category: literaturenote citekey: broughtonprovidingnumericalcontextbritish2010 title: Providing the numerical context for British casualty reduction targets authors: "Broughton, Jeremy; Knowles, Jackie" year: 2010 date: 2010-00-00 2010 doi: 10.1016/j.ssci.2010.01.008 publication: Safety Science url: "https://doi.org/10.1016/j.ssci.2010.01.008" zotero_key: 85BQKHGT zotero_storage: T4JCFCK6 collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Broughton, Jeremy"

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Safety Science

journal homepage: www.elsevier.com/locate/ssci

Providing the numerical context for British casualty reduction targets

Jeremy Broughton ¹ , Jackie Knowles *

Transport Research Laboratory, Wokingham RG40 3GA, United Kingdom

article info

Article history: Received 1 July 2009 Received in revised form 16 December 2009 Accepted 8 January 2010

Keywords: Casualty trends Casualty forecasting Casualty reduction target Secondary safety

abstract

The first national target for reducing road accident casualties in Great Britain was set in 1987, the target year being 2000. As the year 2000 approached, preparations were made for setting a subsequent target, the target year being 2010. A major part of the preparation consisted of forecasting the number of casualties that might be expected in 2010, conditional upon predictions about how the volume of road travel by the various transport modes might change and the type of new road safety measures that the Government might introduce. The forecasts provided the numerical context for the casualty reduction target that the Government announced in March 2000.

This paper summarises the statistical analyses of accident data from 1983 to 1998 upon which the forecasts were based, and compares the approach with alternatives that have been adopted elsewhere. It also describes how progress towards the target has been monitored annually, allowing the Government to judge whether additional efforts might be needed to achieve the target. This examination of the actual data from 1999 to 2007 shows how far the original forecasts have proved to be successful.

The improvement of car secondary safety over the past 15 years has probably been the development that has had the most significant effect on the national casualty total. A statistical model is used to quantify this effect by analysis of accident data, and the results of the most recent analyses are included.

1. Introduction

The first numerical target for reducing road accident casualties in Great Britain was set in 1987, the target year being 2000. The target was set out in the report 'Road Safety: the next steps' (Department of Transport, 1987), which presented the results of a comprehensive review of road safety policy by the main Government Departments involved at that time. The target proposed was to reduce casualties by the year 2000 at least one third from their current level (defined as the 1981–1985 average). The numerical casualty reduction target was based on a table that listed possible new countermeasures and estimates of the casualty reductions that they might achieve. Some estimates were analytically based, but this was not possible for areas such as education and publicity (Sabey, 1991).

As the year 2000 approached, preparations were made for setting a subsequent target. It seemed clear that many of the measures that had been introduced since 1987 by the Government and other public and private bodies would not have been introduced without the review that reported in 1987, so it had been successful in its main aim of bringing forward new road safety measures. On the other hand, although the numbers of fatal and of serious casualties had fallen by more than one third from their 1981–1985 baseline averages, the casualty total had actually risen slightly as a result of the increased number of slight casualties. Thus, with the benefit of hindsight it could be seen that the review had succeeded less well with the difficult task of predicting the future.

Research in the 1990s had provided reasonably successful methods for forecasting casualties, or at least casualty rates. It was decided to build on this research and to set the new casualty reduction target in the light of explicit forecasts of the number of casualties that might be expected in Great Britain in the target year. These forecasts needed to take account of new road safety measures that the Government might introduce and of predictions about how the volume of road travel might develop.

This decision was unprecedented at the time and this paper will summarise the experience of the process in the expectation that this can assist other countries that may be planning to set a casualty reduction target. The forecasts provided the numerical context for the casualty reduction target that the British Government announced in March 2000 (Department of the Environment, Trans port and the Regions, 2000), the target year being 2010.

This paper describes the forecasting methodology that was developed in the late 1990s, and summarises the range of forecasts that were prepared at that time. The passage of almost 10 years means that it is now possible to assess the reliability of the

^* Corresponding author. Tel.: +44 1344 770683.

E-mail addresses: jbroughton@trl.co.uk (J. Broughton), jknowles@trl.co.uk (J. Knowles).

¹ Tel.: +44 1344 770879.

forecasts by examining British casualty trends up to 2007. The paper discusses how the methodology has been used to re-assess annually the progress being made towards the target for 2010 and inform the development of national road safety policy. The improvement of car secondary safety has played an important part in the progress made, so it also summarises the method used to quantify the casualty reductions achieved.

In Great Britain, as in many other countries, there is wide public interest in the topic of road safety, and whether it can be improved. Consequently, an important consideration when developing the statistical approach was the need to be able to present the details in a way that a general audience, most of whom would have limited technical knowledge, could reasonably be expected to understand. The statistical approach needed to be statistically sound yet relatively easy to understand, and the paper shows how this was achieved.

The principal source of statistical information about road accidents in Great Britain is named after the STATS19 report form used (see, for example, DfT (2008) for details of the data collected). All accident statistics used in the analyses reported in this paper come from the STATS19 database.

2. Casualty forecasting in Great Britain

Forecasting casualties for at least 10 years into the future is inevitably an imprecise process, for the outcome will depend upon the future behaviour of travellers and the growth of road travel as well as the means used to promote safe travel over that period. There is, however, a method which has proved successful in forecasting casualties in Great Britain, as well as for various other countries. This is based on the long-term relation between the annual volume of motor traffic in the country and the number of casualties.

Several authors have noted that over several decades, the rate of fatalities per hundred million vehicle-kms travelled has declined by an almost constant proportion each year. The statistical strength of this relation in Great Britain was shown by Broughton (1988) with the model taking two specific safety measures into account: the introduction of compulsory seat belt wearing in 1983 and the short-lived impact of drink-driving legislation that took effect in 1968. Broughton (1991) extended this analysis applying the following model to four data sets from 1949 to 1989:

Logðcasualties=traffic volumeÞ

¼ a þ b year þ seat belt intervention term

The four STATS19 data sets comprised the annual numbers of people killed, killed and seriously injured (KSI), injured (any severity), and the number of road accidents involving human injury. The model was fitted using normal linear regression techniques to estimate the parameters a and b. The annual rate of decline of the casualty rate which, expressed as a percentage was given by:

$$B = 100 * \exp(-b)$$

The confidence interval for B was calculated using the standard error of b.

The fit of the models to the data was good but the residuals were analysed before the models were used for forecasting. There were two reasons for this: to see whether the rate of decline had changed during the period and to check for autocorrelation. The former was important because the fitted model assumes that the rate of decline is constant. An increase in the rate of decline was detected in 1983 for the fatality and KSI rate and the model was expanded to incorporate this change.

The latter reason was equally important, as the use of linear regression to estimate the parameters of a time series model may be criticised as the assumption of independence of the observations that underlies the estimation process does not hold. Repeated observations over time are usually not independent, since last year's number of casualties is often a reasonable predictor for the current year's number. As a consequence, the residuals are serially correlated resulting in biases in the standard errors which lead to inaccurate confidence intervals. The presence of positive autocorrelation was detected in the KSI and the all casualties models but not the fatality model. The Cochrane–Orcutt method was used to take account of the autocorrelation, and the results confirmed the theoretical expectation. Although the parameter estimates from the original regression were unbiased the confidence intervals were shown to have been underestimated: they should have been around 2.5 times greater.

The exponential decline in past casualty rates provided a feasible means of forecasting casualty rates – under the general assumption that road safety measures would be introduced in future at the same rate and with the same effectiveness as in the past. The developed models were used to forecast the casualty rates for the year 2000 using the models with and without the trend change and confidence intervals were calculated making allowances for the positive autocorrelation.

A forecast of the total traffic in 2000 was needed to convert the rates into casualty numbers, and official predictions made by DfT economists were used. These were based on two economic scenarios that represented optimistic and pessimistic combinations of assumptions about growth in GDP and fuel prices: national mileage was predicted to grow by 23–40% between 1989 and 2000. In the event, the traffic growth followed the more pessimistic prediction. This highlights the importance of examining a range of transport scenarios to reflect the uncertainty of the predictions, as was done when casualty forecasts were prepared for 2010 (described below). This method of casualty forecasting has two components, forecasts of casualty rates and forecasts of traffic growth. The same is true of the more elaborate method that is described below, and it is important to understand that the two components are prepared independently. There is a long tradition in Great Britain of using econometric methods to prepare and update official traffic forecasts, for example DfT (2007). The novel element being presented here is the forecasting of casualty rates.When the success of the casualty forecasts is assessed later by comparing actual and predicted data, the focus will be on casualty rates rather than casualty numbers. Any reader with an interest in the evolution of British casualty and exposure data should refer to official publications such as DfT (2008).

2.1. Casualty forecasting for 2010

This experience of casualty forecasting was applied to a major project in the late 1990s. At that time, the Transport Research Laboratory (TRL) had been commissioned by the DETR (now the Department for Transport, DfT) to help with setting a national casualty reduction target for 2010, in succession to the original target set in 1987. That target had been to reduce the casualty total by one third, but the experience of the original casualty reduction target, as summarised in the Introduction, suggested the value of separate targets for ''severe" and slight casualties. This led to the concept for KSI target. It will be seen in Section 2.4 that a target for reducing killed was considered at a later stage, and the likely reasons for not adopting one are discussed.

The task was to develop a numerical target for casualty reduction that would be challenging but achievable. If the target was challenging then the potential for casualty reduction would be maximised; if it was recognised as achievable then road safety professionals and others would feel motivated.

There are various measures of the risks of road travel, each with its strengths and weaknesses. The rate of casualties per billion vehicle km of traffic is arguably the best, so why was the target not expressed in terms of the casualty rate? While a rate-based target has many theoretical advantages, there was a compelling argument in favour of expressing the target in terms of casualty numbers. It was judged that so many people find the concept of a casualty rate difficult to grasp that a target expressed in terms of casualty rates would command less public support than one set in terms of numbers.

While the adoption of the target for 2000 was felt to have contributed appreciably to the national improvement in road safety, it was recognised that an improved approach was required for predicting the future (Broughton et al., 2000). Also, the predictions needed to take account of the effects of road safety policy on national casualty trends as far as they could be established reliably from the national accident data. Few road safety measures affect all road user groups equally, so various groups of road user were treated separately in the analyses. Five groups were used:

car occupants,
motorcyclists,
pedal cyclists,
pedestrians,
others (includes all road users not in the first four groups).

The basic forecasting approach described above was generally suitable for the new forecasts, but it needed to be developed to accommodate the requirement to take account of the effects of road safety measures. Disaggregating the forecasts (i.e. providing forecasts for each of the road user groups rather than for all road users) presented few difficulties, but the incorporation of the effects of road safety policy proved to be more demanding. At the national level, a wide range of road safety measures had been introduced over the years, and further measures might be introduced in future. The effects of some measures on the national casualty data could be identified reliably, but in most cases there were major problems of analysis or interpretation. For example, some measures affect only relatively small groups of casualties, while others such as road safety education are intrinsically difficult to assess. The technical literature reports numerous studies that have demonstrated the effectiveness of specific road safety measures, but virtually all of these have relied on data that were collected specially, or were available in certain areas but not nationally. Thus, the requirement that it should be possible to establish effects reliably from the national accident data proved to be restrictive.

Broughton et al. (2000) concluded that there were only three areas of national policy that had contributed significantly to past casualty reductions, had effects that could be assessed reliably using STATS19 data and could be incorporated into the forecasting process. These were termed the DESS measures, and they are discussed in Section 2.2:

Measures to reduce the level of Drink/driving.
Road safety Engineering.
Improved standards of Secondary Safety (crashworthiness) in cars.

The effects of the three DESS policy areas were assessed and the casualty totals between 1983 and 1998 were adjusted to show what might have occurred if these policies had not been effective. These adjusted totals indicated what had been achieved by all ''other road safety" activities in combination. This combination was referred to as the ''core" road safety activities, comprising the many policies with effects that could not be measured from the national accident data. The analyses suggested that the DESS measures had together been roughly as effective as the core measures in containing the growth of slight casualties. Among KSI, however, the core programme had proved more effective than the three policy measures.

The decision to adjust the casualty data from 1983–1998 to show what might have occurred if the three DESS policies had not been effective has complicated the presentation of results, but had a clear purpose. The future effects of these policies might differ from those identified by analyses of the past, and this adjustment allowed alternative levels of future effect to be modelled.

The casualty forecasts for 2010 had to be sensitive to the measures that might be included in any new road safety strategy. These could be grouped as follows:

Fig. 1. Illustration of the forecasting model – idealised example.

Fig. 2. Adjusted car occupant KSI rates, 1983–1998 and 2010.

the DESS measures,
the core programme,
new measures, comprising all measures which are either innovatory or a substantial expansion of existing measures.

The stages of the procedure for forecasting the consequences of a new road safety strategy by 2010 are illustrated in idealised form in Fig. 1. It shows the steady decline of the actual rate from 1980 to 1998, and the adjusted rate showing the slower decline that would have happened if there had been no DESS measures. Starting from the actual rate in 1998, the baseline forecast is the result of extrapolating this slower decline to 2010. The assumed effect of the new policies is then applied to reach the final forecast.

The stages can be summarised as follows:

1. estimate casualty rates in 2010 to show what would be expected if there were no further DESS measures (e.g. secondary safety remained at the level achieved in the new cars sold in 1998) and only the core road safety activities were undertaken (at the 1998 level of effect) during the period to 2010,
2. prepare a baseline casualty forecast using these estimated rates together with predictions of the volume of road travel in 2010,
3. apply the assumed effects of the measures in the new road safety strategy (including any further DESS measures) to the baseline forecast.

The idealised casualty rate in Fig. 1 follows a precisely exponential decline. Fig. 2 presents an actual example of the type of data that was available in 1998 when the forecasts for 2010 were being finalised. The Figure uses the example of the car occupant KSI rate, and presents the logarithm of the rate to judge whether the decline was actually exponential. The decline of this adjusted casualty rate was approximately exponential over this period, and the forecast in stage 1 assumes that this regular decline will continue until 2010. There was considerable debate when finalising the forecasts about whether to base them on the average trends over the 1983– 1998 or 1991–1998 periods, shown by the red and blue lines respectively. The 1983–1998 period was chosen to forecast this particular rate, which led to lower forecasts, although the shorter period was chosen for several other rates.

The cross for 2010 denotes the log of the adjusted car occupant KSI rate, conditional upon the assumption that the average rate of change seen prior to 1998 would be maintained until 2010. The baseline forecast for the number of car occupants KSI is calculated from this, together with a prediction of the volume of car traffic. Fig. 4 will compare this forecast with the actual development of this rate to 2007.

Fifteen forecasting models were developed: for Killed, KSI and slight casualties for each of the five sets of road users. Broughton et al. (2000) provide details of these models and of the forecasts that were prepared.

2.2. Estimating the effects of the DESS measures

The number of casualties in drink/drive accidents is not known exactly because many drink/drive accidents are not detected; however, the number can be estimated and is published annually by Department for Transport (e.g. Department for Transport, 2008). The estimates are based on two sources:

details of breath tests recorded in the STATS19 database that were carried out after road accidents and
BAC data from post-mortems carried out on people who were killed in road accidents.

The estimates show that the proportion of casualties who were injured in drink/drive accidents fell between 1983 and the early 1990s. In order to remove the benefits of the reduced level of drink/driving, the annual totals of drink/drive casualties were increased by the number required to restore the proportion that existed in 1983.

The benefits of road safety engineering were assessed by analysing the accident records of a sample of sites where road safety engineering had taken place. This analysis, combined with the level of expenditure on these works nationally, indicated that the engineering programme carried out between 1985 and 1995 reduced casualties by an average of 0.5% per year. For example, without the engineering programme, there would have been 5% more casualties in 1995. Hence, 1986–1998 totals were increased progressively to remove the benefits of the programme.

The secondary safety (crashworthiness) of a vehicle refers to the protection offered to its occupants when involved in an accident (as distinct from primary safety, which refers to systems such as steering and brakes which should help to avoid accidents). Thus, if car secondary safety has improved then injuries should tend to be less severe for occupants of more modern cars when involved in accidents. The enhanced STATS19 data includes vehicles' ''year of first registration", and analysis showed this to be true. The benefits of secondary safety were calculated by estimating the increased number of occupants of post-1981 cars who would have been killed or seriously injured if their cars had had the same level of secondary safety as cars first registered in 1980 and 1981. It was assumed that the improvements simply reduced injury severity: with the reduction in the number of car occupants killed or seriously injured matched by an equal increase in the number slightly injured. With this assumption, the calculations suggested that if all cars on the roads in 1996 had only the level of secondary safety found in cars first registered in 1980 and 1981 then overall 12.5% more car occupants would have been killed or seriously injured. The car occupant casualties were increased accordingly to estimate the totals that would have occurred if secondary safety had remained at the level reached among the cars first registered in 1980 and 1981.

Broughton (2003) provides details of the statistical model, developing and updating the original account in Broughton et al. (2000). Both demonstrated that these improvements had brought substantial benefits. Car occupants account for almost half of all casualties in Great Britain, so the benefits of improved secondary safety play a central issue in casualty forecasting. Broughton (2009) analyses the data up to 2007 and shows that the accelerated rate of improvement that had been identified around the 1990 registration year has continued. For example, Table 1 compares the occupant protection of cars registered in 2006–2007 compared with cars registered in 1990–1991 (the reduction is independent of the accident year).

These results play two roles in casualty forecasting. In addition to calculating the adjusted car occupant casualty rates that are extrapolated in stage 1 of the procedure, they also provide the evidence for predicting the casualty reductions from future improvements in secondary safety in stage 3. The actual analysis is carried out with casualty data car drivers, as the number of passengers per car is variable, and the changes are generalised to car occupant casualties.

The method for this second role makes use of the coefficients estimated when fitting the statistical model. It consists of adjusting the casualty data from the latest year to simulate the number of car drivers that would have been killed or seriously injured if the accident-involved cars had been N years newer, where the forecast is for N years ahead. For example, N = 12 when forecasting for 2010 based upon analyses of 1998 casualty data. The improved secondary safety of newer cars means that the severity of each group of casualties would have been less if the cars had been newer, and the casualty reduction can be estimated using the coefficients from the analysis (this assumes that the improvement of secondary safety has no effect on the casualty total but reduces severity, which may be a conservative assumption). The reductions in fatal and serious casualties from the various groups are summed to estimate the overall changes. This leads to overall percentages which are used in stage 3.

The adjustment to allow for newer cars makes use of the most recent modelling results. Taking the example of the 2010 forecasts, the calculation was made with the car driver casualty data from 1998 and the results of the secondary safety analyses of these data. Casualties were grouped by car registration year for the calculation, which has two parts:

(a) Cars registered in year Y (Y 6 1986) are replaced by cars registered in year Y + 12 whose improved level of secondary safety is already represented in the data: this represents the replacement of older cars by more modern cars as part of the continuous renewal of the car fleet.
(b) Cars registered in year Y (Y > 1986) are replaced by cars registered in year Y + 12. These cars do not exist so their collective level of secondary safety is not known and must be estimated using the results of the secondary safety analysis; the 2010 forecasts were obtained by extrapolation.

Table 1 The reduction in the proportion of occupant casualties who were killed or seriously injured in cars registered in 2006–2007, compared with cars registered in 1990–1991.

Speed limit of road (mph)	Killed (%)	Seriously injured (%)
640	67	42
>40	59	43

2.3. Identifying new measures

An important stage in forecasting the number of casualties in 2010 consisted of identifying the new measures which might be included in a future road safety strategy and assessing their likely effectiveness. After extensive consultation and the announcement of the form of the new target, the DETR established the Safety Targets and Accident Reduction Group to work on the development of the new road safety strategy. Eight subgroups were set up to work on specific issues, with mixed membership including road safety professionals and departmental civil servants.

The outcome was a list of nine new measures, in addition to the continuation of the three DESS measures. The potential effectiveness of all measures was assessed, using whatever evidence was available. At one extreme, the evidence of the likely benefits of improved car secondary safety was relatively strong, as described in the previous section. At the other extreme, several measures were more aspirational; a casualty reduction goal could be set but the details of how to achieve that goal were unclear at that time. An example of this was ''additional measures for improved driver behaviour", where the estimated effect was to reduce all categories of casualties by 1% but no clear route to implementation had been identified.

The fruits of these deliberations are summarised by Broughton et al. (2000). In terms of casualty forecasting, the details of a potential future road safety strategy are less important than the overall effectiveness of that strategy, and the problems of estimating the effects of a combination of measures were recognised (i.e. how to allow for the possibility of two measures operating on the same group of accidents). The approach adopted was pragmatic. As far as possible, measures were defined to be independent. When dependency could not be avoided in a group of measures, they were ranked and the incremental effects of the lower-ranking measures were estimated. While the approach adopted may not be ideal in theory, the potential errors are probably dwarfed by the difficulties of estimating the effects of measures that might not be introduced for many years.

Following this account of the work carried out in the late 1990s to assess the effects of new measures, it is relevant to skip forward to 2007. Section 4 describes how progress towards the 2010 casualty reduction target has been monitored since 2000, with two formal reviews in 2004 and 2007. The latter review considered the extent to which the new measures envisaged by Broughton et al. (2000) had been introduced. It also considered whether the effectiveness estimates had been reliable, relying on analyses of the latest STATS19 data, and the findings are summarised by Broughton and Buckle (2007).

It was concluded that, despite the fact that there had been no progress with certain measures, about 44% of the overall predicted benefit had been realised by the end of 2005. It was further estimated that, taking account of what was known at the time about likely future developments, the final benefit from these new measures by 2010 was likely to be about 75% of the overall prediction. In view of the inherent difficulty of the task undertaken a decade earlier, these figures represent an encouraging degree of success.

2.4. The casualty reduction target for 2010

The three-stage forecasting procedure and the key data required to apply it have been described. The final steps in the preparation of the national casualty reduction target for 2010 will now be described.

The forecasts depend upon predictions of the volume of road traffic for 2010 by the five road user groups. A range of ''transport scenarios" was defined to reflect the uncertainty of the predictions. The scenarios did not necessarily exhaust the range of possible outcomes but were sufficient to demonstrate the extent to which road casualty outcomes were sensitive to different activity levels for different road user groups. Each scenario consisted of predictions for 2010 of the levels of traffic (all motor vehicles, cars, motorcycles) that were based on current national road traffic forecasts (NRTF, published in DETR, 1997), also of the relative level of pedestrian and pedal cycle activity. For example, the assumed levels of car traffic based on the NRTF in 2010 were

ACar 35% more than 1996 car traffic (NRTF high forecast),
BCar 25% more than 1996 car traffic (NRTF central forecast),
CCar 15% more than 1996 car traffic (NRTF low forecast) and
DCar 1996 car traffic.

Four alternative levels were defined for pedal cyclists, and three for each of the other groups. Some of the possible combinations were intrinsically implausible; for example, it was unlikely that if car traffic grew strongly then pedestrian activity would also grow strongly. Thirty-six plausible combinations were identified, and a set of casualty forecasts (KSI, slight casualties) was prepared for each of these transport scenarios.

These forecasts provided the numerical input to the political process which led in March 2000 to the announcement of the new casualty reduction target that will be set out in the following section. The selection of this target involved judgements about the likelihood of the various scenarios being realised as well as the likelihood of implementation and confidence in the predicted effectiveness of the various elements of the strategy.

The most common form of casualty reduction target is in terms of reducing the number of people killed, whereas the British target for 2010 refers to reducing the number of people killed or seriously injured, with a secondary target of reducing slight casualties. There appear to be two explanations for this preference for a target in terms of KSI. Firstly, in the light of the relatively low annual number of people killed, there was concern that an ''unusually bad" target year could lead to the target being missed – although these concerns have not prevented other countries with smaller fatality totals from adopting targets in terms of reducing the number killed. Probably more significant was the conclusion of Brough ton et al. (2000) that ''...the fatality reduction that may be expected with the full set of measures and any particular transport scenario would be about 2% points greater than the KSI reduction". The general similarity of the fatality and KSI trends up to 1998 indicated that fatality reductions from 2000 were likely to be broadly parallel to the KSI reductions, so it appeared unnecessary and possibly confusing to introduce a further target for fatalities. In fact, it will be seen that the two trends have diverged since 1998, and Broughton and Knowles (2009) have examined the possible reasons.

3. Monitoring progress

In March 2000, the Government announced the new national casualty reduction target (DETR, 2000) that was informed by the casualty forecasts whose preparation has been described:

''By 2010 we want to achieve, compared with the average for 1994–1998:

a 40% reduction in the number of people killed or seriously injured in road accidents,
a 50% reduction in the number of children killed or seriously injured, and
a 10% reduction in the slight casualty rate, expressed as the number of people slightly injured per 100 million vehicle kms."

Fig. 3. Trends in killed and KSI, 1990–2007.

Fig. 4. Adjusted car occupant KSI rates, 1983–2007.

At the same time, it announced that progress would be reviewed after 3–6 years to determine whether extra efforts might be required to ensure that this target would be achieved.

In fact, progress towards the target has been reviewed annually at TRL, while the Department for Transport published formal reviews in 2004–2007 that were informed by this monitoring of progress. The forecasting methodology described earlier in this paper has provided the basis for this monitoring, comparing actual casualty rates with the original forecasts and preparing fresh casualty forecasts for 2010 based on updated traffic forecasts. A secondary benefit of this monitoring has been the opportunity to assess the reliability of the overall approach to forecasting.

Broughton and Knowles (2009) present the results of analyses of casualty data to 2007. The target reduction of the slight casualty rate was exceeded in 2002, while the child KSI reduction target was exceeded in 2006. They predict that the KSI total will be reduced by about 43% by 2010, so it appears that the target will be achieved in all respects. There has been less success in reducing the number of deaths, however, and they predict that this will fall by only 24% by 2010. Fig. 3 illustrates the divergence of the two trends over the past decade.

The annual reports have compared the earlier predictions with the eventual outcome, and Fig. 4 presents the latest version of Fig. 2. The open squares show the adjusted casualty rates to 1998 which contributed to the original forecast, while the solid squares show the adjusted rates from 1999. These rates have been calculated from the new casualty and traffic data, together with estimates of the effects of the DES measures. It can be seen that the actual rate followed the forecast closely in 1999–2002, but has fallen below the forecast since 2003. This fall in recent years is probably evidence of new measures taking effect, as foreseen in stage 3 of the forecasting procedure. The gap between the actual and predicted values in 2007 represents a 13% reduction in car occupants KSI. For the other road user groups, however, there have been no such positive developments, and indeed there have been increases above the forecast trend for pedal cyclists from 2005. While the slight casualty rates for several road user groups have fallen well below the forecasts, concerns over the reporting of slight accidents to and by the police mean that it would probably be unwise to interpret these as signs of improved road safety.

The fact that the number of deaths has fallen less rapidly than the number of serious casualties has led to greater emphasis on trends for fatal casualties. The same basic approach has proved suitable when forecasting numbers of fatal casualties, although trends have tended to be more variable. This is illustrated by Fig. 5 in the case of car occupants. The most recent forecasts have been based on the 1997–2007 trend, although the low rate in 2007 may suggest that the trend is changing once again. Note that the adjusted rate is shown; the actual fatality rate has fallen but the Figure shows that it would have risen if it had not been for the benefits of improved car secondary safety.

This assessment of the forecasts has focussed on casualty rates rather than casualty numbers as explained in Section 2. In practice, traffic grew less after 2000 than the official central forecast (Broughton and Knowles, 2009) that had been regarded as the most likely, which means that progress towards the target has been faster than it would have been if that forecast had been correct. It appears that the volume of traffic in 2010 will actually be close to the official low forecast.

4. Casualty forecasting in other countries

The methods adopted in Great Britain to forecast casualties have been described in Section 2 and to date have proved to be reasonably reliable and helpful in informing decisions on target setting. Other statistical methods exist for analysing time series; this section briefly reviews relevant experience from other countries and discusses the reasons for adopting this approach in Great Britain.

Fig. 5. Adjusted car occupant fatality rates, 1983–2007.

As explained in Section 2, the main consequence of failing to take account of the positive autocorrelation was that the standard errors were underestimated; however autocorrelation should not lead to biased parameter estimates. As a result, the estimated confidence intervals were too small, but the confidence intervals for forecasts 10 or more years ahead that take account of autocorrelation are so wide that they predict that casualty rates are as likely to increase as to decrease and offer no usable information in target setting. ''Confidence" in the forecasts presented in this paper comes not from conventional statistical tests but from the relative stability of the trends that have been identified. There is no guarantee that a trend that has been stable in the past will not change, and Fig. 5 has provided an example of this. Nonetheless, it is possible for non-statisticians to understand the elements of the forecasting process, including the inherent assumptions, and judge its strengths and weaknesses.

This raises another aspect of ''confidence" in the forecasts. The audience for these forecasts is broad but largely non-statistical; most of the people actively interested in road safety would be unable to understand more elaborate forms of statistical analysis. In Great Britain, and perhaps elsewhere, they would not have confidence in the outcome of a process the details of which they found baffling.

Other countries have developed different approaches to evaluate developments in road traffic safety and some have used these models to forecast. Belgium, Canada, France and Sweden have used ARIMA and DRAG2 models. These models are specific time series models which take the dependencies between the observations in the time series into account. An important requirement of ARIMA based models is that the time series must be stationary (i.e. constant mean and variance over time) which is usually achieved by differencing. These models require a minimum of 6 years of data and are able to forecast usually for 1 year ahead. Structural time series models are the preferred approach in the Netherlands (Reurings and Commandeur, 2006; SWOV 2006). These models also deal explicitly with dependencies in the data allowing the trend to vary slightly over time but do not require the series to be stationary. Bij leveld and Commandeur (2006) used Dutch annual figures for traffic (number of annual motor vehicle kms driven) and fatalities to forecast four years ahead (1999–2003) using state space models and compared the results with the actual known figures. The forecasts clearly underestimated the traffic figures which led to an over estimated fall of Dutch traffic fatalities. Although the true values were within the confidence intervals, the confidence intervals were so wide they could be regarded as not practically useful, especially for forecasting 10 years into the future – a requirement for target setting. It is not clear from the literature which approach provides the most reliable forecasts for 10 or more years into the future.

Few countries have developed models to forecast and monitor progress towards casualty reductions targets. Brüde (1995) developed a model to forecast the number of fatalities in Sweden using data from 1977–1991 to forecast to 2000:

Fatalities ¼ a byear traffic^c

The model parameters were estimated using a generalised linear model under the assumption that the number of fatalities followed a poisson distribution. The historical fit was reported to be good and the forecasts for 1992–1993 were reported to be accurate. Lassarre (2001) used structural time series models to compare the road safety developments among 10 European countries. He

² ARIMA models are auto-regressive integrated moving average models. A ''Demand for Road use, Accidents and their Gravity" (DRAG) model is an extension of the ARIMA model which allows for exposure, accidents and accident severity to be modelled separately, and explanatory variables to be added.

extended the classic model based on a decreasing exponential form of the rate of fatalities per vehicle km to incorporate intervention functions and to replace the deterministic trend by a stochastic one, although found the deterministic trend to be appropriate in the UK. This was not the case for all European countries with the rate of decay of the risk being relatively unstable for the Netherlands. Stipdonk and Wesemann (2007) used state space regression modelling fatality risk and traffic to produce long-term forecasts of road traffic fatalities in the European Union. They forecast seven years ahead. They reported that the main limitation to their method was the modelling of traffic. It was not clear that traffic will develop in accordance with the log linear extrapolation using a state space technique. Other ways of modelling traffic may be more reliable such as using an econometric approach such as that used for the British forecasts (DfT, 2007).

Corben et al. (2008) took a slightly different approach forecasting serious casualties in Australia. The modelling approach operates at a macro level requiring 150 input variables and incorporates road safety initiatives that are expected to have a sizeable impact on serious casualties. Firstly, the level of serious casualties expected to occur in the absence of a significant road safety strategy was estimated. This was done by combining the effect of traffic growth (estimated at 2.6% per year) with an estimate of future improvements in serious casualty rates due to the gradual effects of increasing motorisation (estimated at 1.6% per year) derived from the trend in serious casualties per vehicle km travelled. This resulted in a forecasted general upward trend of 1% per year to 2020. Future savings in serious casualties were forecast for various initiatives in each year until 2020, using evidence based estimates of effectiveness and crash data for Victoria. The effectiveness of a strategy was the total number of serious casualties prevented over the strategy life compared with the level of serious casualties expected to occur in the absence of a significant road safety strategy. Individual countermeasures were then combined into the 'Optimum Safe System Option'. Some sensitivity analysis was carried out using varying estimates of traffic growth and investigating the effects of delays in implementing various strategies.

5. Conclusions

Forecasting the future is generally an uncertain and difficult process. The timescale required for improving road safety means, however, that it is important to prepare long term plans that are soundly based upon current knowledge and that take account of likely future developments. This paper has described the methodology that was developed to forecast the number of casualties Great Britain in 2010 in some detail. The range of forecasts that were prepared in the late 1990s provided the numerical context for the national casualty reduction target for 2010 that was announced in 2000. Since then, the methodology has provided the basis for monitoring progress towards the target, and the results have been used by the two 3-yearly reviews of progress that have been carried out by the Government. Work is underway to provide the numerical context for setting a new casualty reduction target for 2020.

The methodology cannot make allowance for unforeseen future developments, so the forecasts have not proved to be correct in all respects. It does provide, however, a framework for examining the inherent uncertainties about future developments and for making full use of available knowledge, so it has played a valuable role in the process of formulating a new road safety strategy and monitoring the development of road safety.

The Introduction mentioned the hope that the experience summarised in this paper ''can assist other countries that may be planning to set a casualty reduction target". The main points that have emerged may perhaps be summarised as follows:

The value of setting targets based on systematic casualty forecasts that take account as far as possible the effects of road safety measures.
The importance of adopting a statistical methodology that is theoretically sound yet may be understood by non-statisticians.
The need for using disaggregate forecasting models, although the level of disaggregation may be constrained by the need to prepare robust forecasts.
The value of treating explicitly the uncertainty that exists over future changes in the volume of road travel.

In the final analysis, however, it must be acknowledged that since 2000 Great Britain has fallen behind European neighbours such as Sweden and the Netherlands in terms of the most widely used international metric for comparing levels of road safety – the rate of deaths in road accidents per 100,000 population. These countries do not appear to have used such elaborate approaches for monitoring casualty trends. While the methodology described in this paper has provided useful tools, these can only play a secondary role in the national task of improving road safety.

Acknowledgements

The research described in this paper was commissioned by the UK Department for Transport and was carried out in the Statistics and Engineering Group of the Transport Research Laboratory.

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