Bayesian Multivariate Model Research Articles

Bayesian Multivariate Spatial Models for Lattice Data with INLA

The INLAMSM package for the R programming language provides a collection of multivariate spatial models for lattice data that can be used with the INLA package for Bayesian inference. The multivariate spatial models implemented include different structures to model the spatial variation of the variables and the between-variables variability. In this way, fitting multivariate spatial models becomes faster and easier. The use of the different models included in the package is illustrated using two different datasets: the well-known North Carolina SIDS data and mortality by three causes of death in Comunidad Valenciana (Spain).

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

Recent studies have demonstrated that single conflict indicators represent only a fractional aspect of the severity of a traffic interaction. As such, integrating several conflict indicators in a unified model can improve conflict-based crash estimation. This study develops a multivariate Bayesian hierarchical Gaussian copula modeling approach, which comprises a multivariate Gaussian copula and a Bayesian hierarchical structure. The former has generalized extreme value marginals and captures multivariate dependence among several conflict indicators, while the latter combines traffic conflicts from different sites, incorporating several covariates and site-specific unobserved heterogeneity. The copula approach offers the flexibility in modeling multivariate structures including the selection of margins from various parametric families of univariate distribution and the construction of parametric copulas which satisfies different types of dependence structure. A model estimation approach for the multivariate Bayesian hierarchical Gaussian copula model is proposed and applied to estimate rear-end crashes from four signalized intersections in the city of Surrey, British Columbia. The modified time to collision (MTTC), post encroachment time (PET), and deceleration rate to avoid a crash (DRAC) were employed as conflict indicators. Three covariates including traffic volume, shock wave area, and platoon ratio were considered to account for non-stationarity in conflict extremes. The results show that in terms of crash estimation accuracy, the multivariate Bayesian hierarchical Gaussian copula model outperforms both the bivariate Bayesian hierarchical Gaussian copula models and the recently proposed multivariate Bayesian hierarchical model in which multiple traffic conflict indicators were combined by one dependence parameter.

Quantitative Genetics of Growth Rate and Filet Quality Traits in Atlantic Salmon Inferred From a Longitudinal Bayesian Model for the Left-Censored Gaussian Trait Growth Rate.

In selective breeding programs for Atlantic salmon, test fish are slaughtered at an average body weight where growth rate and carcass traits as filet fat (FF), filet pigment (FP) and visceral fat index (FF) are recorded. The objective of this study was to obtain estimates of genetic correlations between growth rate (GR), and the three carcass quality traits when fish from the same 206 families (offspring of 120 sires and 206 dams from 2 year-classes) were recorded both at the same age (SA) and about the same body weight (SW). In the SW group, the largest fish were slaughtered at five different slaughter events and the remaining fish at the sixth slaughter event over 6 months. Estimates of genetic parameters for the traits were obtained from a Bayesian multivariate model for (potentially) truncated Gaussian traits through a Gibbs sampler procedure in which phantom GR values were obtained for the unslaughtered, and thus censored SW group fish at each slaughter event. The heritability estimates for the same trait in each group was similar; about 0.2 for FF, 0.15 for FP and 0.35 for VF and GR. The genetic correlation between the same traits in the two groups was high for growth rate (0.91 ± 0.05) visceral index (0.86 ± 0.05), medium for filet fat (0.45 ± 0.17) and low for filet pigment (0.13 ± 0.27). Within the two groups, the genetic correlation between growth rate and filet fat changed from positive (0.59 ± 0.14) for the SA group to negative (−0.45 ± 0.17) for the SW group, while the genetic correlation between growth rate and filet pigment changed from negative (−0.33 ± 0.22) for the SA group to positive (0.62 ± 0.16) for the SW group. The genetic correlation of growth rate with FF and FP is sensitive to whether the latter traits are measured at the same age or the same body weight. The results indicate that selection for increased growth rate is not expected to have a detrimental effect on the quality traits if increased growth potential is realized through a reduced production time.

Optical flow, behaviour and broiler chicken welfare in the UK and Switzerland

Although systems for automated assessment of broiler chicken welfare have now been developed on a small scale, none are currently in widespread commercial use. We addressed this gap between research and uptake by field testing a camera system that uses the optical flow patterns made by the movements of flocks to monitor bird welfare. We tested the hypothesis that the movement patterns made by flocks of broiler chickens are correlated with two key welfare outcomes – mortality and hockburn. Life-long CCTV monitoring was carried out on 74 commercial broiler flocks (UK = 31; Switzerland = 43) and the resulting data analysed to give daily values of 4 optical flow descriptors: mean, variance, skew and kurtosis. Flock mortality and hockburn data were obtained from information routinely collected on the farms and at abattoirs. Bayesian multivariate regression models were used to analyse data with all 4 optical flow descriptors as input variables, first day-by-day and then cumulatively using information from each day and all previous days. For both the UK and Swiss flocks, the cumulative regression showed that optical flow was significantly (p < 0.01) correlated with % total mortality (by day 1 for the UK flocks and by day 4 for the Swiss flocks). Optical flow was also significantly (p < 0.01) correlated with % birds with end-of-life hockburn (by day 3 for UK flocks and day 2 for Swiss flocks). This ability to distinguish between flocks that will have different final welfare outcomes when the birds are only a few days old is a particularly useful property of this system as it potentially provides farmers with an early warning of problem flocks that are still young enough for interventions to be possible. In conclusion, the optical flow patterns made by the movements of broiler chicken flocks were reliably correlated with two key welfare outcomes - mortality and hockburn - obtained by cumulating information over days as the birds grow. Differences between flocks became apparent within the first few days of life and were similar in the UK and Switzerland, despite differences in environment and management practices, suggesting that this approach to automated welfare assessment has the potential for widespread commercial use.

Bayesian multivariate models for case assessment in dynamic signature cases

Dynamic signatures are recordings of signatures made on digitizing devices such as tablet PCs. These handwritten signatures contain both dynamic and spatial information on every data point collected during the signature movement and can therefore be described in the form of multivariate data. The management of dynamic signatures represents a challenge for the forensic science community through its novelty and the volume of data available. Much as for static signatures, the authenticity of dynamic signatures may be doubted, which leads to a forensic examination of the unknown source signature.The Bayes’ factor, as measure of evidential support, can be assigned with statistical models to discriminate between competing propositions. In this respect, the limitations of existing probabilistic solutions to deal with dynamic signature evidence is pointed out and explained in detail. In particular, the necessity to remove the independence assumption between questioned and reference material is emphasized.

Bayesian Multivariate Mixed-Effects Location Scale Modeling of Longitudinal Relations Among Affective Traits, States, and Physical Activity.

Intensive longitudinal studies and experience sampling methods are becoming more common in psychology. While they provide a unique opportunity to ask novel questions about within-person processes relating to personality, there is a lack of methods specifically built to characterize the interplay between traits and states. We thus introduce a Bayesian multivariate mixed-effects location scale model (M-MELSM). The formulation can simultaneously model both personality traits (the location) and states (the scale) for multivariate data common to personality research. Variables can be included to predict either (or both) the traits and states, in addition to estimating random effects therein. This provides correlations between location and scale random effects, both across and within each outcome, which allows for characterizing relations between any number of personality traits and the corresponding states. We take a fully Bayesian approach, not only to make estimation possible, but also because it provides the necessary information for use in psychological applications such as hypothesis testing. To illustrate the model we use data from 194 individuals that provided daily ratings of negative and positive affect, as well as their physical activity in the form of step counts over 100 consecutive days. We describe the fitted model, where we emphasize, with visualization, the richness of information provided by the M-MELSM. We demonstrate Bayesian hypothesis testing for the correlations between the random effects. We conclude by discussing limitations of the MELSM in general and extensions to the M-MELSM specifically for personality research.

Multivariate Bayesian meta-analysis: joint modelling of multiple cancer types using summary statistics

BackgroundCancer atlases often provide estimates of cancer incidence, mortality or survival across small areas of a region or country. A recent example of a cancer atlas is the Australian cancer atlas (ACA), that provides interactive maps to visualise spatially smoothed estimates of cancer incidence and survival for 20 different cancer types over 2148 small areas across Australia.MethodsThe present study proposes a multivariate Bayesian meta-analysis model, which can model multiple cancers jointly using summary measures without requiring access to the unit record data. This new approach is illustrated by modelling the publicly available spatially smoothed standardised incidence ratios for multiple cancers in the ACA divided into three groups: common, rare/less common and smoking-related. The multivariate Bayesian meta-analysis models are fitted to each group in order to explore any possible association between the cancers in three remoteness regions: major cities, regional and remote areas across Australia. The correlation between the pairs of cancers included in each multivariate model for a group was examined by computing the posterior correlation matrix for each cancer group in each region. The posterior correlation matrices in different remoteness regions were compared using Jennrich’s test of equality of correlation matrices (Jennrich in J Am Stat Assoc. 1970;65(330):904–12. https://doi.org/10.1080/01621459.1970.10481133).ResultsSubstantive correlation was observed among some cancer types. There was evidence that the magnitude of this correlation varied according to remoteness of a region. For example, there has been significant negative correlation between prostate and lung cancer in major cities, but zero correlation found in regional and remote areas for the same pair of cancer types. High risk areas for specific combinations of cancer types were identified and visualised from the proposed model.ConclusionsPublicly available spatially smoothed disease estimates can be used to explore additional research questions by modelling multiple cancer types jointly. These proposed multivariate meta-analysis models could be useful when unit record data are unavailable because of privacy and confidentiality requirements.

A method for the taphonomic assessment of bone tools using 3D surface texture analysis of bone microtopography

Increasingly researchers have employed confocal microscopy and 3D surface texture analysis to assess bone surface modifications in an effort to understand ancient behavior. However, quantitative comparisons between the surfaces of purported archaeological bone tools and experimentally manufactured and used bones are complicated by taphonomic processes affecting ancient bone. Nonetheless, it may be reasonable to assume that bones within the same deposits are altered similarly and thus these alterations are quantifiable. Here we show how unworked bones can be used to quantify the taphonomic effect on bone surfaces and how this effect can then be controlled for and incorporated into an analysis for evaluating the modified surfaces of purported bone tools. To assess the baseline taphonomy of Middle Paleolithic archaeological deposits associated with typologically identified bone artifacts, specifically lissoirs, we directly compare the surface textures of ancient and modern unworked ribs. We then compare the ancient unworked ribs and lissoirs to assess their differences and predict the ancient artifacts’ original surface state using a multilevel multivariate Bayesian model. Our findings demonstrate that three of five tested surface texture parameters (Sa, Spc, and IsT) are useful for distinguishing surface type. Our model predictions show that lissoirs tend to be less rough, have more rounded surface peaks, and exhibit more directionally oriented surfaces. These characteristics are likely due to anthropogenic modifications and would have been more pronounced at deposition. Quantifying taphonomic alterations moves us one step closer to accurately assessing how bone artifacts were made and used in the ancient past.

Remodeling of brain morphology in temporal lobe epilepsy.

BackgroundMesial temporal lobe epilepsy (TLE) is one of the most widespread neurological network disorders. Computational anatomy MRI studies demonstrate a robust pattern of cortical volume loss. Most statistical analyses provide information about localization of significant focal differences in a segregationist way. Multivariate Bayesian modeling provides a framework allowing inferences about inter‐regional dependencies. We adopt this approach to answer following questions: Which structures within a pattern of dynamic epilepsy‐associated brain anatomy reorganization best predict TLE pathology. Do these structures differ between TLE subtypes?MethodsWe acquire clinical and MRI data from TLE patients with and without hippocampus sclerosis (n = 128) additional to healthy volunteers (n = 120). MRI data were analyzed in the computational anatomy framework of SPM12 using classical mass‐univariate analysis followed by multivariate Bayesian modeling.ResultsAfter obtaining TLE‐associated brain anatomy pattern, we estimate predictive power for disease and TLE subtypes using Bayesian model selection and comparison. We show that ipsilateral para‐/hippocampal regions contribute most to disease‐related differences between TLE and healthy controls independent of TLE laterality and subtype. Prefrontal cortical changes are more discriminative for left‐sided TLE, whereas thalamus and temporal pole for right‐sided TLE. The presence of hippocampus sclerosis was linked to stronger involvement of thalamus and temporal lobe regions; frontoparietal involvement was predominant in absence of sclerosis.ConclusionsOur topology inferences on brain anatomy demonstrate a differential contribution of structures within limbic and extralimbic circuits linked to main effects of TLE and hippocampal sclerosis. We interpret our results as evidence for TLE‐related spatial modulation of anatomical networks.

Changes of Occupational Noise-Induced Hearing Loss due to Working in the Steel Industry and Associated Effective Factors: Application of Bayesian Multivariate Multilevel Modeling using Skew Distribution : Rate of NIHL in Steel Workers

Background:There have been a limited number of studies on the relationships between time and occupational and demographical variables with the mean changes of low-frequency hearing (LFH) and high-frequency hearing (HFH). Objectives: This study investigated the rate of occupational noise-induced hearing loss (NIHL) due to working in the steel industry and associated effective factors. Materials and Methods: This historical cohort study was conducted within 2000 to 2010. Two LFH and HFH definitions of NIHL were used in this study. The average changes of LFH and HFL were considered the response variables. In addition, time and occupational (i.e., shift work and work experience) and demographical (i.e., age and educational level) variables were regarded as the independent variables. For data analysis, Bayesian multivariate multilevel modeling using skew distribution and OpenBUGS (version 3.2.2) and R (version 2.13.2) software were used in this study. Results: The present study was performed on 1,959 male workers with a mean age of 36.64±3.92 years. Among these subjects, 913 (46.6%), 134 (6.8%), and 912 (46.6%) participants were day workers, weekly-rotating shift workers, and routinely-rotating shift workers, respectively. The obtained results showed that age, work experience, educational level, and shift work had significant relationships with the changes of LFH and HFH. Conclusion:Overall, the findings of this 10-year historical cohort study demonstrated a relationship between time and demographical and occupational variables with the changes of LFH and HFL. Therefore, it is recommended to design preventive measures to reduce the deleterious effects of such variables on LFH and HFL.

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

Recent studies have developed univariate and bivariate Bayesian hierarchical extreme value models to improve traffic conflict-based crash estimation through addressing the issues of non-stationarity of conflict extremes and individual conflict indicators representing only partial severity aspects of a traffic event. Although the use of bivariate models showed considerable improvements compared to univariate models, two traffic conflict indicators may not be sufficient to cover all severity aspects of a traffic event. Therefore, a high dimensional multivariate Bayesian hierarchical extreme value model based on more than two conflict indicators merits further research. This study develops a multivariate Bayesian hierarchical extreme value modeling approach, which comprises a multivariate extreme value model and a Bayesian hierarchical structure. The former integrates several traffic conflict indicators in a unified framework, while the latter combines traffic conflicts from different sites, incorporating several covariates and site-specific unobserved heterogeneity. A model estimation approach for the multivariate Bayesian hierarchical extreme value model is proposed and applied to estimate rear-end crashes from four signalized intersections in the city of Surrey, British Columbia. The modified time to collision (MTTC), post encroachment time (PET), and deceleration rate to avoid a crash (DRAC) were employed as conflict indicators. Three covariates including traffic volume, shock wave area, and platoon ratio were considered to account for non-stationarity in conflict extremes. The results show that in terms of crash estimation accuracy, the high dimensional multivariate (e.g., trivariate) Bayesian hierarchical extreme value model outperforms both the low dimensional multivariate (e.g., bivariate) and univariate Bayesian hierarchical extreme value models. This is likely due to the multivariate model having the capability of sharing information across several different conflict indicators.

Aging Effects and Test-Retest Reliability of Inhibitory Control for Saccadic Eye Movements.

Neuropsychological studies indicate that healthy aging is associated with a decline of inhibitory control of attentional and behavioral systems. A widely accepted measure of inhibitory control is the antisaccade task that requires both the inhibition of a reflexive saccadic response toward a visual target and the initiation of a voluntary eye movement in the opposite direction. To better understand the nature of age-related differences in inhibitory control, we evaluated antisaccade task performance in 78 younger (20–35 years) and 78 older (60–80 years) participants. In order to provide reliable estimates of inhibitory control for individual subjects, we investigated test–retest reliability of the reaction time, error rate, saccadic gain, and peak saccadic velocity and further estimated latent, not directly observable processed contributing to changes in the antisaccade task execution. The intraclass correlation coefficients (ICCs) for an older group of participants emerged as good to excellent for most of our antisaccade task measures. Furthermore, using Bayesian multivariate models, we inspected age-related differences in the performances of healthy younger and older participants. The older group demonstrated higher error rates, longer reaction times, significantly more inhibition failures, and late prosaccades as compared with young adults. The consequently lower ability of older adults to voluntarily inhibit saccadic responses has been interpreted as an indicator of age-related inhibitory control decline. Additionally, we performed a Bayesian model comparison of used computational models and concluded that the Stochastic Early Reaction, Inhibition and Late Action (SERIA) model explains our data better than PRO-Stop-Antisaccade (PROSA) that does not incorporate a late decision process.

Risk Factors of Mortality among Male Patients with Cardiovascular Disease in Malaysia Using Bayesian Analysis.

Background:Identifying risk factors associated with mortality is important in providing better prognosis to patients. Consistent with that, Bayesian approach offers a great advantage where it rests on the assumption that all model parameters are random quantities and hence can incorporate prior knowledge. Therefore, we aimed to develop a reliable model to identify risk factors associated with mortality among ST-Elevation Myocardial Infarction (STEMI) male patients using Bayesian approach.Methods:A total of 7180 STEMI male patients from the National Cardiovascular Disease Database-Acute Coronary Syndrome (NCVD-ACS) registry for the years 2006–2013 were enrolled. In the development of univariate and multivariate logistic regression model for the STEMI patients, Bayesian Markov Chain Monte Carlo (MCMC) simulation approach was applied. The performance of the model was assessed through convergence diagnostics, overall model fit, model calibration and discrimination.Results:A set of six risk factors for cardiovascular death among STEMI male patients were identified from the Bayesian multivariate logistic model namely age, diabetes mellitus, family history of CVD, Killip class, chronic lung disease and renal disease respectively. Overall model fit, model calibration and discrimination were considered good for the proposed model.Conclusion:Bayesian risk prediction model for CVD male patients identified six risk factors associated with mortality. Among the highest risks were Killip class (OR=18.0), renal disease (2.46) and age group (OR=2.43) respectively.

Multi-response online parameter design based on Bayesian vector autoregression model

With the rapid development of the Internet of Things and sensor technology, some noise factors can be measured or estimated during operation and production. This paper develops a new multi-response optimization method that facilitates online parameter design by using the extra information available about observable noise factors. Bayesian multivariate regression model and Bayesian vector autoregressive model are used to consider the uncertainty of both the response model and the noise model. The Monte Carlo procedure is employed to obtain the predictions of multiple correlated noise factors from their posterior predictive distribution. The proposed method provides a convenient way to continuously update process settings during the production, which helps to further reduce the influence of the variability in the noise factor on product or process quality. Two examples are used to illustrate the effectiveness of the proposed method. The results show that the proposed method outperformance the offline parameter design and another online parameter design that does not consider model parameter uncertainty.

A Bayesian multivariate mixture model for skewed longitudinal data with intermittent missing observations: An application to infant motor development.

In studies of infant growth, an important research goal is to identify latent clusters of infants with delayed motor development-a risk factor for adverse outcomes later in life. However, there are numerous statistical challenges in modeling motor development: the data are typically skewed, exhibit intermittent missingness, and are correlated across repeated measurements over time. Using data from the Nurture study, a cohort of approximately 600 mother-infant pairs, we develop a flexible Bayesian mixture model for the analysis of infant motor development. First, we model developmental trajectories using matrix skew-normal distributions with cluster-specific parameters to accommodate dependence and skewness in the data. Second, we model the cluster-membership probabilities using a Pólya-Gamma data-augmentation scheme, which improves predictions of the cluster-membership allocations. Lastly, we impute missing responses from conditional multivariate skew-normal distributions. Bayesian inference is achieved through straightforward Gibbs sampling. Through simulation studies, we show that the proposed model yields improved inferences over models that ignore skewness or adopt conventional imputation methods. We applied the model to the Nurture data and identified two distinct developmental clusters, as well as detrimental effects of food insecurity on motor development. These findings can aid investigators in targeting interventions during this critical early-life developmental window.

Epidemiology of human papillomavirus-related oropharyngeal cancer in a classically low-burden region of southern Europe

The incidence of human papillomavirus (HPV)-related oropharyngeal cancer is increasing in some regions. Nevertheless, the epidemiology of this disease has not been extensively investigated in southern Europe. We conducted a retrospective cohort study of patients diagnosed with primary oropharyngeal cancer from 1991 to 2016. Cancer tissues underwent histopathological evaluation, DNA quality control, HPV-DNA detection and p16INK4a immunohistochemistry. Data were collected from medical records. Factors associated with HPV positivity and time trends were evaluated with multivariable Bayesian models. The adjusted prevalence of HPV-related cases in 864 patients with a valid HPV-DNA result was 9.7%, with HPV-DNA/p16INK4a double positivity being considered. HPV-related oropharyngeal cancer was likely to occur in non-smokers and non-drinkers, to be located in the tonsil or diagnosed at advanced stages. Time-trend analysis showed an increasing risk of HPV-related oropharyngeal cancer in the most recent periods (5-year period increase of 30%). This increase was highest and with a clear increasing trend only in the most recent years (2012–2016). The prevalence of HPV-related oropharyngeal cancer started to sharply increase in the most recent years in our setting, as occurred two decades ago in areas where most oropharyngeal cancer cases are currently HPV-related. Our results provide a comprehensive assessment of the epidemiological landscape of HPV-related oropharyngeal cancer in a region of southern Europe.

A Bayesian hierarchical model for characterizing the diffusion of new antipsychotic drugs.

New prescription medications are a primary driver of spending growth in the United States. For patients with severe mental illnesses, second-generation antipsychotic (SGA) medications feature prominently. However, many SGAs are costly, particularly before generic entry, and some may increase the risk of diabetes. Because physicians play a prominent role in new prescription adoption, understanding their prescribing behaviors is policy-relevant. Several features of prescription data, such as different antipsychotic choice sets over time, variable physician prescription volumes, and correlation among drug choices within physicians, complicate inferences. We propose a multivariate Bayesian hierarchical model with piecewise random effects to characterize the diffusion of new antipsychotic drugs. This model captures the complex prescriber-specific relationships among the different diffusion processes and takes advantage of the Bayesian paradigm to quantify uncertainty for all parameters straightforwardly. To evaluate the prescribing patterns for each physician, we propose various indices to identify early new SGA adopters. A sample of nearly 17,000 US physicians whose antipsychotic drug prescribing information was collected between January 1, 1997 and December 31, 2007 illustrates the methods. Determinants of high prescription rates and adoption speeds of new SGAs included physician sex, age, hospital affiliation, physician specialty, and office location. Large within- and between-provider variations in prescribing patterns of new SGAs were identified. Early adopters for one drug were not early adopters for anotherdrug.

Exploiting relationships between outcomes in Bayesian multivariate network meta-analysis with an application to relapsing-remitting multiple sclerosis.

In multivariate network meta-analysis (NMA), the piecemeal nature of the evidence base means that there may be treatment-outcome combinations for which no data is available. Most existing multivariate evidence synthesis models are either unable to estimate the missing treatment-outcome combinations, or can only do so under particularly strong assumptions, such as perfect between-study correlations between outcomes or constant effect size across outcomes. Many existing implementations are also limited to two treatments or two outcomes, or rely on model specification that is heavily tailored to the dimensions of the dataset. We present a Bayesian multivariate NMA model that estimates the missing treatment-outcome combinations via mappings between the population mean effects, while allowing the study-specific effects to be imperfectly correlated. The method is designed for aggregate-level data (rather than individual patient data) and is likely to be useful when modeling multiple sparsely reported outcomes, or when varying definitions of the same underlying outcome are adopted by different studies. We implement the model via a novel decomposition of the treatment effect variance, which can be specified efficiently for an arbitrary dataset given some basic assumptions regarding the correlation structure. The method is illustrated using data concerning the efficacy and liver-related safety of eight active treatments for relapsing-remitting multiple sclerosis. The results indicate that fingolimod and interferon beta-1b are the most efficacious treatments but also have some of the worst effects on liver safety. Dimethyl fumarate and glatiramer acetate perform reasonably on all of the efficacy and safety outcomes in the model.

Historic and recent trends in county-level coronary heart disease death rates by race, gender, and age group, United States, 1979-2017.

Given recent slowing of declines in national all-cause, heart disease, and stroke mortality, examining spatiotemporal distributions of coronary heart disease (CHD) death rates and trends can provide data critical to improving the cardiovascular health of populations. This paper documents county-level CHD death rates and trends by age group, race, and gender from 1979 through 2017. Using data from the National Vital Statistics System and a Bayesian multivariate space-time conditional autoregressive model, we estimated county-level age-standardized annual CHD death rates for 1979 through 2017 by age group (35-64 years, 65 years and older), race (white, black, other), and gender (men, women). We then estimated county-level total percent change in CHD death rates during four intervals (1979-1990, 1990-2000, 2000-2010, 2010-2017) using log-linear regression models. For all intervals, national CHD death rates declined for all groups. Prior to 2010, although most counties across age, race, and gender experienced declines, pockets of increasing CHD death rates were observed in the Mississippi Delta, Oklahoma, East Texas, and New Mexico across age groups and gender, and were more prominent among non-white populations than whites. Since 2010, across age, race, and gender, county-level declines in CHD death rates have slowed, with a marked increase in the percent of counties with increasing CHD death rates (e.g. 4.4% and 19.9% for ages 35 and older during 1979-1990 and 2010-2017, respectively). Recent increases were especially prevalent and geographically widespread among ages 35-64 years, with 40.5% of counties (95% CI: 38.4, 43.1) experiencing increases. Spatiotemporal differences in these long term, county-level results can inform responses by the public health community, medical providers, researchers, and communities to address troubling recent trends.

Root phenotypes at maturity in diverse wheat and triticale genotypes grown in three field experiments: Relationships to shoot selection, biomass, grain yield, flowering time, and environment

Abstract Modelling and limited data suggest that crops with deeper and longer roots capture more soil resources and yield more when water is available deeper in soil profiles. Interest has grown in the development of new cultivars with deeper roots. This study provides data from three field experiments to help researchers and breeders continue to assess the value of selecting for deeper roots for yield and water use efficiency gains. We asked: do genotype groups with shoot phenotypes easily selectable in pre-breeding programs express predictable root depth and length at time of grain harvest in the field? Do flowering time and shoot biomass predict deep roots measured directly in the field with coring, such that deeper roots are associated with more shoot growth and yield? Does genotype, including triticale versus wheat types, vary in rooting traits? Thirty-four wheats (Triticum aestivum L.) and two triticales (× Triticosecale) were drawn from ten ‘genotype groups’; selections from breeding programs and commercial cultivars that were distinguished on the basis of height, tillering, winter habit, and early vigour. These were grown at two independent sites and soil conditions in year 1 (experiment 1 and 2), with a subset of six wheats and two triticales repeated in year 2 at year 1 site (experiment 3). Above-ground biomass, flowering date, grain yield and root length and depth were measured with a high level of replication (four replicate plots and four soil cores per plot). Root length density was predicted from root counts obtained using the core-break method on 42 mm diameter, two m deep cores. A Bayesian multivariate mixed-effects model was used with fixed effects of the environment and random effects of genotype groups, genotypes and their interactions with the environment. Variation in rooting depth and length caused by environments was much larger than that caused by genotypes. Positive relationships between biomass, yield and root depth and length were observed across experiments and genotype groups (r = 0.62 for biomass and root depth, r = 0.61 for yield and root depth; r = 0.66 for biomass and root length, r = 0.53 for yield and root length), but the largest effects were driven by differences in soil and rainfall conditions between experiments. However, the smaller genetic effects on rooting depth and yield were positively correlated (r = 0.69). We did not find that easily selectable shoot traits like early vigour, tillering, and height reliably predicted in-field deeper rooting. Notably, the two triticales were 74 % more likely to have a deeper rooting and 82 % more likely to have less total root length, than spring wheats. We conclude that deeper and longer roots at maturity are (1) challenging to pre-select using shoot phenotype prior to field evaluation; (2) depend almost entirely on environment for expression in the field with small effects of genotype; and (3) can grow at no apparent 'cost' to shoot growth or yield and as such can remain a target for breeding.