Comparing multilevel and Bayesian spatial random effects survival models to assess geographical inequalities in colorectal cancer survival: a case study

Background Multilevel and spatial models are being increasingly used to obtain substantive information on area-level inequalities in cancer survival. Multilevel models assume independent geographical areas, whereas spatial models explicitly incorporate geographical correlation, often via a conditional autoregressive prior. However the relative merits of these methods for large population-based studies have not been explored. Using a case-study approach, we report on the implications of using multilevel and spatial survival models to study geographical inequalities in all-cause survival. Methods Multilevel discrete-time and Bayesian spatial survival models were used to study geographical inequalities in all-cause survival for a population-based colorectal cancer cohort of 22,727 cases aged 20–84 years diagnosed during 1997–2007 from Queensland, Australia. Results Both approaches were viable on this large dataset, and produced similar estimates of the fixed effects. After adding area-level covariates, the between-area variability in survival using multilevel discrete-time models was no longer significant. Spatial inequalities in survival were also markedly reduced after adjusting for aggregated area-level covariates. Only the multilevel approach however, provided an estimation of the contribution of geographical variation to the total variation in survival between individual patients. Conclusions With little difference observed between the two approaches in the estimation of fixed effects, multilevel models should be favored if there is a clear hierarchical data structure and measuring the independent impact of individual- and area-level effects on survival differences is of primary interest. Bayesian spatial analyses may be preferred if spatial correlation between areas is important and if the priority is to assess small-area variations in survival and map spatial patterns. Both approaches can be readily fitted to geographically enabled survival data from international settings

Estimation of the time of a linear trend in monitoring survival time

Change point estimation is recognized as an essential tool of root cause analyses within quality control programs as it enables clinical experts to search for potential causes of change in hospital outcomes more effectively. In this paper, we consider estimation of the time when a linear trend disturbance has occurred in survival time following an in-control clinical intervention in the presence of variable patient mix. To model the process and change point, a linear trend in the survival time of patients who underwent cardiac surgery is formulated using hierarchical models in a Bayesian framework. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. We use Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters including the location and the slope size of the trend and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time cumulative sum control chart (CUSUM) control charts for different trend scenarios. In comparison with the alternatives, step change point model and built-in CUSUM estimator, more accurate and precise estimates are obtained by the proposed Bayesian estimator over linear trends. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered.

Do motor vehicle crashes arise from single or multiple unique risk processes? An inquiry into crash causes and modelling

Crashes at any particular transport network location consist of a chain of events arising from a multitude of potential causes and/or contributing factors whose nature is likely to reflect geometric characteristics of the road, spatial effects of the surrounding environment, and human behavioural factors. It is postulated that these potential contributing factors do not arise from the same underlying risk process, and thus should be explicitly modelled and understood. The state of the practice in road safety network management applies a safety performance function that represents a single risk process to explain crash variability across network sites. This study aims to elucidate the importance of differentiating among various underlying risk processes contributing to the observed crash count at any particular network location. To demonstrate the principle of this theoretical and corresponding methodological approach, the study explores engineering (e.g. segment length, speed limit) and unobserved spatial factors (e.g. climatic factors, presence of schools) as two explicit sources of crash contributing factors. A Bayesian Latent Class (BLC) analysis is used to explore these two sources and to incorporate prior information about their contribution to crash occurrence. The methodology is applied to the state controlled roads in Queensland, Australia and the results are compared with the traditional Negative Binomial (NB) model. A comparison of goodness of fit measures indicates that the model with a double risk process outperforms the single risk process NB model, and thus indicating the need for further research to capture all the three crash generation processes into the SPFs.

Criminal histories of crash and non-crash involved Queensland speeding offenders: Evidence supporting the idea that we drive as we live

Evidence increasingly suggests that our behaviour on the road mirrors our behaviour across other aspects of our life. The idea that we drive as we live, described by Tillman and Hobbs more than 65 years ago when examining off-road behaviours of taxi drivers (1949), is the focus of the current paper. As part of a larger study examining the impact of penalty changes on a large cohort of Queensland speeding offenders, criminal (lifetime) and crash history (10 year period) data for a sub-sample of 1000 offenders were obtained. Based on the ‘drive as we live’ maxim, it was hypothesised that crash-involved speeding offenders would be more likely to have a criminal history than non-crash involved offenders. Overall, only 30% of speeding offenders had a criminal history. However, crash-involved offenders were significantly more likely to have a criminal history (49.4%) than non-crash involved offenders (28.6%), supporting the hypothesis. Furthermore, those deemed ‘most at fault’ in a crash were the group most likely to have at least one criminal offence (52.2%). When compared to the non-crash involved offenders, those deemed ‘not most at fault’ in a crash were also more likely to have had at least one criminal offence (46.5%). Therefore, when compared to non-crash involved speeding offenders, those offenders involved in a crash were more likely to have been convicted of at least one criminal offence, irrespective of whether they were deemed ‘most at fault’ in that crash. Implications for traffic offender management and policing are discussed.

The impact of safety measures on the re-offence and crash rates of drink-driving offenders in Victoria

Alcohol is a major factor in road deaths and serious injuries. In Victoria, between 2008 and 2013, 30% of drivers killed were involved in alcohol-related crashes. From the early 1980s Victoria progressively introduced a series of measures, such as driver licence cancellation and alcohol interlocks, to reduce the level of drink-driving on Victoria's roads. This project tracked drink-driving offenders to measure and understand their re-offence and road trauma involvement levels during and after periods of licensing and driving interventions. The methodology controlled for exposure by aggregating crashes and traffic violations within relevant categories (e.g. licence cancelled/relicensed/relicensing not sought) and calculated as rates 'per thousand person-years'. Inferential statistical techniques were used to compare crash and offence rates between control and treatment groups across three distinct time periods, which coincided with the introduction of new interventions. This paper focuses on the extent to which the Victorian drink-driving measures have been successful in reducing re-offending and road trauma involvement during and after periods of licence interventions. It was found that a licence cancellation/ban is an effective drink-driving countermeasure as it reduced drink-driving offending and drink-driving crashes. Interlocks also had a positive effect on drink-driving offences as they were reduced during the interlock period as well as for the entire intervention period. Possible drink-driving policy implications are briefly discussed.

How serious are they? The use of data linkage to explore different definitions of serious road crash injuries

Over recent years, the focus in road safety has shifted towards a greater understanding of road crash serious injuries in addition to fatalities. Police reported crash data are often the primary source of crash information; however, the definition of serious injury within these data is not consistent across jurisdictions and may not be accurately operationalised. This study examined the linkage of police-reported road crash data with hospital data to explore the potential for linked data to enhance the quantification of serious injury. Data from the Queensland Road Crash Database (QRCD), the Queensland Hospital Admitted Patients Data Collection (QHAPDC), Emergency Department Information System (EDIS), and the Queensland Injury Surveillance Unit (QISU) for the year 2009 were linked. Nine different estimates of serious road crash injury were produced. Results showed that there was a large amount of variation in the estimates of the number and profile of serious road crash injuries depending on the definition or measure used. The results also showed that as the definition of serious injury becomes more precise the vulnerable road users become more prominent. These results have major implications in terms of how serious injuries are identified for reporting purposes. Depending on the definitions used, the calculation of cost and understanding of the impact of serious injuries would vary greatly. This study has shown how data linkage can be used to investigate issues of data quality. It has also demonstrated the potential improvements to the understanding of the road safety problem, particularly serious injury, by conducting data linkage.

Crash risk perception of sleepy driving and its comparisons with drink driving and speeding: Which behavior is perceived as the riskiest?

- Objective Driver sleepiness is a major crash risk factor, but may be under-recognized as a risky driving behavior. Sleepy driving is usually rated as less of a road safety issue than more well-known risky driving behaviors, such as drink driving and speeding. The objective of this study was to compare perception of crash risk of sleepy driving, drink driving, and speeding. - Methods In total, 300 Australian drivers completed a questionnaire that assessed crash risk perceptions for sleepy driving, drink driving, and speeding. Additionally, the participants perception of crash risk was assessed for five different contextual scenarios that included different levels of sleepiness (low, high), driving duration (short, long), and time of day/circadian influences (afternoon, night-time) of driving. - Results The analysis confirmed that sleepy driving was considered a risky driving behavior, but not as risky as high levels of speeding (p < .05). Yet, the risk of crashing at 4 am was considered as equally risky as low levels of speeding (10 km over the limit). The comparisons of the contextual scenarios revealed driving scenarios that would arguably be perceived as quite risky due to time of day/circadian influences were not reported as high risk. - Conclusions The results suggest a lack of awareness or appreciation of circadian rhythm functioning, particularly the descending phase of circadian rhythm that promotes increased sleepiness in the afternoon and during the early hours of the morning. Yet, the results suggested an appreciation of the danger associated with long distance driving and driver sleepiness. Further efforts are required to improve the community’s awareness of the impairing effects from sleepiness and in particular, knowledge regarding the human circadian rhythm and the increased sleep propensity during the circadian nadir.

Predicting occupant risk indicators for frontal impacts with redirective crash cushions

Crash cushions are devices deployed on the road network in order to shield fixed roadside hazards and the non-crashworthy ends of road safety barriers. However crash cushions vary in terms of configuration and operation, meaning that different devices may also vary in terms of ability to mitigate occupant risk. In this study, data derived from crash testing of eleven redirective crash cushions is used as the base input to a numerical procedure for calculation of occupant risk indicators Occupant Impact Velocity (OIV), Occupant Ridedown Acceleration (ORA) and longitudinal Acceleration Severity Index (ASI) for a range of simulated impacting vehicles (mass 800 kg to 2,500 kg) impacting each crash cushion at a range of impact speeds (18 m/s to 32 m/s). The results may be interpreted as demonstrating firstly that enhanced knowledge of the performance of a device over a range of impact conditions, i.e., beyond the crash testing, may assist in determining the crash cushion most suited to a particular application; secondly that a more appropriate conformance test for occupant risk would be a frontal impact by a small (light) vehicle travelling parallel to and aligned with the centreline of the crash cushion; and thirdly that current documented numerical procedures for calculating occupant risk indicators may require review.

Induced smoothing for rank regression with censored survival times

Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be monotone in parameter components, and even in this case are step functions, requiring the equivalent of linear programming for computation. The lack of smoothness makes standard error or covariance matrix estimation even more difficult. An induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations, including conventional rank regression. The present paper applies induced smoothing to the Gehan-Wilcoxon weighted rank regression for the accelerated failure time model, for the more difficult case of survival time data subject to censoring, where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions. Smooth monotone parameter estimation and rapid, reliable standard error or covariance matrix estimation is obtained.

Survival, growth and quality of life in children after orthotopic liver transplantation: A 5 year experience

The aims of this study were to investigate outcome and to evaluate areas of potential ongoing concern after orthotopic liver transplantation (OLT) in children. Actuarial survival in relation to age and degree of undernutrition at the time of OLT was evaluated in 53 children (age 0.58-14.2 years) undergoing OLT for endstage liver disease. Follow-up studies of growth and quality of life were undertaken in those with a minimum follow-up period of 12 months (n = 26). The overall 3 year actuarial survival was 70%. Survival rates did not differ between age groups (actuarial 2 year survival for ages <1, 1-5 and >5 years were 70, 70 and 69% respectively) but did differ according to nutritional status at OLT (actuarial 2 year survival for children with Z scores for weight <-1 was 57%, >-1 was 95%; P = 0.004). Significant catch-up weight gain was observed by 18 months post-transplant, while height improved less rapidly. Quality of life (assessed by Vineland Adaptive Behaviour Scales incorporating socialization, daily living skills, communication and motor skills) was good (mean composite score 91 ± 19). All school-aged children except one were attending normal school. Two children had mild to moderate intellectual handicap related to post-operative intracerebral complications. Satisfactory long-term survival can be achieved after OLT in children regardless of age but the importance of pre-operative nutrition is emphasized. Survivors have an excellent chance of a good quality of life and of satisfactory catch-up weight gain and growth.

International survey of bicycling exposure, crash involvement, behaviors, and attitudes: Preliminary results

This paper presents some results from preliminary analyses of the data of an international online survey of bicycle riders, who reported riding at least once a month. On 4 July 2015, data from 7528 participants from 17 countries was available in the survey, and were subsequently cleaned and checked for consistency. The median distance ridden ranged from 30 km/week in Israel to 150 km/week in Greece (overall median 54 km/week). City/hybrid bicycles were the most common type of bicycle ridden (44%), followed by mountain (20%) and road bikes (15%). Almost half (47%) of the respondents rode “nearly daily”. About a quarter rode daily to work or study (27%). Overall, 40% of respondents reported wearing a helmet ‘always’, varying from 2% in the Netherlands to 80% in Norway, while 25% reported ‘never’ wearing a helmet. Thus, individuals appeared to consistently either use or not use helmets. Helmet wearing rates were generally higher when riding for health/fitness than other purposes and appeared to be little affected by the type of riding location, but some divergences in these patterns were found among countries. Almost 29% of respondents reported being involved in at least one bicycle crash in the last year (ranging from 12% in Israel to 53% in Turkey). Among the most severe crashes for each respondent, about half of the crashes involved falling off a bicycle. Just under 10% of the most severe crashes for each respondent were reported to police. Among the bicycle-motor vehicle crashes, only a third were reported to police. Further analyses will address questions regarding the influence of factors such as demographic characteristics, type of bicycle ridden, and attitudes on both bi-cycle use and helmet wearing rates.

Proposed vehicle impact speed: Severe injury probability relationships for selected crash types

Speed is recognised as a key contributor to crash likelihood and severity, and to road safety performance in general. Its fundamental role has been recognised by making Safe Speeds one of the four pillars of the Safe System. In this context, impact speeds above which humans are likely to sustain fatal injuries have been accepted as a reference in many Safe System infrastructure policy and planning discussions. To date, there have been no proposed relationships for impact speeds above which humans are likely to sustain fatal or serious (severe) injury, a more relevant Safe System measure. A research project on Safe System intersection design required a critical review of published literature on the relationship between impact speed and probability of injury. This has led to a number of questions being raised about the origins, accuracy and appropriateness of the currently accepted impact speed–fatality probability relationships (Wramborg 2005) in many policy documents. The literature review identified alternative, more recent and more precise relationships derived from the US crash reconstruction databases (NASS/CDS). The paper proposes for discussion a set of alternative relationships between vehicle impact speed and probability of MAIS3+ (fatal and serious) injury for selected common crash types. Proposed Safe System critical impact speed values are also proposed for use in road infrastructure assessment. The paper presents the methodology and assumptions used in developing these relationships. It identifies further research needed to confirm and refine these relationships. Such relationships would form valuable inputs into future road safety policies in Australia and New Zealand.

Sleep-related crash characteristics: Implications for applying a fatigue definition to crash reports

Sleep-related (SR) crashes are an endemic problem the world over. However, police officers report difficulties in identifying sleepiness as a crash contributing factor. One approach to improving the sensitivity of SR crash identification is by applying a proxy definition post hoc to crash reports. To identify the prominent characteristics of SR crashes and highlight the influence of proxy definitions, ten years of Queensland (Australia) police reports of crashes occurring in ≥100 km/h speed zones were analysed. In Queensland, two approaches are routinely taken to identifying SR crashes. First, attending police officers identify crash causal factors; one possible option is ‘fatigue/fell asleep’. Second, a proxy definition is applied to all crash reports. Those meeting the definition are considered SR and added to the police-reported SR crashes. Of the 65,204 vehicle operators involved in crashes 3449 were police-reported as SR. Analyses of these data found that male drivers aged 16–24 years within the first two years of unsupervised driving were most likely to have a SR crash. Collision with a stationary object was more likely in SR than in not-SR crashes. Using the proxy definition 9739 (14.9%) crashes were classified as SR. Using the proxy definition removes the findings that SR crashes are more likely to involve males and be of high severity. Additionally, proxy defined SR crashes are no less likely at intersections than not-SR crashes. When interpreting crash data it is important to understand the implications of SR identification because strategies aimed at reducing the road toll are informed by such data. Without the correct interpretation, funding could be misdirected. Improving sleepiness identification should be a priority in terms of both improvement to police and proxy reporting.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Survival probability for a diffusive process on a growing domain

We consider the motion of a diffusive population on a growing domain, 0 < x < L(t ), which is motivated by various applications in developmental biology. Individuals in the diffusing population, which could represent molecules or cells in a developmental scenario, undergo two different kinds of motion: (i) undirected movement, characterized by a diffusion coefficient, D, and (ii) directed movement, associated with the underlying domain growth. For a general class of problems with a reflecting boundary at x = 0, and an absorbing boundary at x = L(t ), we provide an exact solution to the partial differential equation describing the evolution of the population density function, C(x,t ). Using this solution, we derive an exact expression for the survival probability, S(t ), and an accurate approximation for the long-time limit, S = limt→∞ S(t ). Unlike traditional analyses on a nongrowing domain, where S ≡ 0, we show that domain growth leads to a very different situation where S can be positive. The theoretical tools developed and validated in this study allow us to distinguish between situations where the diffusive population reaches the moving boundary at x = L(t ) from other situations where the diffusive population never reaches the moving boundary at x = L(t ). Making this distinction is relevant to certain applications in developmental biology, such as the development of the enteric nervous system (ENS). All theoretical predictions are verified by implementing a discrete stochastic model.