Uncorrelated Heterogeneity Research Articles

Dynamical and combinatorial coding by MAPK p38 and NFκB in the inflammatory response of macrophages

Macrophages sense pathogens and orchestrate specific immune responses. Stimulus specificity is thought to be achieved through combinatorial and dynamical coding by signaling pathways. While NFκB dynamics are known to encode stimulus information, dynamical coding in other signaling pathways and their combinatorial coordination remain unclear. Here, we established live-cell microscopy to investigate how NFκB and p38 dynamics interface in stimulated macrophages. Information theory and machine learning revealed that p38 dynamics distinguish cytokine TNF from pathogen-associated molecular patterns and high doses from low, but contributed little to information-rich NFκB dynamics when both pathways are considered. This suggests that immune response genes benefit from decoding immune signaling dynamics or combinatorics, but not both. We found that the heterogeneity of the two pathways is surprisingly uncorrelated. Mathematical modeling revealed potential sources of uncorrelated heterogeneity in the branched pathway network topology and predicted it to drive gene expression variability. Indeed, genes dependent on both p38 and NFκB showed high scRNAseq variability and bimodality. These results identify combinatorial signaling as a mechanism to restrict NFκB-AND-p38-responsive inflammatory cytokine expression to few cells.

Bayesian Disease Mapping: A Literature Review With an Application, Using WinBugs Software

In this paper we review the improper and proper conditional autoregressive (CAR) models. A set of spatially correlated Gaussian random effects are assumed. The CAR model which contains components from both the uncorrelated heterogeneity (UH) and correlated heterogeneity (CH) models, have been applied to the South African acute pericarditis 2014 data set, where a Poisson model is used. Acute pericarditis is caused by an inflammation of the pericardium in the heart. The data set has been used to examine whether there is a significant difference between the proper conditional autoregressive prior and the intrinsic conditional autoregressive prior for the correlated heterogeneity component in a convolution model. Both the hyperpriors of the precision for the uncorrelated heterogeneity components were modelled by using the Jeffreys’ prior. The sensitivity of the hyperprior has also been investigated. The deaths from this disease in 2014 in South Africa have been considered, where disease maps and the relative risk of acquiring and dying from acute pericarditis have been investigated, as well as the standardised mortality ratio (SMR). The convergence and burn-in period of the models were assessed by the Brook-Gelman-Rubin (BGR) diagnostic. The deviance information criterion (DIC) was used to assess the models.

Interval Estimation for Age-Adjusted Rate Ratios Using Bayesian Convolution Model.

Spatial correlation raises challenges in estimating confidence intervals for region specific event rates and rate ratios between geographic units that are nested. Methods have been proposed to incorporate spatial correlation by assuming various distributions for the structure of autocorrelation patterns. However, the derivation of these statistics based on approximation may have to condition on the distributional assumption underlying the data generating process, which may not hold for certain situations. This paper explores the feasibility of utilizing a Bayesian convolution model (BCM), which includes an uncorrelated heterogeneity (UH) and a conditional autoregression (CAR) component to accommodate both uncorrelated and correlated spatial heterogeneity, to estimate the 95% confidence intervals for age-adjusted rate ratios among geographic regions with existing spatial correlations. A simulation study is conducted and a BCM method is applied to two cancer incidence datasets to calculate age-adjusted rate/ratio for the counties in the State of Kentucky relative to the entire state. In comparison to three existing methods, without and with spatial correlation, the Bayesian convolution model-based estimation provides moderate shrinkage effect for the point estimates based on the neighbor structure across regions and produces a wider interval due to the inclusion of uncertainty in the spatial autocorrelation parameters. The overall spatial pattern of region incidence rate from BCM approach appears to be like the direct estimates and other methods for both datasets, even though “smoothing” occurs in some local regions. The Bayesian Convolution Model allows flexibility in the specification of risk components and can improve the accuracy of interval estimates of age-adjusted rate ratios among geographical regions as it considers spatial correlation.

Joint Estimation of Relative Risk for Dengue and Zika Infections, Colombia, 2015-2016.

We jointly estimated relative risk for dengue and Zika virus disease (Zika) in Colombia, establishing the spatial association between them at the department and city levels for October 2015–December 2016. Cases of dengue and Zika were allocated to the 87 municipalities of 1 department and the 293 census sections of 1 city in Colombia. We fitted 8 hierarchical Bayesian Poisson joint models of relative risk for dengue and Zika, including area- and disease-specific random effects accounting for several spatial patterns of disease risk (clustered or uncorrelated heterogeneity) within and between both diseases. Most of the dengue and Zika high-risk municipalities varied in their risk distribution; those for Zika were in the northern part of the department and dengue in the southern to northeastern parts. At city level, spatially clustered patterns of dengue high-risk census sections indicated Zika high-risk areas. This information can be used to inform public health decision making.

Simulation of Channelized Gas Flow Pattern in Heterogeneous Porous Media: A Feasibility Study of Continuum Simulation at Bench Scale

Core Ideas A continuum model can predict quantitative and qualitative properties of gas flow patterns. Correlated spatial variability can capture dynamic features of gas flow channels. Connectivity metrics, like Euler number, provide a practical method for quantifying gas channels. In remediation technologies, air or O2 gas is injected into a polluted aquifer to remove organic contaminants. A gas injection process is also applied in enhanced oil recovery and CO2 sequestration. The wide range of gas injection processes into porous media necessitates accurate gas flow modeling. The focus of this study was to determine whether a continuum model with stochastic parameters can represent the properties of gas flow patterns. We applied stochastic heterogeneity in TOUGH2 simulation and used the experimental observations to validate simulation results. We created two types of stochastic heterogeneity: correlated heterogeneity, generated by an assigned covariance function, and uncorrelated heterogeneity, which distributes uniformly. We used Euler characteristics to quantify the gas channel properties and to determine whether the heterogeneity applied in a continuum model can represent gas channel properties. The results of this investigation confirm that the continuum model, which includes correlated heterogeneity, can predict the quantitative properties of gas flow, such as gas volume. Also, it can create gas channels that have Euler characteristics close to those obtained by experimental observation. In conclusion, the continuum model can predict the properties of gas flow if the spatial variability and correlation structure of the characteristic properties applied to the model are representative of the medium.

Anomalous elasticity, fluctuations and disorder in elastic membranes

Motivated by freely suspended graphene and polymerized membranes in soft and biological matter we present a detailed study of a tensionless elastic sheet in the presence of thermal fluctuations and quenched disorder. The manuscript is based on an extensive draft dating back to 1993, that was circulated privately. It presents the general theoretical framework and calculational details of numerous results, partial forms of which have been published in brief Letters (Le Doussal and Radzihovsky, 1992; 1993). The experimental realization atom-thin graphene sheets (Novoselov et al., 2004) have driven a resurgence in this fascinating subject, making our dated predictions and their detailed derivations timely. To this end we analyze the statistical mechanics of a generalized D-dimensional elastic “membrane” embedded in d dimensions using a self-consistent screening approximation (SCSA), that has proved to be unprecedentedly accurate in this system, exact in three complementary limits: (i) d→∞, (ii) D→4, and (iii) D=d. Focusing on the critical “flat” phase, for a homogeneous two-dimensional (D=2) membrane embedded in three dimensions (d=3), we predict its universal roughness exponent ζ=0.590, length-scale dependent elastic moduli exponents η=0.821 and ηu=0.358, and an anomalous Poisson ratio, σ=−1∕3. In the presence of random uncorrelated heterogeneity the membrane exhibits a glassy wrinkled ground state, characterized by ζ′=0.775,η′=0.449,ηu′=1.101 and a Poisson ratio σ′=−1∕3. Motivated by a number of physical realizations (charged impurities, disclinations and dislocations) we also study power-law correlated quenched disorder that leads to a variety of distinct glassy wrinkled phases. Finally, neglecting self-avoiding interaction we demonstrate that at high temperature a “phantom” sheet undergoes a continuous crumpling transition, characterized by a radius of gyration exponent, ν=0.732 and η=0.535. Many of these universal predictions have received considerable support from simulations. We hope that this detailed presentation of the SCSA theory will be useful to further theoretical developments and corresponding experimental investigations on freely suspended graphene.

A segment level analysis of multi-vehicle motorcycle crashes in Ohio using Bayesian multi-level mixed effects models

Multi-vehicle motorcycle crashes combine elements of design, behavior, and traffic. One challenge with working with motorcycle data are the inherit difficulties associated with missing data – such as motorcycle-specific: vehicle miles traveled (VMT) and average daily traffic (ADT). To address the challenges of the missing data, a random effects Bayesian negative binomial model is developed for the state of Ohio. In this study, the random effect terms improve the general model by describing the spatial correlation with fixed effects, the neighborhood criteria, and the uncorrelated heterogeneity for all the multi-vehicle motorcycle crashes that occurred on the 32,289 state-maintained roadway segments in Ohio. Some key findings from this study include regional data improves the goodness-of-fit, and further improvement of the models may be gained through a distance-based neighborhood specification of conditional autoregressive (CAR). In addition to the model improvement using the random effect terms, key variables such as smaller lane and shoulder widths, increases in the horizontal degree of curvature and increases in the maximum vertical grade will increase the prediction of a crash.

Evaluation of putative hazard tests under background risk heterogeneity

AbstractIn this paper, an evaluation of some tests for adverse health effects around fixed locations (putative hazard sites) is made. We address the situation where a heterogeneous background is included both in terms of correlated and uncorrelated heterogeneity (UH). In addition, we examine a set of tests for case event data (residential case addresses) including both distance and directional effects. The tests include distance and directional score tests (DIR), integrated intensity tests, the Besag & Newell (BES) test, and Kulldorff's focus clustering scan test. Monte Carlo power of the tests is evaluated and power curves are finally presented. Interesting results from this work include the lack of power found when correlated heterogeneity (CH) is present. This is not found with UH. The BES and Scan tests have lower power than the integrated intensity tests and score tests in general. The integrated intensity test demonstrates its omnibus ability to detect either distance or directional effects. Copyright © 2008 John Wiley & Sons, Ltd.

Modelling area-wide count outcomes with spatial correlation and heterogeneity: An analysis of London crash data

Count models such as negative binomial (NB) regression models are normally employed to establish a relationship between area-wide traffic crashes and the contributing factors. Since crash data are collected with reference to location measured as points in space, spatial dependence exists among the area-level crash observations. Although NB models can take account of the effect of unobserved heterogeneity (due to omitted variables in the model) among neighbourhoods, such models may not account for spatial correlation areas. It is then essential to adopt an econometric model that takes account of both spatial dependence and uncorrelated heterogeneity simultaneously among neighbouring units. In studying the spatial pattern of traffic crashes, two types of spatial models may be employed: (i) classical spatial models for higher levels of spatial aggregation such as states, counties, etc. and (ii) Bayesian hierarchical models for all spatial units, especially for smaller scale area-aggregations. Therefore, the primary objectives of this paper is to develop a series of relationships between area-wide different traffic casualties and the contributing factors associated with ward characteristics using both non-spatial models (such as NB models) and spatial models and to identify the similarities and differences among these relationships. The spatial units of the analysis are the 633 census wards from the Greater London metropolitan area. Ward-level casualty data are disaggregated by severity of the casualty (such as fatalities, serious injuries, and slight injuries) and by severity of the casualty related to various road users. The analysis implies that different ward-level factors affect traffic casualties differently. The results also suggest that Bayesian hierarchical models are more appropriate in developing a relationship between area-wide traffic crashes and the contributing factors associated with the road infrastructure, socioeconomic and traffic conditions of the area. This is because Bayesian models accurately take account of both spatial dependence and uncorrelated heterogeneity.

Characterizing Spatial and Environmental Determinants of Prostate Cancer Using a Geographic Information System

ISEE-652 Objective: Prostate cancer (PrCA) incidence in South Carolina (SC) exceeds the national average, particularly among African Americans (AAs). A Geographic Information System (GIS) was used to evaluate spatial and environmental determinants of PrCA in SC, a cancer for which there are few established risk factors. Materials and Methods: Age-adjusted PrCA incidence, standardized incidence ratios (SIRs), and 95% confidence intervals were calculated for census tracts using SC Central Cancer Registry data (1996–2002). Demographic data (groundwater consumption, age, race, median income, land use) were obtained from census data. Metal concentrations in groundwater and soil were obtained from existing federal and state databases to test hypotheses that zinc and selenium are protective, and that cadmium and uranium increase PrCA incidence. Census tract-specific exposure estimates included: geometric mean groundwater and soil metal concentrations, proportion of samples exceeding background, and census tract-centroid concentration obtained via spatial modeling (kriging). A GIS was used to map incidence rates, SIRs, and exposures. Statistical procedures (linear and Poisson regression) were applied with and without censoring of tracts with <50% groundwater consumption per capita (N = 173 and 854, respectively). An adjacency matrix was generated and spatial statistical models were performed using WinBUGS software, with adjustment for correlated and uncorrelated heterogeneity. Results: There were 18,091 PrCA cases; 30% AA and 69% European American. Among uncensored tracts with elevated groundwater zinc, 7 had PrCA rates below expected incidence, and this inverse relationship also was observed using linear regression (P = 0.02). There were 96 census tracts with both elevated soil selenium concentrations and reduced SIRs. Three tracts had both elevated soil cadmium and higher SIRs. Conclusions: A decreasing trend in PrCA rates was observed among SC census tracts with elevated zinc in soil or groundwater. Relationships between environmental factors and cancer incidence can be efficiently explored using GIS, spatial statistics, and existing population databases.

Evaluation of Bayesian models for focused clustering in health data

AbstractThis paper examines the ability of Bayesian hierarchical models to recover evidence of disease risk excess around a fixed location. This location can be a putative source of health hazard, such as an incinerator, mobile phone mast or dump site. While Bayesian models are convenient to use for modeling, it is useful to consider how well these models perform in the true risk scenarios. In what follows, we evaluate the ability of these models to recover the true risk under simulation. It is surprising that the resulting posterior parameters estimates are heavily biased. Using the credible intervals for distance decline parameter to assess ‘coverage or power’ of detecting distance effect, the ‘power’ decreases with increasing correlation in the background population effect. The inclusion of correlated heterogeneity in models does affect the ability of the models to detect the stronger distance decline scenarios. The uncorrelated heterogeneity seems little affect this ability however. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Spatial distribution of Escherichia coli O157-positive farms in Scotland

Using a sample of 949 Scottish farms with finishing cattle, the spatial distribution of Escherichia coli O157-positive farms was investigated using disease mapping models. The overall prevalence of E. coli O157-positive farms was estimated as 22%. The regions used in this study were the 16 postcode areas of Scotland. For each region, the posterior relative risk (RR) was estimated as a model-based alternative to the saturated standardized morbidity ratio (SMR), i.e., the ratio between observed and expected cases in a region. Three Bayesian hierarchical models with generalized linear modeling of the area-specific risks were used to estimate the posterior relative risk of E. coli O157-positive farms in the postcode areas: a random-effects model incorporating only spatially uncorrelated heterogeneity; a model incorporating both spatially correlated and uncorrelated heterogeneity; and a pseudo-mixture model with unstructured correlation and a weighted mix of two variance components representing the spatial correlation and a jump structure. None of the models identified any areas with a significant increase or decrease in risk. The deviance information criteria slightly favored the simplest model (RR range: 0.92–1.09). However, this model appeared to smooth out more of the variation in the RR compared to the pseudo-mixture model, which gave a more informative pattern of the posterior relative risks (range: 0.81–1.22).