Space-time variation of malaria incidence in Yunnan province, China

Abstract Background Understanding spatio-temporal variation in malaria incidence provides a basis for effective disease control planning and monitoring. Methods Monthly surveillance data between 1991 and 2006 for Plasmodium vivax and Plasmodium falciparum malaria across 128 counties were assembled for Yunnan, a province of China with one of the highest burdens of malaria. County-level Bayesian Poisson regression models of incidence were constructed, with effects for rainfall, maximum temperature and temporal trend. The model also allowed for spatial variation in county-level incidence and temporal trend, and dependence between incidence in June–September and the preceding January–February. Results Models revealed strong associations between malaria incidence and both rainfall and maximum temperature. There was a significant association between incidence in June–September and the preceding January–February. Raw standardised morbidity ratios showed a high incidence in some counties bordering Myanmar, Laos and Vietnam, and counties in the Red River valley. Clusters of counties in south-western and northern Yunnan were identified that had high incidence not explained by climate. The overall trend in incidence decreased, but there was significant variation between counties. Conclusion Dependence between incidence in summer and the preceding January–February suggests a role of intrinsic host-pathogen dynamics. Incidence during the summer peak might be predictable based on incidence in January–February, facilitating malaria control planning, scaled months in advance to the magnitude of the summer malaria burden. Heterogeneities in county-level temporal trends suggest that reductions in the burden of malaria have been unevenly distributed throughout the province.

Determinants of pre-hospital care non-usage for patients with emergency care needs [including commentary by Snooks H.]

Objective-To establish the demographic, health status and insurance determinants of pre-hospital ambulance non-usage for patients with emergency medical needs. Methods-Triage category, date of birth, sex, marital status, country of origin, method and time of arrival, ambulance insurance status, diagnosis, and disposal were collected for all patients who presented over a four month period (n=10 229) to the emergency department of a major provincial hospital. Data for patients with urgent (n=678) or critical care needs (n=332) who did not use pre-hospital care were analysed using Poisson regression. Results-Only a small percentage (6.6%) of the total sample were triaged as having urgent medical needs or critical care needs (3.2%). Predictors of usage for those with urgent care needs included age greater than 65 years (prevalence ratio (PR)=0.54; 95% confidence interval (CI)= 0.35 to 0.83), being admitted to intensive care or transferred to another hospital (PR=0.62; 95% CI=0.44 to 0.89) or ward (PR=0.72; 95% CI=0.56 to 0.93) and ambulance insurance status (PR=0.67; 95% CI=052 to 0.86). Sex, marital status, time of day and country of origin were not predictive of usage and non-usage. Predictors of usage for those with critical care needs included age 65 years or greater (PR=0.45; 95% CI=0.25 to 0.81) and a diagnosis of trauma (PR=0.49; 95% CI=0.26 to 0.92). A non-English speaking background was predictive of non-usage (PR=1.98; 95% CI=1.06 to 3.70). Sex, marital status, time of day, triage and ambulance insurance status were not predictive of non-usage. Conclusions-Socioeconomic and medical factors variously influence ambulance usage depending on the severity or urgency of the medical condition. Ambulance insurance status was less of an influence as severity of condition increased suggesting that, at a critical level of urgency, patients without insurance are willing to pay for a pre-hospital ambulance service.

Vision, functional and cognitive determinants of motor vehicle incidents in older drivers

Background: The proportion of older individuals in the driving population is predicted to increase in the next 50 years. This has important implications for driving safety as abilities which are important for safe driving, such as vision (which accounts for the majority of the sensory input required for driving), processing ability and cognition have been shown to decline with age. The current methods employed for screening older drivers upon re-licensure are also vision based. This study, which investigated social, behavioural and professional aspects involved with older drivers, aimed to determine: (i) if the current visual standards in place for testing upon re-licensure are effective in reducing the older driver fatality rate in Australia; (ii) if the recommended visual standards are actually implemented as part of the testing procedures by Australian optometrists; and (iii) if there are other non-standardised tests which may be better at predicting the on-road incident-risk (including near misses and minor incidents) in older drivers than those tests recommended in the standards. Methods: For the first phase of the study, state-based age- and gender-stratified numbers of older driver fatalities for 2000-2003 were obtained from the Australian Transportation Safety Bureau database. Poisson regression analyses of fatality rates were considered by renewal frequency and jurisdiction (as separate models), adjusting for possible confounding variables of age, gender and year. For the second phase, all practising optometrists in Australia were surveyed on the vision tests they conduct in consultations relating to driving and their knowledge of vision requirements for older drivers. Finally, for the third phase of the study to investigate determinants of on-road incident risk, a stratified random sample of 600 Brisbane residents aged 60 years and were selected and invited to participate using an introductory letter explaining the project requirements. In order to capture the number and type of road incidents which occurred for each participant over 12 months (including near misses and minor incidents), an important component of the prospective research study was the development and validation of a driving diary. The diary was a tool in which incidents that occurred could be logged at that time (or very close in time to which they occurred) and thus, in comparison with relying on participant memory over time, recall bias of incident occurrence was minimised. Association between all visual tests, cognition and scores obtained for non-standard functional tests with retrospective and prospective incident occurrence was investigated. Results: In the first phase,rivers aged 60-69 years had a 33% lower fatality risk (Rate Ratio [RR] = 0.75, 95% CI 0.32-1.77) in states with vision testing upon re-licensure compared with states with no vision testing upon re-licensure, however, because the CIs are wide, crossing 1.00, this result should be regarded with caution. However, overall fatality rates and fatality rates for those aged 70 years and older (RR=1.17, CI 0.64-2.13) did not differ between states with and without license renewal procedures, indicating no apparent benefit in vision testing legislation. For the second phase of the study, nearly all optometrists measured visual acuity (VA) as part of a vision assessment for re-licensing, however, 20% of optometrists did not perform any visual field (VF) testing and only 20% routinely performed automated VF on older drivers, despite the standards for licensing advocating automated VF as part of the vision standard. This demonstrates the need for more effective communication between the policy makers and those responsible for carrying out the standards. It may also indicate that the overall higher driver fatality rate in jurisdictions with vision testing requirements is resultant as the tests recommended by the standards are only partially being conducted by optometrists. Hence a standardised protocol for the screening of older drivers for re-licensure across the nation must be established. The opinions of Australian optometrists with regard to the responsibility of reporting older drivers who fail to meet the licensing standards highlighted the conflict between maintaining patient confidentiality or upholding public safety. Mandatory reporting requirements of those drivers who fail to reach the standards necessary for driving would minimise potential conflict between the patient and their practitioner, and help maintain patient trust and goodwill. The final phase of the PhD program investigated the efficacy of vision, functional and cognitive tests to discriminate between at-risk and safe older drivers. Nearly 80% of the participants experienced an incident of some form over the prospective 12 months, with the total incident rate being 4.65/10 000 km. Sixty-three percent reported having a near miss and 28% had a minor incident. The results from the prospective diary study indicate that the current vision screening tests (VA and VF) used for re-licensure do not accurately predict older drivers who are at increased odds of having an on-road incident. However, the variation in visual measurements of the cohort was narrow, also affecting the results seen with the visual functon questionnaires. Hence a larger cohort with greater variability should be considered for a future study. A slightly lower cognitive level (as measured with the Mini-Mental State Examination [MMSE]) did show an association with incident involvement as did slower reaction time (RT), however the Useful-Field-of-View (UFOV) provided the most compelling results of the study. Cut-off values of UFOV processing (>23.3ms), divided attention (>113ms), selective attention (>258ms) and overall score (moderate/ high/ very high risk) were effective in determining older drivers at increased odds of having any on-road incident and the occurrence of minor incidents. Discussion: The results have shown that for the 60-69 year age-group, there is a potential benefit in testing vision upon licence renewal. However, overall fatality rates and fatality rates for those aged 70 years and older indicated no benefit in vision testing legislation and suggests a need for inclusion of screening tests which better predict on-road incidents. Although VA is routinely performed by Australian optometrists on older drivers renewing their licence, VF is not. Therefore there is a need for a protocol to be developed and administered which would result in standardised methods conducted throughout the nation for the screening of older drivers upon re-licensure. Communication between the community, policy makers and those conducting the protocol should be maximised. By implementing a standardised screening protocol which incorporates a level of mandatory reporting by the practitioner, the ethical dilemma of breaching patient confidentiality would also be resolved. The tests which should be included in this screening protocol, however, cannot solely be ones which have been implemented in the past. In this investigation, RT, MMSE and UFOV were shown to be better determinants of on-road incidents in older drivers than VA and VF, however, as previously mentioned, there was a lack of variability in visual status within the cohort. Nevertheless, it is the recommendation from this investigation, that subject to appropriate sensitivity and specificity being demonstrated in the future using a cohort with wider variation in vision, functional performance and cognition, these tests of cognition and information processing should be added to the current protocol for the screening of older drivers which may be conducted at licensing centres across the nation.

How does ambulance service utilisation impact demand for Emergency Departments in Queensland, Australia?

Background: There are indications that pre-hospital emergency care and management of patients can help reduce the demand for hospital emergency departments (EDs). Ambulance services play a significant role at this stage of care. In 2003, the Queensland Government introduced a Community Ambulance Cover (CAC) levy in return for a free ambulance service at the point of access to all Queenslanders. This may have led to the impression in consumers of an entitlement to free ambulance services under any circumstances regardless of the urgency of the matter which may have in turn contributed to the crowding of EDs in Queensland. Objectives: This paper aims to answer the following questions: - How many patients arrive at hospital EDs by ambulance in Queensland, compared to other modes of arrival? - How has this changed over time, particularly after the CAC introduction in 2003? What percentage of ambulance arrivals are urgent ED patients? - Has the perceived free ambulance services created extra demand for EDs in Queensland, compared with other Australian jurisdictions that charge patients for ambulance services? Methods: We will secondary analyse the data from sources such as Queensland Ambulance Services, Department of Health and Australian Bureau of Statistics to answer the research questions. Findings and Conclusions Queensland has the highest utilization rate of ambulance services (about 18% in 2007-08) and the highest annual growth rate in demand for these services (7.7% on average since 2000-01), well above the population growth. On the other hand, the proportion of ED patients arriving by ambulance in Queensland has increased by about 4% annually. However, when compared with other states and territories with charge at the point of access, it seems that the growth in demand for EDs cannot be explained solely or mainly by CAC or ambulance utilisation in Queensland.

Krylov subspace methods for approximating functions of symmetric positive definite matrices with applications to applied statistics and anomalous diffusion

Matrix function approximation is a current focus of worldwide interest and finds application in a variety of areas of applied mathematics and statistics. In this thesis we focus on the approximation of A^(-α/2)b, where A ∈ ℝ^(n×n) is a large, sparse symmetric positive definite matrix and b ∈ ℝ^n is a vector. In particular, we will focus on matrix function techniques for sampling from Gaussian Markov random fields in applied statistics and the solution of fractional-in-space partial differential equations. Gaussian Markov random fields (GMRFs) are multivariate normal random variables characterised by a sparse precision (inverse covariance) matrix. GMRFs are popular models in computational spatial statistics as the sparse structure can be exploited, typically through the use of the sparse Cholesky decomposition, to construct fast sampling methods. It is well known, however, that for sufficiently large problems, iterative methods for solving linear systems outperform direct methods. Fractional-in-space partial differential equations arise in models of processes undergoing anomalous diffusion. Unfortunately, as the fractional Laplacian is a non-local operator, numerical methods based on the direct discretisation of these equations typically requires the solution of dense linear systems, which is impractical for fine discretisations. In this thesis, novel applications of Krylov subspace approximations to matrix functions for both of these problems are investigated. Matrix functions arise when sampling from a GMRF by noting that the Cholesky decomposition A = LL^T is, essentially, a `square root' of the precision matrix A. Therefore, we can replace the usual sampling method, which forms x = L^(-T)z, with x = A^(-1/2)z, where z is a vector of independent and identically distributed standard normal random variables. Similarly, the matrix transfer technique can be used to build solutions to the fractional Poisson equation of the form ϕn = A^(-α/2)b, where A is the finite difference approximation to the Laplacian. Hence both applications require the approximation of f(A)b, where f(t) = t^(-α/2) and A is sparse. In this thesis we will compare the Lanczos approximation, the shift-and-invert Lanczos approximation, the extended Krylov subspace method, rational approximations and the restarted Lanczos approximation for approximating matrix functions of this form. A number of new and novel results are presented in this thesis. Firstly, we prove the convergence of the matrix transfer technique for the solution of the fractional Poisson equation and we give conditions by which the finite difference discretisation can be replaced by other methods for discretising the Laplacian. We then investigate a number of methods for approximating matrix functions of the form A^(-α/2)b and investigate stopping criteria for these methods. In particular, we derive a new method for restarting the Lanczos approximation to f(A)b. We then apply these techniques to the problem of sampling from a GMRF and construct a full suite of methods for sampling conditioned on linear constraints and approximating the likelihood. Finally, we consider the problem of sampling from a generalised Matern random field, which combines our techniques for solving fractional-in-space partial differential equations with our method for sampling from GMRFs.

A robust reactive scheduling model for intensive care units

The ICU is an integral part of any hospital and is under great load from patient arrivals as well as resource limitations. Scheduling of patients in the ICU is complicated by the two general types; elective surgery and emergency arrivals. This complicated situation is handled by creating a tentative initial schedule and then reacting to uncertain arrivals as they occur. For most hospitals there is little or no flexibility in the number of beds that are available for use now or in the future. We propose an integer programming model to handle a parallel machine reacting system for scheduled and unscheduled arrivals.

Socio-environmental factors and suicide in Queensland, Australia

Suicide has drawn much attention from both the scientific community and the public. Examining the impact of socio-environmental factors on suicide is essential in developing suicide prevention strategies and interventions, because it will provide health authorities with important information for their decision-making. However, previous studies did not examine the impact of socio-environmental factors on suicide using a spatial analysis approach. The purpose of this study was to identify the patterns of suicide and to examine how socio-environmental factors impact on suicide over time and space at the Local Governmental Area (LGA) level in Queensland. The suicide data between 1999 and 2003 were collected from the Australian Bureau of Statistics (ABS). Socio-environmental variables at the LGA level included climate (rainfall, maximum and minimum temperature), Socioeconomic Indexes for Areas (SEIFA) and demographic variables (proportion of Indigenous population, unemployment rate, proportion of population with low income and low education level). Climate data were obtained from Australian Bureau of Meteorology. SEIFA and demographic variables were acquired from ABS. A series of statistical and geographical information system (GIS) approaches were applied in the analysis. This study included two stages. The first stage used average annual data to view the spatial pattern of suicide and to examine the association between socio-environmental factors and suicide over space. The second stage examined the spatiotemporal pattern of suicide and assessed the socio-environmental determinants of suicide, using more detailed seasonal data. In this research, 2,445 suicide cases were included, with 1,957 males (80.0%) and 488 females (20.0%). In the first stage, we examined the spatial pattern and the determinants of suicide using 5-year aggregated data. Spearman correlations were used to assess associations between variables. Then a Poisson regression model was applied in the multivariable analysis, as the occurrence of suicide is a small probability event and this model fitted the data quite well. Suicide mortality varied across LGAs and was associated with a range of socio-environmental factors. The multivariable analysis showed that maximum temperature was significantly and positively associated with male suicide (relative risk [RR] = 1.03, 95% CI: 1.00 to 1.07). Higher proportion of Indigenous population was accompanied with more suicide in male population (male: RR = 1.02, 95% CI: 1.01 to 1.03). There was a positive association between unemployment rate and suicide in both genders (male: RR = 1.04, 95% CI: 1.02 to 1.06; female: RR = 1.07, 95% CI: 1.00 to 1.16). No significant association was observed for rainfall, minimum temperature, SEIFA, proportion of population with low individual income and low educational attainment. In the second stage of this study, we undertook a preliminary spatiotemporal analysis of suicide using seasonal data. Firstly, we assessed the interrelations between variables. Secondly, a generalised estimating equations (GEE) model was used to examine the socio-environmental impact on suicide over time and space, as this model is well suited to analyze repeated longitudinal data (e.g., seasonal suicide mortality in a certain LGA) and it fitted the data better than other models (e.g., Poisson model). The suicide pattern varied with season and LGA. The north of Queensland had the highest suicide mortality rate in all the seasons, while there was no suicide case occurred in the southwest. Northwest had consistently higher suicide mortality in spring, autumn and winter. In other areas, suicide mortality varied between seasons. This analysis showed that maximum temperature was positively associated with suicide among male population (RR = 1.24, 95% CI: 1.04 to 1.47) and total population (RR = 1.15, 95% CI: 1.00 to 1.32). Higher proportion of Indigenous population was accompanied with more suicide among total population (RR = 1.16, 95% CI: 1.13 to 1.19) and by gender (male: RR = 1.07, 95% CI: 1.01 to 1.13; female: RR = 1.23, 95% CI: 1.03 to 1.48). Unemployment rate was positively associated with total (RR = 1.40, 95% CI: 1.24 to 1.59) and female (RR=1.09, 95% CI: 1.01 to 1.18) suicide. There was also a positive association between proportion of population with low individual income and suicide in total (RR = 1.28, 95% CI: 1.10 to 1.48) and male (RR = 1.45, 95% CI: 1.23 to 1.72) population. Rainfall was only positively associated with suicide in total population (RR = 1.11, 95% CI: 1.04 to 1.19). There was no significant association for rainfall, minimum temperature, SEIFA, proportion of population with low educational attainment. The second stage is the extension of the first stage. Different spatial scales of dataset were used between the two stages (i.e., mean yearly data in the first stage, and seasonal data in the second stage), but the results are generally consistent with each other. Compared with other studies, this research explored the variety of the impact of a wide range of socio-environmental factors on suicide in different geographical units. Maximum temperature, proportion of Indigenous population, unemployment rate and proportion of population with low individual income were among the major determinants of suicide in Queensland. However, the influence from other factors (e.g. socio-culture background, alcohol and drug use) influencing suicide cannot be ignored. An in-depth understanding of these factors is vital in planning and implementing suicide prevention strategies. Five recommendations for future research are derived from this study: (1) It is vital to acquire detailed personal information on each suicide case and relevant information among the population in assessing the key socio-environmental determinants of suicide; (2) Bayesian model could be applied to compare mortality rates and their socio-environmental determinants across LGAs in future research; (3) In the LGAs with warm weather, high proportion of Indigenous population and/or unemployment rate, concerted efforts need to be made to control and prevent suicide and other mental health problems; (4) The current surveillance, forecasting and early warning system needs to be strengthened, to trace the climate and socioeconomic change over time and space and its impact on population health; (5) It is necessary to evaluate and improve the facilities of mental health care, psychological consultation, suicide prevention and control programs; especially in the areas with low socio-economic status, high unemployment rate, extreme weather events and natural disasters.

Addressing issues in sparseness, ecological bias and formulation of the adjacency matrix in Bayesian spatio-temporal analysis of disease counts

The main objective of this PhD was to further develop Bayesian spatio-temporal models (specifically the Conditional Autoregressive (CAR) class of models), for the analysis of sparse disease outcomes such as birth defects. The motivation for the thesis arose from problems encountered when analyzing a large birth defect registry in New South Wales. The specific components and related research objectives of the thesis were developed from gaps in the literature on current formulations of the CAR model, and health service planning requirements. Data from a large probabilistically-linked database from 1990 to 2004, consisting of fields from two separate registries: the Birth Defect Registry (BDR) and Midwives Data Collection (MDC) were used in the analyses in this thesis. The main objective was split into smaller goals. The first goal was to determine how the specification of the neighbourhood weight matrix will affect the smoothing properties of the CAR model, and this is the focus of chapter 6. Secondly, I hoped to evaluate the usefulness of incorporating a zero-inflated Poisson (ZIP) component as well as a shared-component model in terms of modeling a sparse outcome, and this is carried out in chapter 7. The third goal was to identify optimal sampling and sample size schemes designed to select individual level data for a hybrid ecological spatial model, and this is done in chapter 8. Finally, I wanted to put together the earlier improvements to the CAR model, and along with demographic projections, provide forecasts for birth defects at the SLA level. Chapter 9 describes how this is done. For the first objective, I examined a series of neighbourhood weight matrices, and showed how smoothing the relative risk estimates according to similarity by an important covariate (i.e. maternal age) helped improve the model’s ability to recover the underlying risk, as compared to the traditional adjacency (specifically the Queen) method of applying weights. Next, to address the sparseness and excess zeros commonly encountered in the analysis of rare outcomes such as birth defects, I compared a few models, including an extension of the usual Poisson model to encompass excess zeros in the data. This was achieved via a mixture model, which also encompassed the shared component model to improve on the estimation of sparse counts through borrowing strength across a shared component (e.g. latent risk factor/s) with the referent outcome (caesarean section was used in this example). Using the Deviance Information Criteria (DIC), I showed how the proposed model performed better than the usual models, but only when both outcomes shared a strong spatial correlation. The next objective involved identifying the optimal sampling and sample size strategy for incorporating individual-level data with areal covariates in a hybrid study design. I performed extensive simulation studies, evaluating thirteen different sampling schemes along with variations in sample size. This was done in the context of an ecological regression model that incorporated spatial correlation in the outcomes, as well as accommodating both individual and areal measures of covariates. Using the Average Mean Squared Error (AMSE), I showed how a simple random sample of 20% of the SLAs, followed by selecting all cases in the SLAs chosen, along with an equal number of controls, provided the lowest AMSE. The final objective involved combining the improved spatio-temporal CAR model with population (i.e. women) forecasts, to provide 30-year annual estimates of birth defects at the Statistical Local Area (SLA) level in New South Wales, Australia. The projections were illustrated using sixteen different SLAs, representing the various areal measures of socio-economic status and remoteness. A sensitivity analysis of the assumptions used in the projection was also undertaken. By the end of the thesis, I will show how challenges in the spatial analysis of rare diseases such as birth defects can be addressed, by specifically formulating the neighbourhood weight matrix to smooth according to a key covariate (i.e. maternal age), incorporating a ZIP component to model excess zeros in outcomes and borrowing strength from a referent outcome (i.e. caesarean counts). An efficient strategy to sample individual-level data and sample size considerations for rare disease will also be presented. Finally, projections in birth defect categories at the SLA level will be made.

What measure of temperature is the best predictor of mortality?

Hot and cold temperatures significantly increase mortality rates around the world, but which measure of temperature is the best predictor of mortality is not known. We used mortality data from 107 US cities for the years 1987–2000 and examined the association between temperature and mortality using Poisson regression and modelled a non-linear temperature effect and a non-linear lag structure. We examined mean, minimum and maximum temperature with and without humidity, and apparent temperature and the Humidex. The best measure was defined as that with the minimum cross-validated residual. We found large differences in the best temperature measure between age groups, seasons and cities, and there was no one temperature measure that was superior to the others. The strong correlation between different measures of temperature means that, on average, they have the same predictive ability. The best temperature measure for new studies can be chosen based on practical concerns, such as choosing the measure with the least amount of missing data.

Nurturing Needs: Literacy Achievement for Refugee students

Yeronga State School, located 7 km from the city in Brisbane, Queensland, opened in 1871. YSS caters for a middle class inner-suburban community, however, from the mid 1990s enrolments brought new forms of socio-economic, cultural and linguistic diversity. Initially, ESL students were enrolled due to their immigrant parents enrolling in the neighbouring TAFE. Then refugee families from Bosnia and the Middle East became part of the YSS community. In recent years, refugee numbers have accounted for up to 23% of the school population. Many of these new arrivals left behind families in war-torn circumstances, were orphaned or came to live with unknown relatives. Some family members were victims of torture which may have been witnessed by the children. Trauma for some or all family members was a very real concern. Others were born in refugee camps, where food was scarce, belongings needed to be guarded and safety was never guaranteed.

Excess deaths during the 2004 heatwave in Brisbane, Australia

The paper examines whether there was an excess of deaths and the relative role of temperature and ozone in a heatwave during 7–26 February 2004 in Brisbane, Australia, a subtropical city accustomed to warm weather. The data on daily counts of deaths from cardiovascular disease and non-external causes, meteorological conditions, and air pollution in Brisbane from 1 January 2001 to 31 October 2004 were supplied by the Australian Bureau of Statistics, Australian Bureau of Meteorology, and Queensland Environmental Protection Agency, respectively. The relationship between temperature and mortality was analysed using a Poisson time series regression model with smoothing splines to control for nonlinear effects of confounding factors. The highest temperature recorded in the 2004 heatwave was 42°C compared with the highest recorded temperature of 34°C during the same periods of 2001–2003. There was a significant relationship between exposure to heat and excess deaths in the 2004 heatwave estimated increase in non-external deaths: 75 [(95% confidence interval, CI: 11–138; cardiovascular deaths: 41 (95% CI: −2 to 84)]. There was no apparent evidence of substantial short-term mortality displacement. The excess deaths were mainly attributed to temperature but exposure to ozone also contributed to these deaths.

On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites