Forecasting crashes at the planning level: Simultaneous negative binomial crash model applied in Tucson, Arizona

At least two important transportation planning activities rely on planning-level crash prediction models. One is motivated by the Transportation Equity Act for the 21st Century, which requires departments of transportation and metropolitan planning organizations to consider safety explicitly in the transportation planning process. The second could arise from a need for state agencies to establish incentive programs to reduce injuries and save lives. Both applications require a forecast of safety for a future period. Planning-level crash prediction models for the Tucson, Arizona, metropolitan region are presented to demonstrate the feasibility of such models. Data were separated into fatal, injury, and property-damage crashes. To accommodate overdispersion in the data, negative binomial regression models were applied. To accommodate the simultaneity of fatality and injury crash outcomes, simultaneous estimation of the models was conducted. All models produce crash forecasts at the traffic analysis zone level. Statistically significant (p-values < 0.05) and theoretically meaningful variables for the fatal crash model included population density, persons 17 years old or younger as a percentage of the total population, and intersection density. Significant variables for the injury and property-damage crash models were population density, number of employees, intersections density, percentage of miles of principal arterial, percentage of miles of minor arterials, and percentage of miles of urban collectors. Among several conclusions it is suggested that planning-level safety models are feasible and may play a role in future planning activities. However, caution must be exercised with such models.

Modeling crash outcome probabilities at rural intersections: Application of hierarchical binomial logistic models

It is important to examine the nature of the relationships between roadway, environmental, and traffic factors and motor vehicle crashes, with the aim to improve the collective understanding of causal mechanisms involved in crashes and to better predict their occurrence. Statistical models of motor vehicle crashes are one path of inquiry often used to gain these initial insights. Recent efforts have focused on the estimation of negative binomial and Poisson regression models (and related deviants) due to their relatively good fit to crash data. Of course analysts constantly seek methods that offer greater consistency with the data generating mechanism (motor vehicle crashes in this case), provide better statistical fit, and provide insight into data structure that was previously unavailable. One such opportunity exists with some types of crash data, in particular crash-level data that are collected across roadway segments, intersections, etc. It is argued in this paper that some crash data possess hierarchical structure that has not routinely been exploited. This paper describes the application of binomial multilevel models of crash types using 548 motor vehicle crashes collected from 91 two-lane rural intersections in the state of Georgia. Crash prediction models are estimated for angle, rear-end, and sideswipe (both same direction and opposite direction) crashes. The contributions of the paper are the realization of hierarchical data structure and the application of a theoretically appealing and suitable analysis approach for multilevel data, yielding insights into intersection-related crashes by crash type.

Generalized binomial Tau-leap method for biochemical kinetics incorporating both delay and intrinsic noise

The delay stochastic simulation algorithm (DSSA) by Barrio et al. [Plos Comput. Biol.2, 117–E (2006)] was developed to simulate delayed processes in cell biology in the presence of intrinsic noise, that is, when there are small-to-moderate numbers of certain key molecules present in a chemical reaction system. These delayed processes can faithfully represent complex interactions and mechanisms that imply a number of spatiotemporal processes often not explicitly modeled such as transcription and translation, basic in the modeling of cell signaling pathways. However, for systems with widely varying reaction rate constants or large numbers of molecules, the simulation time steps of both the stochastic simulation algorithm (SSA) and the DSSA can become very small causing considerable computational overheads. In order to overcome the limit of small step sizes, various τ-leap strategies have been suggested for improving computational performance of the SSA. In this paper, we present a binomial τ- DSSA method that extends the τ-leap idea to the delay setting and avoids drawing insufficient numbers of reactions, a common shortcoming of existing binomial τ-leap methods that becomes evident when dealing with complex chemical interactions. The resulting inaccuracies are most evident in the delayed case, even when considering reaction products as potential reactants within the same time step in which they are produced. Moreover, we extend the framework to account for multicellular systems with different degrees of intercellular communication. We apply these ideas to two important genetic regulatory models, namely, the hes1 gene, implicated as a molecular clock, and a Her1/Her 7 model for coupled oscillating cells.

Application of a new discreet form of Gauss’ theorem for measuring volume

Volume measurements are useful in many branches of science and medicine. They are usually accomplished by acquiring a sequence of cross sectional images through the object using an appropriate scanning modality, for example x-ray computed tomography (CT), magnetic resonance (MR) or ultrasound (US). In the cases of CT and MR, a dividing cubes algorithm can be used to describe the surface as a triangle mesh. However, such algorithms are not suitable for US data, especially when the image sequence is multiplanar (as it usually is). This problem may be overcome by manually tracing regions of interest (ROIs) on the registered multiplanar images and connecting the points into a triangular mesh. In this paper we describe and evaluate a new discreet form of Gauss’ theorem which enables the calculation of the volume of any enclosed surface described by a triangular mesh. The volume is calculated by summing the vector product of the centroid, area and normal of each surface triangle. The algorithm was tested on computer-generated objects, US-scanned balloons, livers and kidneys and CT-scanned clay rocks. The results, expressed as the mean percentage difference ± one standard deviation were 1.2 ± 2.3, 5.5 ± 4.7, 3.0 ± 3.2 and −1.2 ± 3.2% for balloons, livers, kidneys and rocks respectively. The results compare favourably with other volume estimation methods such as planimetry and tetrahedral decomposition.

Exploring the fundamental theorem of arithmetic in excel 2007

This paper discusses how fundamentals of number theory, such as unique prime factorization and greatest common divisor can be made accessible to secondary school students through spreadsheets. In addition, the three basic multiplicative functions of number theory are defined and illustrated through a spreadsheet environment. Primes are defined simply as those natural numbers with just two divisors. One focus of the paper is to show the ease with which spreadsheets can be used to introduce students to some basics of elementary number theory. Complete instructions are given to build a spreadsheet to enable the user to input a positive integer, either with a slider or manually, and see the prime decomposition. The spreadsheet environment allows students to observe patterns, gain structural insight, form and test conjectures, and solve problems in elementary number theory.

The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Exploratory spatial analysis of social and environmental factors associated with the incidence of Ross River Virus in Brisbane, Australia

We used geographic information systems and a spatial analysis approach to explore the pattern of Ross River virus (RRV) incidence in Brisbane, Australia. Climate, vegetation and socioeconomic data in 2001 were obtained from the Australian Bureau of Meteorology, the Brisbane City Council and the Australian Bureau of Statistics, respectively. Information on the RRV cases was obtained from the Queensland Department of Health. Spatial and multiple negative binomial regression models were used to identify the socioeconomic and environmental determinants of RRV transmission. The results show that RRV activity was primarily concentrated in the northeastern, northwestern, and southeastern regions in Brisbane. Multiple negative binomial regression models showed that the spatial pattern of RRV disease in Brisbane seemed to be determined by a combination of local ecologic, socioeconomic, and environmental factors.

Population Monte Carlo Algorithm in High Dimensions

The population Monte Carlo algorithm is an iterative importance sampling scheme for solving static problems. We examine the population Monte Carlo algorithm in a simplified setting, a single step of the general algorithm, and study a fundamental problem that occurs in applying importance sampling to high-dimensional problem. The precision of the computed estimate from the simplified setting is measured by the asymptotic variance of estimate under conditions on the importance function. We demonstrate the exponential growth of the asymptotic variance with the dimension and show that the optimal covariance matrix for the importance function can be estimated in special cases.

Latitude variation in pancreatic cancer mortality in Australia

Objectives: Ecological studies support the hypothesis that there is an association between vitamin D and pancreatic cancer (PaCa) mortality, but observational studies are somewhat conflicting. We sought to contribute further data to this issue by analyzing the differences in PaCa mortality across the eastern states of Australia and investigating if there is a role of vitamin D-effective ultraviolet radiation (DUVR), which is related to latitude. ---------- Methods: Mortality data from 1968 to 2005 were sourced from the Australian General Record of Incidence and Mortality books. Negative binomial models were fitted to calculate the association between state and PaCa mortality. Clear sky monthly DUVR in each capital city was also modeled. ---------- Results: Mortality from PaCa was 10% higher in southern states than in Queensland, with those in Victoria recording the highest mortality risk (relative risk, 1.13; 95% confidence interval, 1.09-1.17). We found a highly significant association between DUVR and PaCa mortality, with an estimated 1.5% decrease in the risk per 10-kJ/m2 increase in yearly DUVR. ---------- Conclusions: These data show an association between latitude, DUVR, and PaCa mortality. Although this study cannot be used to infer causality, it supports the need for further investigations of a possible role of vitamin D in PaCa etiology.

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.

Analysing Seasonal Health Data

Seasonal patterns have been found in a remarkable range of health conditions, including birth defects, respiratory infections and cardiovascular disease. Accurately estimating the size and timing of seasonal peaks in disease incidence is an aid to understanding the causes and possibly to developing interventions. With global warming increasing the intensity of seasonal weather patterns around the world, a review of the methods for estimating seasonal effects on health is timely. This is the first book on statistical methods for seasonal data written for a health audience. It describes methods for a range of outcomes (including continuous, count and binomial data) and demonstrates appropriate techniques for summarising and modelling these data. It has a practical focus and uses interesting examples to motivate and illustrate the methods. The statistical procedures and example data sets are available in an R package called ‘season’. Adrian Barnett is a senior research fellow at Queensland University of Technology, Australia. Annette Dobson is a Professor of Biostatistics at The University of Queensland, Australia. Both are experienced medical statisticians with a commitment to statistical education and have previously collaborated in research in the methodological developments and applications of biostatistics, especially to time series data. Among other projects, they worked together on revising the well-known textbook "An Introduction to Generalized Linear Models," third edition, Chapman Hall/CRC, 2008. In their new book they share their knowledge of statistical methods for examining seasonal patterns in health.