chinook salmon, Oncorhynchus tshawytscha, from the North Bering Sea of Alaska. The results show an improved accuracy for estimates using an integrated multistage framework, compared to the conventional framework of using separate hierarchical steps. The integrated multistage framework allows GSI of a wide geographic area without first developing a large scale, high-resolution genetic baseline or dividing a mixture sample into smaller regions beforehand. This approach is more cost-effective than updating range-wide baselines with all regionally important markers.

Bayesian hierarchical modeling in interim futility analysis for two parallel clinical trials.

Incorporating interim analysis into a trial design is gaining popularity in the field of confirmatory clinical trials, where two studies may be conducted in parallel (ie, twin studies) in order to provide substantial evidence per the requirement of FDA guidance. Interim futility analysis provides a chance to check for the "disaster" scenario when the treatment has a high probability to be not more efficacious than the control. Therefore, it is an efficient tool to mitigate risk of running a complete and expansive trial under such scenario. There is no agreement among trial designers that interim analysis should be based on individual study data or pooled data under the twin study scenario. In fact, it is a dilemma for most scientists when specifying the interim analysis strategy at the design stage as the true treatment effects of the twin studies are unknown no matter how similar they are intended to be. To address the issue, we developed a Bayesian hierarchical modeling method to allow dynamic data borrowing between twin studies and demonstrated a favorable characteristic of the new method over the separate and pooled analyses. We evaluated a wide spectrum of the heterogeneity hyperparameters and visualized its critical impact on the Bayesian model's characteristic. Based on the evaluation, we made a suggestion on the heterogeneity hyperparameter selection independent of any a priori knowledge. We also applied our method to a case study where predictive powers of different methods are compared.

Easy, bias-free Bayesian hierarchical modeling of the psychometric function using the Palamedes Toolbox.

A hierarchical Bayesian method is proposed that can be used to fit multiple psychometric functions (PFs) simultaneously across conditions and subjects. The method incorporates the generalized linear model and allows easy reparameterization of the parameters of the PFs, for example, to constrain parameter values across conditions or to code for experimental effects (e.g., main effects and interactions in a factorial design). Simulations indicate that fitting PFs for multiple conditions and observers simultaneously using the hierarchical structure effectively eliminates bias and improves precision in parameter estimates relative to fitting PFs individually in each condition. The method is further validated by analyzing human psychophysical data obtained in an experiment investigating the effect of attention on correspondence matching in an ambiguous long-range motion display. The method converges successfully, even for experiments that use a low number of trials per subject, without the need for fine-tuning by the user and while using the default essentially uninformative priors. The latter may make the method more acceptable to those critical of applying informative priors. The method is implemented in the freely downloadable Palamedes Toolbox, which also includes routines that graphically display the fitted psychometric functions alongside the data, and derive and display posterior distributions of parameters, summary statistics, and diagnostic measures. Overall, these features make hierarchical Bayesian modeling of PFs easily available to researchers who wish to use Bayesian statistics but lack the expertise to implement these methods themselves.

Bayesian workflow for the investigation of hierarchical classification models from tau-PET and structural MRI data across the Alzheimer's disease spectrum.

Background: Alzheimer's disease (AD) diagnosis in its early stages remains difficult with current diagnostic approaches. Though tau neurofibrillary tangles (NFTs) generally follow the stereotypical pattern described by the Braak staging scheme, the network degeneration hypothesis (NDH) has suggested that NFTs spread selectively along functional networks of the brain. To evaluate this, we implemented a Bayesian workflow to develop hierarchical multinomial logistic regression models with increasing levels of complexity of the brain from tau-PET and structural MRI data to investigate whether it is beneficial to incorporate network-level information into an ROI-based predictive model for the presence/absence of AD. Methods: This study included data from the Translational Biomarkers in Aging and Dementia (TRIAD) longitudinal cohort from McGill University's Research Centre for Studies in Aging (MCSA). Baseline and 1 year follow-up structural MRI and [18F]MK-6240 tau-PET scans were acquired for 72 cognitive normal (CN), 23 mild cognitive impairment (MCI), and 18 Alzheimer's disease dementia subjects. We constructed the four following hierarchical Bayesian models in order of increasing complexity: (Model 1) a complete-pooling model with observations, (Model 2) a partial-pooling model with observations clustered within ROIs, (Model 3) a partial-pooling model with observations clustered within functional networks, and (Model 4) a partial-pooling model with observations clustered within ROIs that are also clustered within functional brain networks. We then investigated which of the models had better predictive performance given tau-PET or structural MRI data as an input, in the form of a relative annualized rate of change. Results: The Bayesian leave-one-out cross-validation (LOO-CV) estimate of the expected log pointwise predictive density (ELPD) results indicated that models 3 and 4 were substantially better than other models for both tau-PET and structural MRI inputs. For tau-PET data, model 3 was slightly better than 4 with an absolute difference in ELPD of 3.10 ± 1.30. For structural MRI data, model 4 was considerably better than other models with an absolute difference in ELPD of 29.83 ± 7.55 relative to model 3, the second-best model. Conclusion: Our results suggest that representing the data generating process in terms of a hierarchical model that encompasses both ROI-level and network-level heterogeneity leads to better predictive ability for both tau-PET and structural MRI inputs over all other model iterations.

Cognitive-attentional mechanisms of cooperation-with implications for attention-deficit hyperactivity disorder and cognitive neuroscience.

People's cooperativeness depends on many factors, such as their motives, cognition, experiences, and the situation they are in. To date, it is unclear how these factors interact and shape the decision to cooperate. We present a computational account of cooperation that not only provides insights for the design of effective incentive structures but also redefines neglected social-cognitive characteristics associated with attention-deficit hyperactivity disorder (ADHD). Leveraging game theory, we demonstrate that the source and magnitude of conflict between different motives affected the speed and frequency of cooperation. Integrating eye-tracking to measure motivation-based information processing during decision-making shows that participants' visual fixations on the gains of cooperation rather than its costs and risks predicted their cooperativeness on a trial-by-trial basis. Using Bayesian hierarchical modeling, we find that a situation's prosociality and participants' past experience each bias the decision-making process distinctively. ADHD characteristics explain individual differences in responsiveness across contexts, highlighting the clinical importance of experimentally studying reactivity in social interactions. We demonstrate how the use of eye-tracking and computational modeling can be used to experimentally investigate social-cognitive characteristics in clinical populations. We also discuss possible underlying neural mechanisms to be investigated in future studies.

Handling missing within-study correlations in the evaluation of surrogate endpoints.

Rigorous evaluation of surrogate endpoints is performed in a trial-level analysis in which the strength of the association between treatment effects on the clinical and surrogate endpoints is quantified across a collection of previously conducted trials. To reduce bias in measures of the performance of the surrogate, the statistical model must account for the sampling error in each trial's estimated treatment effects and their potential correlation. Unfortunately, these within-study correlations can be difficult to obtain, especially for meta-analysis of published trial results where individual patient data is not available. As such, these terms are frequently partially or completely missing in the analysis. We show that improper handling of these missing terms can meaningfully alter the perceived quality of the surrogate and we introduce novel strategies to handle the missingness.

Transient demographic dynamics of recovering fish populations shaped by past climate variability, harvest, and management.

Large-scale commercial harvesting and climate-induced fluctuations in ocean properties shape the dynamics of marine populations as interdependent drivers at varied timescales. Persistent selective removals of larger, older members of a population can distort its demographic structure, eroding resilience to fluctuations in habitat conditions and thus amplifying volatility in transient dynamics. Many historically depleted marine fish stocks have begun showing signs of recovery in recent decades following the implementation of stricter management measures. But these interventions coincide with accelerated changes in the oceans triggered by increasingly warmer, more variable climates. Applying multilevel models to annual estimates of demographic metrics of 38 stocks comprising 11 species across seven northeast Atlantic ecoregions, this study explores how time-varying local and regional climates contributed to the transient dynamics of recovering populations exposed to variable fishing pressures moderated by management actions. Analyses reveal that progressive reductions in fishing pressure and shifting climate conditions discontinuously shaped rebuilding patterns of the stocks through restorations of maternal demographic structure (reversing age truncation) and reproductive capacity. As the survival rate and demographic structure of reproductive fish improved, transient growth became less sensitive to variability in recruitment and juvenile survival and more to that in adult survival. As the biomass of reproductive fish rose, recruitment success also became increasingly regulated by density-dependent processes involving higher numbers of older fish. When reductions in fishing pressure were insufficient or delayed, however, stocks became further depleted, with more eroded demographic structures. Although warmer local climates in spawning seasons promoted recruitment success in some ecoregions, changing climates in recent decades began adversely affecting reproductive performances overall, amplifying sensitivities to recruitment variability. These shared patterns underscore the value of demographic transients in developing robust strategies for managing marine resources. Such strategies could form the foundation for effective applications of adaptive measures resilient to future environmental change.

Upgrade of D+ software for hierarchical modeling of X-ray scattering data from complex structures in solution, fibers and single orientations.

This article presents an upgrade of the D+ software [Ginsburg et al. (2019 ▸). J. Appl. Cryst. 52, 219-242], expanding its hierarchical solution X-ray scattering modeling capabilities for fiber diffraction and single crystallographic orientations. This upgrade was carried out using the reciprocal grid algorithm [Ginsburg et al. (2016 ▸). J. Chem. Inf. Model. 56, 1518-1527], providing D+ its computational strength. Furthermore, the extensive modifications made to the Python API of D+ are described, broadening the X-ray analysis performed with D+ to account for the effects of the instrument-resolution function and polydispersity. In addition, structure-factor and radial-distribution-function modules were added, taking into account the effects of thermal fluctuations and intermolecular interactions. Finally, numerical examples demonstrate the usage and potential of the added features.

A hierarchical modeling approach to predict the distribution and density of Sierra Nevada Red Fox (Vulpes vulpes necator).

Carnivores play critical roles in ecosystems, yet many species are declining worldwide. The Sierra Nevada Red Fox (Vulpes vulpes necator; SNRF) is a rare and endangered subspecies of red fox limited to upper montane forests, subalpine, and alpine environments of California and Oregon, United States. Having experienced significant distribution contractions and population declines in the last century, the subspecies is listed as at-risk by relevant federal and state agencies. Updated information on its contemporary distribution and density is needed to guide and evaluate conservation and management actions. We combined 12 years (2009-2020) of detection and nondetection data collected throughout California and Oregon to model the potential distribution and density of SNRFs throughout their historical and contemporary ranges. We used an integrated species distribution and density modeling approach, which predicted SNRF density in sampled locations based on observed relationships between environmental covariates and detection frequencies, and then projected those predictions to unsampled locations based on the estimated correlations with environmental covariates. This approach provided predictions that serve as density estimates in sampled regions and projections in unsampled areas. Our model predicted a density of 1.06 (95% credible interval = 0.8-1.36) foxes per 100 km2 distributed throughout 22,926 km2 in three distinct regions of California and Oregon-Sierra Nevada, Lassen Peak, and Oregon Cascades. SNRFs were most likely to be found in areas with low minimum temperatures and high snow water equivalent. Our results provide a contemporary baseline to inform the development and evaluation of conservation and management actions, and guide future survey efforts.

Evaluation of predictive capability of Bayesian spatio-temporal models for Covid-19 spread.

BACKGROUND: Bayesian models have been applied throughout the Covid-19 pandemic especially to model time series of case counts or deaths. Fewer examples exist of spatio-temporal modeling, even though the spatial spread of disease is a crucial factor in public health monitoring. The predictive capabilities of infectious disease models is also important. METHODS: In this study, the ability of Bayesian hierarchical models to recover different parts of the variation in disease counts is the focus. It is clear that different measures provide different views of behavior when models are fitted prospectively. Over a series of time horizons one step predictions have been generated and compared for different models (for case counts and death counts). These Bayesian SIR models were fitted using MCMC at 28 time horizons to mimic prospective prediction. A range of goodness of prediction measures were analyzed across the different time horizons. RESULTS: A particularly important result is that the peak intensity of case load is often under-estimated, while random spikes in case load can be mimicked using time dependent random effects. It is also clear that during the early wave of the pandemic simpler model forms are favored, but subsequently lagged spatial dependence models for cases are favored, even if the sophisticated models perform better overall. DISCUSSION: The models fitted mimic the situation where at a given time the history of the process is known but the future must be predicted based on the current evolution which has been observed. Using an overall 'best' model for prediction based on retrospective fitting of the complete pandemic waves is an assumption. However it is also clear that this case count model is well favored over other forms. During the first wave a simpler time series model predicts case counts better for counties than a spatially dependent one. The picture is more varied for morality. CONCLUSIONS: From a predictive point of view it is clear that spatio-temporal models applied to county level Covid-19 data within the US vary in how well they fit over time and also how well they predict future events. At different times, SIR case count models and also mortality models with cumulative counts perform better in terms of prediction. A fundamental result is that predictive capability of models varies over time and using the same model could lead to poor predictive performance. In addition it is clear that models addressing the spatial context for case counts (i.e. with lagged neighborhood terms) and cumulative case counts for mortality data are clearly better at modeling spatio-temporal data which is commonly available for the Covid-19 pandemic in different areas of the globe.

General and Specific Factors of Environmental Stress and Their Associations With Brain Structure and Dimensions of Psychopathology.

Background: Early-life stressors can adversely affect the developing brain. While hierarchical modeling has established the existence of a general factor of psychopathology, no studies have modeled a general factor of environmental stress and related this factor to brain development. Using a large sample of children from the ABCD (Adolescent Brain Cognitive Development) Study, the current study aimed to identify general and specific factors of environmental stress and test their associations with brain structure and psychopathology. Methods: In a sample of 11,878 children, bifactor modeling and higher-order (second-order) modeling identified general and specific factors of environmental stress: family dynamics, interpersonal support, neighborhood socioeconomic status deprivation, and urbanicity. Structural equation modeling was performed to examine associations between these factors and regional gray matter volume (GMV) and cortical thickness as well as general and specific factors of psychopathology. Results: The general environmental stress factor was associated with globally smaller cortical and subcortical GMV as well as thinner cortices across widespread regions. Family dynamics and neighborhood socioeconomic status deprivation were associated with smaller GMV in focal regions. Urbanicity was associated with larger cortical and subcortical GMV and thicker cortices in frontotemporal regions. The environmental factors were associated with psychopathology in the expected directions. The general factors of environmental stress and psychopathology were both predictors of smaller GMV in children, while remaining distinct from each other. Conclusions: This study reveals a unifying model of environmental influences that illustrates the inherent organization of environmental stressors and their relationship to brain structure and psychopathology.

Hierarchical Geodesic Polynomial Model for Multilevel Analysis of Longitudinal Shape.

Longitudinal analysis is a core aspect of many medical applications for understanding the relationship between an anatomical subject's function and its trajectory of shape change over time. Whereas mixed-effects (or hierarchical) modeling is the statistical method of choice for analysis of longitudinal data, we here propose its extension as hierarchical geodesic polynomial model (HGPM) for multilevel analyses of longitudinal shape data. 3D shapes are transformed to a non-Euclidean shape space for regression analysis using geodesics on a high dimensional Riemannian manifold. At the subject-wise level, each individual trajectory of shape change is represented by a univariate geodesic polynomial model on timestamps. At the population level, multivariate polynomial expansion is applied to uni/multivariate geodesic polynomial models for both anchor points and tangent vectors. As such, the trajectory of an individual subject's shape changes over time can be modeled accurately with a reduced number of parameters, and population-level effects from multiple covariates on trajectories can be well captured. The implemented HGPM is validated on synthetic examples of points on a unit 3D sphere. Further tests on clinical 4D right ventricular data show that HGPM is capable of capturing observable effects on shapes attributed to changes in covariates, which are consistent with qualitative clinical evaluations. HGPM demonstrates its effectiveness in modeling shape changes at both subject-wise and population levels, which is promising for future studies of the relationship between shape changes over time and the level of dysfunction severity on anatomical objects associated with disease.