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Predicting and Monitoring Casualty Numbers in Great Britain

Predicting and Monitoring Casualty Numbers in Great Britain

Robert Raeside
Transport Research Institute
Napier University
Sighthill Court
Edinburgh EH11 4BN Scotland
Email: r.raeside@napier.ac.uk


This paper presents analyses and forecasts of trends related to road traffic and pedestrian casualties and fatalities in Great Britain. For people killed and seriously injured, these forecasts are based on extrapolation of the absolute number of casualties. For casualties classified as slight, forecasts are made of the rate of casualties per 100 million vehicle-kilometers. Forecasts, using autoregressive models, are then compared with government targets and show that at the aggregate level it is unlikely that, for the numbers who are killed or seriously injured, these targets will be achieved.


One of the key performance measures of the safety of a nation's transport system is the number of people who are killed or seriously injured in road accidents. Apart from the human tragedy, estimates show that each fatal road accident in Great Britain costs £1,447,490 (approximately $2,665,000) while a serious casualty costs £168,260 (approximately $310,000) (DETR 2002). National governments provide targets that traffic managers, infrastructure designers, vehicle manufacturers, and the legal system strive to achieve. The latest set of targets for Great Britain is for the year 2010. Compared with the average of 1994 to 1998, hoped-for reductions are as follows:

  • the number of fatal or serious injuries in road accidents by 40%,
  • the number of children killed or seriously injured by 50%, and
  • slight injuries per 100 million vehicle-kilometers by 10%.

This paper reports on an exploration of recent casualty1 time series in Great Britain and forecasts these series up to 2010 to determine if it is likely that targets set by the government of Great Britain are achievable. As will be discussed, most forecasting approaches predict the casualties per 100 million vehicle-kilometers; however, this paper attempts to conduct the straightforward forecasting of the time series of the number of casualties. These are then compared with the casualty reduction targets. It is hoped this will be useful to those involved with road safety to determine if targets for the number of those killed or seriously injured in vehicle accidents can be met or if more effort is required.

For the previous targets, which were set in 1987, the aim was to reduce deaths and serious injuries by one-third by 2000 compared with the average for 1981 to 1985. This target was surpassed; in fact, road deaths fell by 39% and serious injuries by 45%. The success in Great Britain has come about through legislative changes aimed at altering driver behavior and improving infrastructure and vehicle crash protection.

The number of casualties is of concern throughout Europe, where there are over 40,000 deaths and 1.7 million people injured per year, directly costing some 160 billion Euros—and the young are most affected (European Commission 2003).

In 2000, the European Commission initiated the European Road Safety action program with the intention of halving the number of those killed or seriously injured in road accidents by 2010. It took 30 years for the previous halving of rates, so this must be seen as ambitious. The focus of the program is on:

  1. Improving driver behavior through education and enforcement of speed limits, use of safety belts, and penalties for drinking/drug use while driving.
  2. Encouraging improvements in vehicle design and technological advances to enhance both occupant protection and pedestrian survivability.
  3. Encouraging improvement of the road infrastructure.
  4. Reducing the risk to people during the transport of commercial goods and while using public transport.
  5. Improving emergency services and care for road accident victims.
  6. Promoting research into transport safety and improving accident data collection and dissemination.

To enact these policies, the European Commission has produced a European Road Safety Charter as an exemplar of good practice. Government agencies are required to sign and have their compliance with the charter monitored and publicized—hence the need to predict and monitor the casualty series.

Great Britain is now one of the safest of the European countries in terms of road traffic injuries and compares favorably with all Organization for Economic Cooperation and Development (OECD) countries (OECD 2003). However, there is still room for improvement, especially for child pedestrian fatality rates per 100,000 people. As of 2001, Great Britain lagged behind many similar western European countries (Scottish Executive 2002). Of particular concern is that since 1991 the total number of road traffic casualties in Great Britain has shown a slight but significant upward trend. In figure 1, the slope of the fitted trend line indicates an increase of 11.69 each month, which is statistically significant with a P-value of 0.013.

Figure 2, which is broken down by type of casualty, presents a somewhat different picture from the total. The numbers of fatal and serious casualties have decreased markedly over the period, whereas the number of slight injuries has increased. (This last change may reflect improved reporting systems, especially as insurance companies require a police report if anyone is injured.) Given that in Great Britain since 1991 the number of vehicle-kilometers traveled has increased by more than 15%, the risk of fatal or serious injury has been substantially reduced (by 24.5% and 28.1%, respectively, over the period 1991 to 2001).


An often-used approach to forecasting killed and seriously injured (KSI) casualties has been to take a time series of annual rates and extrapolate a fitted negative exponential model. Sometimes allowance is made through the use of disturbance terms for special events, such as the introduction of legislation to make seat-belt wearing compulsory, but in general the models are univariate in nature and incorporate little in the way of explanatory variables. A good example is the work of Broughton (1991) who fitted extensions of the model

log(casualties/traffic volume) = a + b*year + an intervention term               (1)

to data on Great Britain road casualties from 1949 to 1989. This model gave good forecasts of the number of fatal casualties in 2000: 3,312 with a 90% prediction interval of 2,892 to 3,826. There were, in fact, 3,409 fatalities. Broughton's forecasts of KSI casualty numbers and all casualty numbers underpredicted by 4.8% and 24.8%, respectively. This approach requires the number of vehicle-kilometers driven to be forecast ahead. Thus, either official forecasts of the amount of kilometers driven must be made, or the growth of this series will need to be modeled, perhaps using a sigmoid model, as Oppe (1989) suggested.

Although supported by Nilsson (1997), the use of kilometers as a denominator is problematic because most casualty accidents occur relatively close to the place of residence of the person or persons involved (Petch and Henson 2000; Scottish Executive 2002). Also, the certainty of estimation of a nation's annual driving is not clear. However, an argument can be made that using kilometers as a denominator would serve as a proxy for the number of people driving.

Harvey and Durbin (1986) applied structural time series methods using ARIMA models with an intervention term to the monthly data series of the numbers killed and seriously injured in Great Britain from January 1969 to December 1984. The results demonstrated the effectiveness of the introduction of seat belt legislation. Raeside and White (2004) used ARIMA models for the monthly series of KSIs from 1991 to 2001. From these models, they projected the numbers of fatal and serious casualties in 2010 to show that targets set by the government of Great Britain may be met. But using ARIMA models to predict eight years ahead from this short time series must be regarded as speculative, and this is reflected in the relatively wide prediction intervals of these models. A more precise means of assessing progress to targets is required.

Haight (1991), in his editorial commentary on a special issue of Accident Analysis and Prevention, advocated models for predicting fatalities with year and traffic volume as variables.

Fatalities = a × b year × Traffic c           (2)

The models were transformed and fitted using Poisson regression. Brude (1995) successfully applied a version of these models to forecast the number of fatalities in Sweden to the year 2000 from data covering 1977 to 1991. Guria and Mara (2001) incorporated this type of modeling into a control chart to give the "probability of achieving the target given the past outcomes of the year." They highlighted the importance of day and month effects on the variability of the casualty series.

Lassarre (2001) extended Smeed's (1949) work to develop a family of structural time series models using Harvey's (1989) approach to estimate fatality time series across 10 European countries. He found that, since 1962, fatalities have decreased at an average annual rate of 6%. Balkin and Ord (2001) applied a stochastic structural equation modeling approach to predict the effect of speed limit changes on the number of fatal crashes on both urban and rural interstate highways in the United States. Seasonal influences can be accounted for in their approach, and comparisons between states were made. They found that the view that higher speeds means more fatalities could not be universally supported.

Page (2001) modeled safety trends in OECD countries from 1980 to 1994 and constructed a safety index comprising population variables, numbers of buses and coaches, employment rates, and rates of alcohol consumption. Page then used these variables in regression models to demonstrate that fatality rates per billion vehicle-kilometers have generally decreased. The OECD countries with the highest index (safest) were Sweden, the Netherlands, Norway, the United Kingdom, and Switzerland, and the lowest were Greece, Belgium, the United States, Portugal, and Spain.

Much discussion of the improving casualty trends has appeared in the literature, some of which is summarized in Raeside and White (2004). These trends appear to be the result primarily of improvements in road infrastructure and the crashworthiness of vehicles. Behavioral and legislative influence appear, from the literature, to be of second order. Figure 2 provides some support for this, as the total number of accidents seems to have remained about the same but fatal and serious accidents have decreased, which indicates greater levels of personal protection. Accident rates have also improved as a result of changes in behavior, especially reductions in rates for child pedestrians and bicycling (DiGuiseppi et al. 1997; Stone and Broughton 2003).

Little use has been made of explanatory models in predicting casualties, with the notable exception of Brannas (1995), who used a Poisson regression model. He based his work on that of Zeger (1988) to successfully forecast road accidents in Vasterbotten County in Sweden using variables representing exposure and weather, plus daylight variables. The model Brannas considered is as follows:

uppercase p lowercase r (lowercase y subscript {lowercase t}) = lowercase lambda superscript {lowercase y subscript {lowercase t}} subscript {lowercase t} times lowercase e superscript {negative lowercase lambda subscript {lowercase t}} divided by lowercase lambda subscript {lowercase t} exclaimation point (t = 1....., T)            (3)


lowercase lambda subscript {lowercase t} = lowercase e superscript {lowercase x subscript {lowercase t} times lowercase beta}

and xt is a 1 x k vector of covariates representing weather and daylight. This, however, is more suited to forecasting for micro areas than for national forecasts. The same is true for the numerous Poisson models developed by civil engineers. They are similar to equation (2) but contain variables representing the geometry of the junction, the nature of the conflict, traffic volumes, and major road features, and they can be used to predict accidents at particular road junctions (Maher and Summersgill 1995).

Unfortunately, little has been done to use the predictive models to assess the probability of meeting casualty reduction targets. To achieve this aim, this paper employs simple models based on Broughton's (1991) approach to produce predictive distributions based on numbers rather than rates per 100 million vehicle-kilometers driven. The models do not incorporate traffic volumes (except for slight injuries).


The annual data series of the numbers of fatal, serious, and slight casualties were taken from table 9.10 of Road Accidents Great Britain 2002 (DETR 2002). The series were then modeled using autoregressive and linear trend terms. Natural logarithms were used for fatalities and for the serious casualties, so that the models would be negative exponential in nature and similar to that of Broughton (1991), but using the numbers rather than rates per billion vehicle-kilometers and not employing an intervention term. For slight casualties, results of the natural logarithm of the casualty rate per 100,000 vehicle-kilometers allowed comparisons with the official target. The trend variable was formed by subtracting 1970 from the year. The autoregressive models were fitted using SPSS; the exact maximum likelihood method was used. The models for fatal and serious injuries may be written as:

ln(casualties in year t) = a + b*(year–1970) + c*ln(casualties in year t–1)            (4)

For slight injuries, casualties per 100 million vehicle-kilometers were used instead of casualty numbers. Table 1 shows the coefficients and fit parameters of the models. The models all fitted well, and it should be noted that all models show a significant downward trend.

Figure 3 presents the forecasts generated by each of these models, with the lower and upper prediction level limits (LPL and UPL) also displayed. The forecast of fatalities for 2010 ranges over a 95% prediction interval from 2,246 to 3,142 with an expectation of 2,656 deaths. This is a 26% reduction from the 1994 to 1998 average of 3,578, which is used as the government's baseline for measuring improvements. This is disappointing for planners and policymakers—if the predictive distribution for the log of causalities is considered approximately normal, then the chance of attaining or exceeding the 40% reduction target is less than 14%. By adding the forecasts of the number of serious casualties to the forecasts of fatalities, we get a 95% prediction interval for KSI casualties of 26,002 to 38,989, with an expectation of 31,839. The expected value of KSI casualties is only 33% less than the baseline figure of 47,656. The probability of meeting or exceeding the target of 40% is only 31.2%. Thus, the attainment of this target is unlikely.

The government target for slight injuries was a 10% reduction from the 1994 to 1998 baseline of 46.30 slight injuries per 100 million vehicle-kilometers. The forecasts show that a reduction of just over 9% is expected. The probability of achieving or surpassing the 10% target is 0.476. Thus it appears that in Great Britain, the road casualty improvement targets for slight injuries may not be reached. However, the prospects are more optimistic than for the KSI series if injuries are assumed to be a function of the number of trips and not the number of vehicle-kilometers. This "optimism" may well be the consequence of increased traffic volumes rather than improved safety.

The other important target of halving the number of children who are killed or seriously injured by 2010 and the pedestrian casualty series will be examined next. Table 2 presents coefficients of the model of the natural logarithm for child and pedestrian KSIs. Again the models fitted well and displayed a significant downward trend. The forecasts along with the LPLs and UPLs produced from these models are displayed in figure 4.

Child KSI casualties are forecasted to fall to 3,482 with a 95% prediction interval of 2,899 to 4,182, a reduction of just over 50% from the 1994 to 1998 baseline. Although this is close to the target of 50%, the probability of meeting or exceeding the target is 0.530. Pedestrian casualties are projected to be reduced by 43%, with the number of KSI pedestrians falling from 11,667 to 6,652. As no target is given for pedestrian casualty reduction, no probabilities of attainment can be computed. Table 3 shows the probabilities of attaining the targets where targets are available.


Governments of many developed countries set periodic road safety targets. The latest targets in Great Britain are for 2010 and relate to the number of people killed or seriously injured on Britain's roads and the rate of slight injuries per 100 million vehicle-kilometers driven. For effective use of resources it is important to monitor progress to these targets. This paper presents a methodology for forecasting casualty trends and monitoring progress toward targets.

The paper presents trends in casualty numbers for fatal, serious, and slight injuries, as well as those involving pedestrians (with a separate category for children). Progress in improving casualty numbers seems promising for children and for slight injuries, but attaining the reduction targets for 2010 is uncertain. For the killed and seriously injured category, the probability of attaining a 40% reduction is fairly slim, and a greater effort is needed to ensure convergence on this target. One possibility for reducing casualties is to apply and enforce measures to reduce traffic levels in Great Britain. While targets should be aspirational rather than set at easily attainable levels, the issue of road traffic accidents is politically contentious. Accounting for the marked seasonality of the data may provide targets that are more likely to be attainable. This is the subject of future research.


I wish to gratefully acknowledge the suggestions for improvements and changes to the paper made by the referees and editors.


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KEYWORDS: National road safety trends, statistical forecasting, casualty and fatality prediction.

1. Casualties are fatal, serious, or slight injuries.

Updated: Saturday, May 20, 2017