The use of Poisson regression in the sociological study of suicide

This paper explains how Poisson regression can be used in studies in which the dependent variable describes the number of occurrences of some rare event such as suicide. After pointing out why ordinary linear regression is inappropriate for treating dependent variables of this sort, we go on to present the basic Poisson regression model and show how it fits in the broad class of generalized linear models. Then we turn to discussing a major problem of Poisson regression known as overdispersion and suggest possible solutions, including the correction of standard errors and negative binomial regression. The paper ends with a detailed empirical example, drawn from our own research on suicide.

Development of safety performance functions for empirical Bayes estimation of crash reduction factors

Crash reduction factors (CRFs) are used to estimate the potential number of traffic crashes expected to be prevented from investment in safety improvement projects. The method used to develop CRFs in Florida has been based on the commonly used before-and-after approach. This approach suffers from a widely recognized problem known as regression-to-the-mean (RTM). The Empirical Bayes (EB) method has been introduced as a means to addressing the RTM problem. This method requires the information from both the treatment and reference sites in order to predict the expected number of crashes had the safety improvement projects at the treatment sites not been implemented. The information from the reference sites is estimated from a safety performance function (SPF), which is a mathematical relationship that links crashes to traffic exposure. The objective of this dissertation was to develop the SPFs for different functional classes of the Florida State Highway System. Crash data from years 2001 through 2003 along with traffic and geometric data were used in the SPF model development. SPFs for both rural and urban roadway categories were developed. The modeling data used were based on one-mile segments that contain homogeneous traffic and geometric conditions within each segment. Segments involving intersections were excluded. The scatter plots of data show that the relationships between crashes and traffic exposure are nonlinear, that crashes increase with traffic exposure in an increasing rate. Four regression models, namely, Poisson (PRM), Negative Binomial (NBRM), zero-inflated Poisson (ZIP), and zero-inflated Negative Binomial (ZINB), were fitted to the one-mile segment records for individual roadway categories. The best model was selected for each category based on a combination of the Likelihood Ratio test, the Vuong statistical test, and the Akaike's Information Criterion (AIC). The NBRM model was found to be appropriate for only one category and the ZINB model was found to be more appropriate for six other categories. The overall results show that the Negative Binomial distribution model generally provides a better fit for the data than the Poisson distribution model. In addition, the ZINB model was found to give the best fit when the count data exhibit excess zeros and over-dispersion for most of the roadway categories. While model validation shows that most data points fall within the 95% prediction intervals of the models developed, the Pearson goodness-of-fit measure does not show statistical significance. This is expected as traffic volume is only one of the many factors contributing to the overall crash experience, and that the SPFs are to be applied in conjunction with Accident Modification Factors (AMFs) to further account for the safety impacts of major geometric features before arriving at the final crash prediction. However, with improved traffic and crash data quality, the crash prediction power of SPF models may be further improved.

Visual impairment, postural stability and falls among older adults with glaucoma

Purpose: To investigate the impact of glaucomatous visual impairment on postural sway and falls among older adults.Methods: The sample comprised 72 community-dwelling older adults with open-angle glaucoma, aged 74.0 5.8 years (range 62 to 90 years). Measures of visual function included binocular visual acuity (high-contrast), binocular contrast sensitivity (Pelli- Robson) and binocular visual fields (merged monocular HFA 24-2 SITA-Std). Postural stability was assessed under four conditions: eyes open and closed, on a firm and on a foam surface. Falls were monitored for six months with prospective falls diaries. Regression models, adjusting for age and gender, examined the association between vision measures and postural stability (linear regression) and the number of falls (negative binomial regression). Results: Greater visual field loss was significantly associated with poorer postural stability with eyes open, both on firm (r = 0.34, p < 0.01) and foam (r = 0.45, p < 0.001) surfaces. Eighteen (25 per cent) participants experienced at least one fall: 12 (17 per cent) participants fell only once and six (eight per cent) participants fell two or more times (up to five falls). Visual field loss was significantly associated with falling; the rate of falls doubled for every 10 dB reduction in field sensitivity (rate ratio = 1.08, 95% CI = 1.02–1.13). Importantly, in a model comprising upper and lower field sensitivity, only lower field loss was significantly associated with the number of falls (rate ratio = 1.17, 95% CI = 1.04–1.33). Conclusions: Binocular visual field loss was significantly associated with postural instability and falls among older adults with glaucoma. These findings provide valuable directions for developing falls risk assessment and falls prevention strategies for this population.

Identifying large truck hot spots using crash counts and PDOEs

Large trucks are involved in a disproportionately small fraction of the total crashes but a disproportionately large fraction of fatal crashes. Large truck crashes often result in significant congestion due to their large physical dimensions and from difficulties in clearing crash scenes. Consequently, preventing large truck crashes is critical to improving highway safety and operations. This study identifies high risk sites (hot spots) for large truck crashes in Arizona and examines potential risk factors related to the design and operation of the high risk sites. High risk sites were identified using both state of the practice methods (accident reduction potential using negative binomial regression with long crash histories) and a newly proposed method using Property Damage Only Equivalents (PDOE). The hot spots identified via the count model generally exhibited low fatalities and major injuries but large minor injuries and PDOs, while the opposite trend was observed using the PDOE methodology. The hot spots based on the count model exhibited large AADTs, whereas those based on the PDOE showed relatively small AADTs but large fractions of trucks and high posted speed limits. Documented site investigations of hot spots revealed numerous potential risk factors, including weaving activities near freeway junctions and ramps, absence of acceleration lanes near on-ramps, small shoulders to accommodate large trucks, narrow lane widths, inadequate signage, and poor lighting conditions within a tunnel.

Inferior field loss increases rate of falls in older adults with glaucoma

PURPOSE: To examine the visual predictors of falls and injurious falls among older adults with glaucoma. METHODS: Prospective falls data were collected for 71 community-dwelling adults with primary open-angle glaucoma, mean age 73.9 ± 5.7 years, for one year using monthly falls diaries. Baseline assessment of central visual function included high-contrast visual acuity and Pelli-Robson contrast sensitivity. Binocular integrated visual fields were derived from monocular Humphrey Field Analyser plots. Rate ratios (RR) for falls and injurious falls with 95% confidence intervals (CIs) were based on negative binomial regression models. RESULTS: During the one year follow-up, 31 (44%) participants experienced at least one fall and 22 (31%) experienced falls that resulted in an injury. Greater visual impairment was associated with increased falls rate, independent of age and gender. In a multivariate model, more extensive field loss in the inferior region was associated with higher rate of falls (RR 1.57, 95%CI 1.06, 2.32) and falls with injury (RR 1.80, 95%CI 1.12, 2.98), adjusted for all other vision measures and potential confounding factors. Visual acuity, contrast sensitivity, and superior field loss were not associated with the rate of falls; topical beta-blocker use was also not associated with increased falls risk. CONCLUSIONS: Falls are common among older adults with glaucoma and occur more frequently in those with greater visual impairment, particularly in the inferior field region. This finding highlights the importance of the inferior visual field region in falls risk and assists in identifying older adults with glaucoma at risk of future falls, for whom potential interventions should be targeted. KEY WORDS: glaucoma, visual field, visual impairment, falls, injury

On the commonly accepted assumptions regarding observed motor vehicle crash counts at transport system locations

Readily accepted knowledge regarding crash causation is consistently omitted from efforts to model and subsequently understand motor vehicle crash occurrence and their contributing factors. For instance, distracted and impaired driving accounts for a significant proportion of crash occurrence, yet is rarely modeled explicitly. In addition, spatially allocated influences such as local law enforcement efforts, proximity to bars and schools, and roadside chronic distractions (advertising, pedestrians, etc.) play a role in contributing to crash occurrence and yet are routinely absent from crash models. By and large, these well-established omitted effects are simply assumed to contribute to model error, with predominant focus on modeling the engineering and operational effects of transportation facilities (e.g. AADT, number of lanes, speed limits, width of lanes, etc.) The typical analytical approach—with a variety of statistical enhancements—has been to model crashes that occur at system locations as negative binomial (NB) distributed events that arise from a singular, underlying crash generating process. These models and their statistical kin dominate the literature; however, it is argued in this paper that these models fail to capture the underlying complexity of motor vehicle crash causes, and thus thwart deeper insights regarding crash causation and prevention. This paper first describes hypothetical scenarios that collectively illustrate why current models mislead highway safety researchers and engineers. It is argued that current model shortcomings are significant, and will lead to poor decision-making. Exploiting our current state of knowledge of crash causation, crash counts are postulated to arise from three processes: observed network features, unobserved spatial effects, and ‘apparent’ random influences that reflect largely behavioral influences of drivers. It is argued; furthermore, that these three processes in theory can be modeled separately to gain deeper insight into crash causes, and that the model represents a more realistic depiction of reality than the state of practice NB regression. An admittedly imperfect empirical model that mixes three independent crash occurrence processes is shown to outperform the classical NB model. The questioning of current modeling assumptions and implications of the latent mixture model to current practice are the most important contributions of this paper, with an initial but rather vulnerable attempt to model the latent mixtures as a secondary contribution.

A national satellite-based land-use regression model for air pollution exposure assessment in Australia

Land-use regression (LUR) is a technique that can improve the accuracy of air pollution exposure assessment in epidemiological studies. Most LUR models are developed for single cities, which places limitations on their applicability to other locations. We sought to develop a model to predict nitrogen dioxide (NO2) concentrations with national coverage of Australia by using satellite observations of tropospheric NO2 columns combined with other predictor variables. We used a generalised estimating equation (GEE) model to predict annual and monthly average ambient NO2 concentrations measured by a national monitoring network from 2006 through 2011. The best annual model explained 81% of spatial variation in NO2 (absolute RMS error=1.4 ppb), while the best monthly model explained 76% (absolute RMS error=1.9 ppb). We applied our models to predict NO2 concentrations at the ~350,000 census mesh blocks across the country (a mesh block is the smallest spatial unit in the Australian census). National population-weighted average concentrations ranged from 7.3 ppb (2006) to 6.3 ppb (2011). We found that a simple approach using tropospheric NO2 column data yielded models with slightly better predictive ability than those produced using a more involved approach that required simulation of surface-to-column ratios. The models were capable of capturing within-urban variability in NO2, and offer the ability to estimate ambient NO2 concentrations at monthly and annual time scales across Australia from 2006–2011. We are making our model predictions freely available for research.

Bivariate genome-wide association study of genetically correlated neuroimaging phenotypes from DTI and MRI through a seemingly unrelated regression model

Large multisite efforts (e.g., the ENIGMA Consortium), have shown that neuroimaging traits including tract integrity (from DTI fractional anisotropy, FA) and subcortical volumes (from T1-weighted scans) are highly heritable and promising phenotypes for discovering genetic variants associated with brain structure. However, genetic correlations (rg) among measures from these different modalities for mapping the human genome to the brain remain unknown. Discovering these correlations can help map genetic and neuroanatomical pathways implicated in development and inherited risk for disease. We use structural equation models and a twin design to find rg between pairs of phenotypes extracted from DTI and MRI scans. When controlling for intracranial volume, the caudate as well as related measures from the limbic system - hippocampal volume - showed high rg with the cingulum FA. Using an unrelated sample and a Seemingly Unrelated Regression model for bivariate analysis of this connection, we show that a multivariate GWAS approach may be more promising for genetic discovery than a univariate approach applied to each trait separately.

Non-linear regression model for spatial variation in precipitation chemistry for South India

Chemical composition of rainwater changes from sea to inland under the influence of several major factors - topographic location of area, its distance from sea, annual rainfall. A model is developed here to quantify the variation in precipitation chemistry under the influence of inland distance and rainfall amount. Various sites in India categorized as 'urban', 'suburban' and 'rural' have been considered for model development. pH, HCO3, NO3 and Mg do not change much from coast to inland while, SO4 and Ca change is subjected to local emissions. Cl and Na originate solely from sea salinity and are the chemistry parameters in the model. Non-linear multiple regressions performed for the various categories revealed that both rainfall amount and precipitation chemistry obeyed a power law reduction with distance from sea. Cl and Na decrease rapidly for the first 100 km distance from sea, then decrease marginally for the next 100 km, and later stabilize. Regression parameters estimated for different cases were found to be consistent (R-2 similar to 0.8). Variation in one of the parameters accounted for urbanization. Model was validated using data points from the southern peninsular region of the country. Estimates are found to be within 99.9% confidence interval. Finally, this relationship between the three parameters - rainfall amount, coastline distance, and concentration (in terms of Cl and Na) was validated with experiments conducted in a small experimental watershed in the south-west India. Chemistry estimated using the model was in good correlation with observed values with a relative error of similar to 5%. Monthly variation in the chemistry is predicted from a downscaling model and then compared with the observed data. Hence, the model developed for rain chemistry is useful in estimating the concentrations at different spatio-temporal scales and is especially applicable for south-west region of India. (C) 2008 Elsevier Ltd. All rights reserved.

Land use regression model (LUR) for ultrafine particles in Brisbane

Traffic-related air pollution has been associated with a wide range of adverse health effects. One component of traffic emissions that has been receiving increasing attention is ultrafine particles(UFP, < 100 nm), which are of concern to human health due to their small diameters. Vehicles are the dominant source of UFP in urban environments. Small-scale variation in ultrafine particle number concentration (PNC) can be attributed to local changes in land use and road abundance. UFPs are also formed as a result of particle formation events. Modelling the spatial patterns in PNC is integral to understanding human UFP exposure and also provides insight into particle formation mechanisms that contribute to air pollution in urban environments. Land-use regression (LUR) is a technique that can use to improve the prediction of air pollution.

Fast and slow climate responses to CO2 and solar forcing: A linear multivariate regression model characterizing transient climate change

Climate change in response to a change in external forcing can be understood in terms of fast response to the imposed forcing and slow feedback associated with surface temperature change. Previous studies have investigated the characteristics of fast response and slow feedback for different forcing agents. Here we examine to what extent that fast response and slow feedback derived from time-mean results of climate model simulations can be used to infer total climate change. To achieve this goal, we develop a multivariate regression model of climate change, in which the change in a climate variable is represented by a linear combination of its sensitivity to CO2 forcing, solar forcing, and change in global mean surface temperature. We derive the parameters of the regression model using time-mean results from a set of HadCM3L climate model step-forcing simulations, and then use the regression model to emulate HadCM3L-simulated transient climate change. Our results show that the regression model emulates well HadCM3L-simulated temporal evolution and spatial distribution of climate change, including surface temperature, precipitation, runoff, soil moisture, cloudiness, and radiative fluxes under transient CO2 and/or solar forcing scenarios. Our findings suggest that temporal and spatial patterns of total change for the climate variables considered here can be represented well by the sum of fast response and slow feedback. Furthermore, by using a simple 1-D heat-diffusion climate model, we show that the temporal and spatial characteristics of climate change under transient forcing scenarios can be emulated well using information from step-forcing simulations alone.

Validation of a semi-Lagrangian, canonical regression model of climates in the southwestern United States

EXTRACT (SEE PDF FOR FULL ABSTRACT): A local climate model (LCM) has been developed to simulate the modern and 18 ka climate of the southwestern United States. ... LCM solutions indicate summers were about 1°C cooler and winters 11°C cooler at 18 ka. Annual PREC increased 68% at 18 ka, with large increases in spring and fall PREC and diminished summer monsoonal PREC. ... Validation of simulations of 18 ka climate indicate general agreement with proxy estimates of climate for that time. However, the LCM estimates of summer temperatures are about 5 to 10°C higher than estimates from proxy reconstructions.