Fractions of fatal crashes attributable to speeding: Evolution for the period 2001–2010 in France

Accident Analysis and Prevention 52 (2013) 250–256

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Fractions of fatal crashes attributable to speeding: Evolution for the period 2001–2010 in France Vivian Viallon a,b,c,∗,1 , Bernard Laumon a,b,c,1 a b c

Université de Lyon, F-69000, Lyon, France IFSTTAR, UMRESTTE, F-69500, Bron, France Université Lyon 1, UMRESTTE, F-69000, Lyon, France

a r t i c l e

i n f o

Article history: Received 10 August 2012 Received in revised form 13 December 2012 Accepted 19 December 2012 Keywords: Speed Speeding Crashes Fatalities Modelling

a b s t r a c t Road safety is a major concern in the West, especially in France. Among all the established risk factors for fatal crashes, speed is specific in two ways: every road-user is exposed to it, and it increases not only crash rates but also the severity of crashes. Thus, speed regulation is of primary importance in road-safety policy and has also generated much public debate. To contribute to this debate, we constructed a power-model which relates the number of fatal crashes to speed raised to the power four. Despite its simplicity, this model fitted the data well. Notably, it enabled the fractions of fatal crashes attributable to various levels of speeding to be estimated. Data for secondary roads over the period 2001–2010 showed that the fraction of fatal crashes attributable to high-level speeding (>20 kph over the speed limit) decreased from 25% to 6% and that attributable to medium-level speeding (10–20 kph over the speed limit) decreased from 13% to 9%, whereas that attributable to low-level speeding progressively increased from 7% to 13%. Similar trends were observed on main roads. These results highlight the effectiveness of the speed regulation policies introduced during the study period with respect to high-level speeding. They also suggest that future policy should focus on low and medium-level speeding in order further to reduce road deaths significantly, since these levels now correspond to the major fraction of fatal crashes. © 2013 Elsevier Ltd. All rights reserved.

1. Introduction Common sense tells us that speed is at the core of road safety for two main reasons. Firstly, every road user is exposed to speed (both their own and other users’). Secondly, it is obvious that if all vehicles’ speeds were 0 kph, then no crashes, fatal or otherwise, would occur. According to the European Road Safety Observatory (ERSO), speed is an essential contributory factor in around 30% of fatal crashes in Europe (see http://ec.europa.eu/transport/road safety/specialist/). More precisely, inappropriate speed is the essential contributory factor, as speed as such is truistically implicated in 100% of crashes, whether fatal or not. A fundamental property of the relationship between speed and road safety is that speed affects both the risk of being involved in a crash and the consequences of the crash in terms of injury.

∗ Corresponding author at: Université de Lyon, F-69000, Lyon, France. Tel.: +33 4 72 14 25 10; fax: +33 4 72 37 68 37. E-mail addresses: [email protected] (V. Viallon), [email protected] (B. Laumon). 1 Both authors equally contributed to this work. 0001-4575/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.aap.2012.12.024

The increased risk of crash with increasing speed can be explained by reduced stopping distance, exceeding critical speed on a curve, loss of friction between tires and road, and the reduced capacity of the driver to detect and react to hazards (Patterson et al., 2000). Increased crash severity with increasing speed can be explained by the fact that the higher the speed, the greater the energy released in a collision with another vehicle, road user or obstacle. Crash severity for vehicle occupants typically depends on the rapid speed change the vehicle undergoes in a crash, often referred to as “deltaV” (see TRB, 1998; Evans, 1991). The energy released during a crash according to delta-V is the kinetic energy built up by the movement of an object, and is proportional to the square of the speed: Fildes and Lee (1993) stated that a 20% increase in speed results in a mean 44% increase in the kinetic energy dissipated in a crash. This relation between kinetic energy and crash severity is illustrated by the study conducted by the Peugeot-Renault biomechanics laboratory on 100,000 occupants of small cars fitted with seatbelts (see OECD/ECMT, 1996): at speeds up to 35 kph there were practically no fatalities, while at 70 kph almost 50% of vehicle occupants were killed. Many epidemiological studies have confirmed this naturally intuitive relationship between speed and both crash rates and crash severity. In their review of the subject, Aarts and van Schagen

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(2006) distinguished two types of study: several authors studied individual vehicle speed and established that crash rate increases with speed according to either a power function (Maycock et al., 1998; Quimby et al., 1999) or an exponential function (Fildes et al., 1991; Kloeden et al., 1997, 2001, 2002) of vehicle speed; others, focusing on average speed at road section level, generally found a power function (Finch et al., 1994; Nilsson, 1981, 2004), although other functions have also been reported (Baruya, 1998). Aarts and van Schagen (2006) highlighted Kloeden et al.’s exponential function and Nilsson’s power functions as best describing the relationship between crash rate and, respectively, individual speed and average speed at road section level. In particular, Nilsson’s power functions have been shown to fit various data for different road types (Nilsson, 2004; Elvik et al., 2004). Although every road user is exposed to speed, this exposure is not homogeneous since speed distribution is generally widely scattered, even in a given network (e.g., freeways). Several studies related speed dispersion on a given road section to crash rate (Kloeden et al., 1997, 2001, 2002; Garber and Gadiraju, 1989; Taylor et al., 2000, 2002). Some suggested that low-speed vehicles could be partly responsible for increased crash frequency (Solomon, 1964; Cirillo, 1968; RTI, 1970), but it is now usually taken as read that the increased crash rate associated with speed variability is almost exclusively due to the fastest traveling vehicles (see Aarts and van Schagen, 2006 for more detail). Common sense, basic physics and epidemiology thus all converge to highlight a very strong relationship between high speed and both crash rates and crash severity. This is why a large majority of drivers consider speed to be a very important problem for road safety: more than 80% of European drivers stated that driving too fast is often, very often or always a contributory factor in road crashes (SARTRE 3, 2004). However, the ERSO estimated that 40–50% of drivers exceed speed limits and that 10–20% do so by more than 10 kph. This has naturally led to various speed enforcement measures in Europe: for instance, the use of fixed speed cameras has been widely generalized since 2003 in France. Most people consider that this accounts for the observed reduction in average road speeds as well as the significant reduction in the number of fatal crashes in France (by about 46% between 2001 and 2010). This general impression is in agreement with the conclusions of most epidemiological studies on the subject, which showed the effectiveness of speed cameras in reducing the number of road traffic collisions and related casualties; levels of confidence, however, were generally poor (Pilkington and Kinra, 2005) and the use of speed cameras and speed regulation policies in general remain highly controversial. In particular, some people argue that low-level speeding (less than 10 kph over the speed limit) is not dangerous and should not be punished – whereas fines in France currently range between 45 and 450 euros for such an offense, plus a loss of 1 out of 12 points on the driver’s license. One way of contributing to this debate is to determine the fraction of fatal crashes attributable to low-level speeding and its recent evolution. This is the main objective of the present paper. More precisely, the relationship between speed distribution and number of fatal crashes is first described on a power model, which enables the fractions of fatal crashes attributable to various levels of speeding to be estimated.

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2.1. The data Data for speed distributions and numbers of fatal crashes over the 2001–2010 period were obtained from the NIORS (French National Interministerial Observatory for Road Safety). For more than a decade, the NIORS has been implementing a survey providing a representative sample of speed distributions on the entire French road network (see Appendix for a more detailed description) and intended to guarantee a faithful representation of evolution over the long term (NIORS, 2010). Speed distribution was then computed after adjustment for period of the year (divided in three: January–April, May–August and September–December), period of the day (daytime and night-time), type of network (freeway [autoroute], main roads [routes nationales], secondary roads [routes départementales], etc.) and vehicle type (truck, car, bike, etc.). Speed, however, is not measured during the night on certain networks, for reasons of personnel safety: this is notably the case for secondary roads. Moreover, for technical reasons, data for the last third of 2008 were not available. In France, as in many other countries, fatal crashes have been recorded for decades by the authorities. The NIORS provides their distribution according to the same criteria as for speed (three thirds of the year, daytime versus night-time, road type, vehicle type). Before 2004, crashes were recorded as fatal if at least one person involved in the crash died within 6 days, and after 2005 within 30 days. The NIORS uses a correction factor of 1.069 to estimate numbers of deaths within 30 days from numbers of deaths within 6 days (e.g., in international comparisons of road mortality before 2004), and the present study applied a correction factor of 1.065 for numbers of fatal crashes. This was derived from the distribution of the number of deaths per fatal crash over the 2001–2010 period and the NIORS correction factor of 1.069 for numbers of road traffic deaths; other correction factor values were also tested (in the range [1.055–1.075]), with only marginal differences in results. To improve the homogeneity and precision of our results, and also because it is the main issue of current debate, only crashes involving personal cars were considered in the study. Likewise, it was decided to focus on secondary roads, where most fatal crashes occur. Some data for one-lane main roads are also provided, mainly for comparison. Only daytime observations were used, since data for the night–time are not available for secondary roads, as mentioned above. The NIORS provided numbers of fatal crashes (n) and speed distributions ((fj )1 ≤ j≤ J ) for each third of the year over the study period, except for the last third of 2008. Here, fj stands for the proportion of cars traveling at speed vj , where (vj )1 ≤ j≤ J is a categorization of speed (the classes ≤40 kph,]40–50] kph, . . .,]180,190] kph and >190 kph will be used hereafter). Twenty-nine observations for ni and (fij )1 ≤ j≤ J were available (each observation i corresponding to a particular third of a particular year). The NIORS also provided the number of cars on main roads for each third of the year between 2001 and 2010; as will be made clearer below, only trends are needed for the latter data and these trends are likely to be very similar on main and secondary roads.

2.2. The model 2. Materials and methods In this section, a power model is described, which relates the number of fatal crashes to speed distribution. We also present the methods used (i) to estimate the coefficients and (ii) to deduce the fractions of fatal crashes attributable to various levels of speeding. Firstly, we briefly describe the data set used.

2.2.1. Basic model, following standard physical rules The rationale of the present model is similar to that of Nilsson (1981, 2004). In particular, only speed is taken as affecting fatal crash rates (i.e., only the marginal effect of speed on fatal crashes rates is taken to be of interest). In this context, a natural assumption, made by Nilsson (1981, 2004), is that fatal crash rates increase with speed at least as fast as does kinetic energy. Thus, for traffic

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consisting of N vehicles, all driving at speed v, the probability p and number n of fatal crashes will be: p=

K 

˛k vk

and n = Np + ε = N

k=1

K 

˛k vk + ε

k=1

for some integer K ≥ 2 and parameters ˛k , k ≥ 1. In this equation, ε denotes random noise. Because both n and p have to be nondecreasing functions of speed , it is further assumed that ˛k ≥ 0. The parameter K is set at K = 4, which is the value used in Nilsson’s equation relating average speed to number of fatal crashes (Nilsson, 1981, 2004); this value is intuitively appealing, since both crash risk and risk of death in a crash can be expected to be proportional to kinetic energy. In practice, however, even focusing on a specific road network (such as secondary roads during the daytime), speed is still highly heterogeneous. Given a categorization {v1 ,. . ., vJ } for speed, and with fj denoting the proportion of cars driving at speed vj , the model writes: n = Np + ε=N

J K  

fj ˛k vkj +ε =

j=1 k=1

K 

˛k N

k=1

J

J 

fj vkj + ε =

j=1

K 

˛k Xk + ε (1)

j

Xi,k = Ni j=1 fi,j vkj , estimates of parameters ˛k in model (1) can be obtained by solving the following optimization problem: ˆK = ˛ ˆ 1 , ..., ˛

arg min ˛1 ≥0,...,˛K ≥0

 i

ni −



2

K

˛k Xik

ni =

(2)

K 

(˛k + k I[Qi = 2])Xik + εi

(3)

k=1

where I[.] denotes the indicator function: i.e., I[Qi = 2]=1 if Qi = 2, and 0 otherwise. The model was also improved by taking account of the fact that it is generally agreed that both car and road safety have improved over time. It was therefore decided to include calendar year in the model. However, because speed distribution was also closely related to calendar year over the 2001–2010 period, a two-step estimation procedure was employed. Model (3) was first fitted using the penalized package to ensure that ˛ ˆ k ≥ 0. This led to initial estimators n˜ i for ni , of the form

k=1

where Xk = N j=1 fj vkj . Note that values vj are set at the center of the class for classes of the form[40–50] kph, at 35 kph for class ≤40 kph, and at 195 kph for class >190 kph. Model (1) belongs to the family of power models, as do Nilsson’s equations. With ni , Ni and fi,j denoting respectively the number of fatal crashes, the number of cars on the road and the proportion of cars driving at speed vj for a given period of time i, and with



during Q2. More importantly, daytime is about 45% longer during Q2 than either Q1 or Q3, which obviously affects the total number of exposed vehicles on the road during daytime. To take this specificity of Q2 into account, interaction terms between Xk and Q2 were included in the model. With Q denoting a variable with value 1, 2 or 3 for observations collected during Q1, Q2 or Q3 respectively, model (1) becomes

n˜ i =

K 

(˛ ˆ k + ˆ k I[Qi = 2])Xik

k=1

Then, with Yi = ni − n˜ i , a standard linear model of the form Yi = ˇ0 + ˇ1 (yeari − 2001) +  i was fitted using ordinary leastˆ 0 and ˇ ˆ 1 for parameters ˇ0 and ˇ1 squares, yielding estimators ˇ respectively. Final estimators nˆ i were then computed as nˆ i =

K 

ˆ0 + ˇ ˆ 1 (year − 2001) (˛ ˆ k + ˆ k I[Qi = 2])Xik + ˇ i

(4)

k=1

where again Xik = Ni

J 

fij vkj .

j=1

k=1

known in the literature as non-negative least-squares, using the penalized package of the R software for instance. It is noteworthy that the model can be re-parameterized by defining Ni as the ratio of the number of cars on the road for observation i to the number of cars on the road for observation 1 (so that N1 = 1). With this new definition for Ni , parameter ˛k actu˜ 1 is the number of cars on the ˜ 1 , where N ally corresponds to ˛k N road for the first observation (first third of year 2001). In this way, only trends for numbers of cars on the road need to be known; trends were, as mentioned above, available only for main roads, but trends for secondary roads can be assumed to be very similar. This re-parameterization was therefore adopted, with Ni computed from data available for main roads. 2.2.2. Improvements to the basic model Numbers of fatal crashes and speed distributions on secondary and main roads during the daytime were available for each third of the year or “quadrimester” (Q1: January–April, Q2: May–August and Q3: September–December). Fig. 1 describes the average speeds and numbers of fatal crashes on secondary roads over the 2001–2010 period for each third of the year. Trends on main roads were very similar (results not shown). No difference in average speed was observed between thirds of the year. However, many more fatal crashes occurred during the second third of the year than during the other two. Several explanations may be put forward. First, in France three official long weekends in May and June as well as most summer holidays occur in Q2, and the number of vehicles on the road can therefore assumed to be much higher

2.3. Fractions of fatal crashes attributable to speeding ˆ 0, ˇ ˆ 1 (˛ Given estimators ˇ ˆ k , ˆ k )1≤k≤K , estimators of numbers of fatal crashes nˆ i were derived from Eq. (4). It was also straightforward to get estimators of numbers of fatal crashes that would have occurred with different speed distributions. For instance, with (0)

Xik = Ni

J 

fij [min (vj , 90]k , the number of fatal crashes nˆ i

(0)

that

j=1

would have occurred if no car had exceeded the speed limit (90 kph on secondary and main roads in France) can be estimated by: (0)

nˆ i

=

K 

(0) ˆ0 + ˇ ˆ 1 (year − 2001) (˛ ˆ k + ˆ k I[Qi = 2])Xik + ˇ i

k=1

Similarly, the numbers of fatal crashes that would have occurred under various scenarios can be estimated. Four such alternative scenarios were considered. (i) If only low-level speeding (<10 kph over the speed limit) is eliminated, cars in class] 90–100] kph would be (2) in class] 80–90] kph; this would result in ni fatal crashes, esti(1)

mated by nˆ i . (ii) If only medium-level speeding ([10–20] kph over the speed limit) is eliminated, cars in class [100–110] kph would (2) be in class [80–90] kph; this would result in n1 fatal crashes, esti(2)

mated by nˆ i . (iii) If only high-level speeding ([20–30] kph over the speed limit) is eliminated, cars in class [110–120] kph would be in (3) class [80–90] kph; this would result in ni fatal crashes, estimated (3)

by nˆ i . Finally, (iv), if only “very-high-level” speeding (≥30 kph

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253

Fig. 1. (Left) Evolution of average speed. (Right) Evolution of number of fatal crashes (solid lines) along with the estimate based on the model (dashed lines). Features are adjusted for thirds of the year (Q1, Q2, Q3), and are those observed or estimated for the 2001–2010 period on secondary roads in France during daytime (car crashes only). Data for the last third of year 2008 were obtained by simple interpolation. Table 1 Evolution of proportions of cars driving below or at 90 kph (no speeding), between 90 and 100 kph (<10 kph speeding), between 100 and 110 kph ([10,20] kph speeding), between 110 and 120 kph ([20,30] kph speeding) and above 120 kph (>30 kph speeding) on secondary roads during the daytime in France over the period 2001–2010.

No speeding <10 kph speeding [10,20] kph speeding [20,30] kph speeding >30 kph speeding

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

44.6% 23.2% 18.0% 8.6% 5.7%

46.3% 24.8% 16.0% 7.9% 5.0%

53.8% 24.9% 13.6% 5.1% 2.6%

60.4% 23.9% 10.9% 3.0% 1.9%

65.7% 21.2% 9.1% 2.8% 1.2%

69.6% 20.4% 7.2% 1.9% 0.8%

72.0% 20.0% 5.8% 1.5% 0.7%

75.4% 17.5% 5.1% 1.4% 0.6%

73.8% 19.3% 5.1% 1.4% 0.4%

75.0% 18.2% 5.2% 1.2% 0.5%

over the speed limit) is eliminated, cars in classes [120–130] kph [130–140] kph, . . ., >190 kph would be in class [80–90] kph; this (4) (4) would result in ni fatal crashes, estimated by nˆ i . From these quantities, fractions of fatal crashes attributable to speeding (e.g., all levels of speeding  for S = 0,  low-level speeding only for S = 1, etc.) were estimated as

(S)

nˆ i − nˆ i

/nˆ i , S = 0, . . . , 4.

3. Results 3.1. Description of the data Average speed and number of fatal crashes on secondary roads are shown in Fig. 1. In particular, average speed progressively decreased from about 92.5 kph in 2001 to about 81.5 kph in 2010. However, most of this decrease took place between 2003 and 2007 (most fixed speed cameras have been deployed only since 2003 in France). Table 1 gives more detail of the evolution of speed distribution. 55.4% of vehicles were driving above the speed limit in 2001, progressively dropping to 25% by 2010. It is also clear from Table 1 that the average speed decrease depicted in Fig. 1 was mostly due to a drop in the proportion of moderate to high level speeding (>10 kph above the limit): 32.3% of vehicles were driving at more than 10 kph above the limit in 2001, versus only 6.9% in 2010. The proportion of low-level speeding (less than 10 kph above the speed limit) decreased more slowly: it was about 23% for the 2001–2005 period, 20% for 2006–2007 and about 18% for 2007–2010. The number of fatal crashes progressively decreased from 1035 in 2001 to 561 in 2010. This tendency was observed for every third of the year but, overall, Q2 clearly showed more fatal crashes (at least partly explained by the specificities of Q2 mentioned in Section 2.2.2). (Results for main roads were very similar and are therefore omitted, to save space.) The number of cars on the road increased linearly by 20% over the period 2001–2010, for each third of the year. On average, the ratio of number of cars on the

road during the second and third thirds of the year to that during the first third was about 1.25 and 1.05 respectively (these ratios were approximately constant over the 2001–2010 period). 3.2. Model fitting Parameter estimates are presented in Table 2 for secondary roads (estimates obtained on main roads were similar; results not shown). For the coefficients (˛k , k )1≤k≤4 , only coefficients ˛ ˆ 4 , ˆ 4 were retained by the selection procedure, bringing the model even closer to Nilsson’s equation, where the fourth power term ˆ1 > 0 is also the only one included. In addition, it is found that ˇ confirming the assumption that both car and road safety have progressively improved over time. Given these estimates, numbers of fatal crashes can be estimated and compared to the observed values for each third of the year over the 2001–2010 period; Fig. 1 presents the results of this comparison. Despite the relative simplicity of the model, which comprises only 4 coefficients, agreement is good: R2 is 0.84 for secondary roads, and as high as 0.91 for main roads. 3.3. Fractions of fatal crashes attributable to speeding Numbers of fatal crashes due to the various levels of speeding were estimated as described in Section 2.3, and are presented in Fig. 2 (left) for secondary roads. Since speed distribution was not available for the last third of year 2008, estimates obtained by Table 2 Parameter estimates for the model for secondary roads: ˛4 corresponds to the effect of speed to the power 4, while  4 corresponds to the effect of its interaction with the second third of the year (Q2). ˇ1 corresponds to the average drop in the number of fatal crashes per year, while ˇ0 can be viewed as an intercept term, for year 2001. Parameter

ˇ0

ˇ1

˛4

4

Estimation

27.00

7.14

2.7e–6

5.4e–7

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Fig. 2. (Left) Estimation of the numbers of fatal crashes attributable to various levels of speeding on secondary roads. (Right) Estimation of the numbers of fatal crashes attributable to various levels of speeding on main roads. In both figures, estimates for the last third of year 2008 were obtained by simple interpolation.

simple interpolation are presented for this particular third. Overall, the number of fatal crashes attributable to speeding and to each level of speeding all decreased over the 2001–2010 period. More precisely, the number of fatal crashes attributable to low-level speeding (<10 kph over the speed limit) decreased very slowly (and can be regarded as roughly constant) while the numbers of fatal crashes attributable to very-high-level and high-level speeding (more than 30 kph and between 20 and 30 kph above the speed limit, respectively) were those which dropped the most rapidly, especially between 2003 and 2004 (i.e., right after the implementation of the automated speed enforcement program in France). The fractions of fatal crashes attributable to speeding show an impressive decrease (from 25% to 6% on secondary roads) in the fraction attributable to high-level and very-high-level speeding (>20 kph over the speed limit), mostly between 2003 and 2004. Over the 2001–2010 period, the fraction of fatal crashes attributable to medium-level speeding (10–20 kph over the speed limit) decreased from 13% to 9%, while the fraction attributable to low-level speeding progressively increased from 7% to 13%. Low-level speeding represented about 16% of the 425 fatal crashes attributable to speeding in 2001, compared to about 46% of the 133 fatal crashes attributable to speeding in 2010. Fig. 2 (right) presents results for main roads. Trends were very similar to those for secondary roads, although the absolute numbers were much lower (because traffic is much higher on secondary roads in France). 4. Discussion Over the 2001–2010 period, the proportions of high-level and very-high-level speeding dropped dramatically, mostly between 2003 and 2007, while the proportion of low-level speeding decreased much more slowly. As a result, according to the present simple power model, the fraction of speed-related fatal crashes attributable to low-level speeding rose from 16% in 2001 to 46% in 2010. It should be pointed out that the model relates speed distribution to number of fatal crashes, rather than to number of fatalities: fatality data are typically not statistically independent, as there may be multiple fatalities in a single crash. The present findings would therefore probably be amplified if based on fatality, as the average number of deaths per fatal crash tends to increase with speed (and conversely decreased regularly, from 1.12 to 1.08, over the 2001–2010 period in France). This is further suggested by Elvik et al. (2004), who reported that the exponent of speed in Nilsson’s equations was greater when fatalities rather than fatal crashes were analyzed (see also Cameron and Elvik, 2010).

A more fundamental question is that of the validity of our reasoning about the estimation of the fractions of fatal crashes attributable to speeding. The basic assumption is a strong one: drivers driving at 110 kph would reduce their risk to the level of drivers driving at 90 kph if they were to actually reduce their speed to the 90 kph limit. Other factors that also influence crash rates (e.g., driving under the influence of alcohol, implicated about one in three crashes in France), however, are not necessarily equally distributed across speed classes: for instance, driving above the speed limit and under the influence of alcohol are not independent. For a fast driver, simply reducing speed to within the speed limit may not in itself reduce risk to the level associated with respecting the speed limit, if other features of fast driving (telephoning while driving, driving under the influence of alcohol, etc.) persist. This objection, however, may not be valid here for several reasons. Firstly, even if drunk driving is associated with higher speed, the association is neither systematic (many drivers under the influence of alcohol are careful to keep to the speed limit) nor dominant (most drivers, irrespective of their speed, are not under the influence of alcohol). In addition, some crash risk factors are not associated with higher speed; some, indeed, may be associated with low speed (e.g., physical decline with aging). There may thus be some factors that approximately balance out the “high-speed” effect associated with other factors. More generally, a range of factors are associated with crash rates, most of which are not related to speed at all: they would affect the square effect of speed only on crash risk, and not on severity. Thirdly, and more fundamentally, the model relies on a power law with exponent 4, following basic concepts in physics, which was not the one that fits the present data best: a power law with exponent 6 fitted the data most closely (results not shown). Such alternative functions may, however, have wrongly attributed certain effects, such as those described above, to speed. Lastly, it should be remembered that the present study focused on evolution over the last decade, which is a relatively short period and one during which average speed has significantly decreased in France, whereas the distributions of other crash risk factors probably evolved very little over the same period. For instance, as pointed out by Hauer (2010), no significant road infrastructure work was undertaken between 2001 and 2010. Were this not the case, such patterns of evolution would have been at least partly taken into account by the calendar year variable. A further point is that it could be argued that driving at high speed reduces the time exposure, and thus the likelihood of a crash (see Pei et al., 2012). In the present model, the probability p can be regarded as an instantaneous risk. The number of fatal crashes over a given third of the year would then be NP, with P the cumulative risk over this third of the year. This cumulative risk would

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be obtained by integrating p over exposure time, which corresponds to the sum of traveling times at a given speed over this third of the year. Since traveling time is inversely proportional to speed, P would therefore be proportional to speed raised to the power three, multiplied by the distance traveled at this speed. This kind of model would perhaps be in better agreement with the real data, but cannot in practice be implemented, as data for overall distance traveled at a given speed are not available on any network. Moreover, the power law underlying the model is very similar to Nilsson’s equations, which relate fatal crashes to average speed and have shown a good fit for many data and road networks (Elvik et al., 2004; Cameron and Elvik, 2010). Both power laws notably rely on speed raised to the power four. With va and vb being the mean or median traffic speed respectively before and after a change in speed limit, and na and nb denoting the number of fatal crashes before and after this change, Nilsson’s equation gives nb = na

 v 4 b

va

The main difference in the present model is that the whole distribution of speed and not only the average speed is considered, and road safety improvement over the years is also taken into account. The conclusions drawn from either model are, however, very similar. On secondary roads for instance, very-high-level speeding concerned only 0.5% of drivers in 2010, so that eliminating it would result in only a 0.25% reduction in average speed, corresponding to a 1% reduction in fatal crashes according to Nilsson’s equation (to be compared to the 3% reduction predicted by the present model). On the other hand, eliminating low-level speeding would result in a 2.3% reduction in average speed, corresponding to a 10% reduction in fatal crashes (to be compared to a 13% reduction according to the present model). This fair fit to Nilsson’s equation supports the good quality of the present data. The data collection for numbers of fatal crashes was a tried and tested process, the quality and adequacy of which is not really open to question. The survey’s data harvesting procedure for speed distribution, on the other hand, has never to the best of our knowledge been assessed, and thus its representativeness could be questioned; the methodology, however, was unchanged over the years, so that the available data can be taken as reliably describing the evolution of speed distribution. The relevance of the model and its fair fit to Nilsson’s equation justify confidence in the representativeness of the present data.

5. Conclusion The present results suggest that the actual speed regulation policy has proved effective in reducing high-level speeding. They further suggest that future policy should target low-level and medium-level speeding in order to reduce road traffic deaths significantly, since these now represent the main fraction of fatal crashes. That said, speed cameras may not be the solution: the number of fatal crashes would be reduced if drivers driving at 90 kph drove at 80 kph (or even lower speeds) instead. Speed regulation policy cannot be solely based on an expected reduction of fatal crashes. Finally, we presume that the present conclusions regarding the current predominance of low-level speeding in the overall number of fatal crashes due to speeding can be extrapolated to other French road networks (such as urban roads and freeways) and to other countries, although additional studies will be needed to confirm this claim.

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Acknowledgements The authors are grateful to Louis Fernique and the NIORS for providing the data used in this work, especially Serge Boyer and Christian Roy.

Appendix. Description of the NIORS survey methodology to measure speed distribution This paragraph is an abbreviated translation of the description provided on pages 308–309 of the NIORS report (2010). Survey methodology remained largely stable over the years, so as to guarantee the integrity of trends over the long term. The objective was to measure speed, but only for drivers who were free to choose it. Therefore, only flat and straight road sections without traffic disturbances or any crossings or traffic lights within one kilometer (or a few hundred meters in medium-size cities) were included. Moreover, selected sections where a speed camera was installed during the 2001–2010 period were at that point replaced by an “equivalent” section. For the whole French network (including secondary roads, main roads, freeways, etc.), 362 representative sections were selected (285 for daytime, 77 for night-time). On secondary and main roads, speed is measured by a speed camera in the trunk of an unmarked car, parked on the roadside. Each year, three campaigns are run (one for each third of the year). More precisely, 50 cars successively go to each selected road section, on a predefined day of the month at a predefined time of day. Four months later, they go to the same section, on the same day and time, and so forth. Overall, more than 200,000 speed measures are collected each year. They uniformly cover each month of each third of the year, each day and each time slot (between 9.30 am and 4.30 pm during the daytime and between 10.00 pm and 2.00 am during the night-time). Almost all daytime measures are therefore off-peak, to ensure that drivers were able to chose their speed freely.

References Aarts, L., van Schagen, I., 2006. Driving speed and the risk of road crashes: a review. Accident Analysis and Prevention 38, 215–224. Baruya, B., 1998. Speed-accident relationships on European roads. In: Proceedings of the Conference Road Safety in Europe, vol. 10, Bergisch Gladbach, Germany, September 21–23, 1998, pp. 1–17, VTI Konferens No. 10A, Part. Cameron, M.H., Elvik, R., 2010. Nilsson’s power model connecting speed and road trauma: applicability by road type and alternative models for urban roads. Accident Analysis and Prevention 42, 1908–1915. Cirillo, J.A., 1968. Interstate system crash research; study II, interim report II. Public Roads 35 (3), 71–76. Elvik, R., Christensen, P., Amundsen, A., 2004. Speed and road accidents An evaluation of the Power Model. TØI report 740/2004. Institute of Transport Economics TOI, Oslo, Norway http://www.toi.no/getfile.php/Publikasjoner/ T%D8I%20rapporter/2004/740-2004/740-2004.pdf Evans, L., 1991. Traffic Safety and the Driver. Van Nostrad Reinhold, New York. Fildes, B.N., Lee, S.J., 1993. The Speed Review: Road Environment, Behaviour, Speed Limits Enforcement and Crashes. Monash University Accident Research Centre, Prepared for Road Safety Bureau/Federal Office of Road Safety, New South Wales, Canberra. Fildes, B.N., Rumbold, G., Leening, A., 1991. Speed behaviour and drivers’ attitude to speeding. General Report No. 16. VIC Roads, Hawthorn, Vic. Finch, D.J., Kompfner, P., Lockwood, C.R., Maycock, G., 1994. Speed, speed limits and crashes. Project Record S211G/RB/Project Report PR 58. Transport Research Laboratory TRL, Crowthorne, Berkshire. Garber, N.J., Gadiraju, R., 1989. Factors Affecting Speed Variance and Its Influence on Accidents. 1989-01-01 1213. Transportation Research Record, Washington, DC. Hauer, E., 2010. White Papers for Toward Zero Deaths: A National Strategy on Highway Safety. http://safety.transportation.org/doc/web9%20Lessons%20Learned %20White%20Paper.pdf Kloeden, C.N., McLean, A.J., Glonek, G., 2002. Reanalysis of travelling speed and the rate of crash involvement in Adelaide South Australia. Report No. CR 207. Australian Transport Safety Bureau ATSB, Civic Square, ACT. Kloeden, C.N., McLean, A.J., Moore, V.M., Ponte, G., 1997. Travelling speed and the rate of crash involvement. Vol. 1: findings. Report No. CR 172. Federal Office of Road Safety FORS, Canberra.

256

V. Viallon, B. Laumon / Accident Analysis and Prevention 52 (2013) 250–256

Kloeden, C.N., Ponte, G., McLean, A.J., 2001. Travelling speed and the rate of crash involvement on rural roads. Report No. CR 204. Australian Transport Safety Bureau ATSB, Civic Square, ACT. Maycock, G., Brocklebank, P.J., Hall, R.D., 1998. Road layout design standards and driver behaviour. TRL Report No. 332. Transport Research Laboratory TRL, Crowthorne, Berkshire. Nilsson, G., 1981. The effects of speed limits on traffic crashes in Sweden. In: Proceedings of the International Symposium on the Effects of Speed Limits on Traffic Crashes and Fuel Consumption, Dublin. OECD, Paris. Nilsson, G., 2004. Traffic safety dimensions and the Power Model to describe the effect of speed on safety Bulletin 221. Lund Institute of Technology, Department of Technology and Society, Traffic Engineering, Lund, Sweden http://www.dissertations.se/dissertation/a9952d343f/ NIORS, 2010. La sécurité routière en France, Bilan de l’année 2010, La Documentation Franc¸aise, Paris, France. http://www.securite-routiere.gouv.fr/ la-securite-routiere/l-observatoire-national-interministeriel-de-la-securiteroutiere/bilans-annuels/bilans-annuels-de-la-securite-routiere-en-france OECD/ECMT, 1996. Road Safety: Speed Moderation Joint OECD/ECMT Transport Research Center. Patterson, T.L., Frith, W.J., Small, M.W., 2000. Down with speed: a review of the literature, and the impact of speed on New Zealanders. Accident Compensation Corporation and Land Transport Safety Authority, Wellington, New Zealand.

Pei, X., Wong, S.C., Szeb, N.N., 2012. The roles of exposure and speed in road safety analysis. Accident Analysis and Prevention 48, 464–471. Pilkington, P., Kinra, S., 2005. Effectiveness of speed cameras in preventing road traffic collisions and related casualties: systematic review. British Medical Journal 330 (7487), 331–334. Quimby, A., Maycock, G., Palmer, C., Buttress, S., 1999. The factors that influence a driver’s choice of speed: a questionnaire study. TRL Report No. 325. Transport Research Laboratory TRL, Crowthorne, Berkshire. RTI, 1970. Speed and Accidents, vols. I &II. Research Triangle Institute, RTI, North Carolina. SARTRE 3, 2004. European Drivers and Road Risk. Part 1: Report on Principal Results. INRETS, Paris. Solomon, D., 1964. Crashes on main rural highways related to speed, driver and vehicle. In: In: Bureau of Public Roads. U.S. Department of Commerce. United States Government Printing Office, Washington, DC. Taylor, M., Lynam, D.A., Baruya, A., 2000. The Effect of Drivers’ Speed on the Frequency of Accidents. TRL Report TRL421. Transport Research Laboratory, Crowthorne. Taylor, M., Baruya, A., Kennedy, J.V., 2002. The Relationship Between Speed and Accidents on Rural Single Carriageway Roads. TRL Report TRL511. Transport Research Laboratory, Crowthorne. TRB, 1998. Managing speed; review of current practice for setting and enforcing speed limits Special Report 254. Transportation Research Board (TRB). National Academy Press, Washington, DC.