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The British index for comparing the accident record of car models
Accid. Anal. and Prev., Vol. 28, No. 1, pp. 101-109, 1996 Elwier Science Ltd. Printed in Great Britain
oool-4575(95)ooo49-6
THE BRITISH INDEX FOR COMPARING THE ACCIDENT RECORD OF CAR MODELS* JEREMY BROUGHTON Transport Research Laboratory, Crowthorne, Berkshire, RGll
6AU, U.K.
(Received 6 April 1994; accepted 18 July 1995) Abstract-This paper describes the second part of a study of the ways in which the accident records of different models of car can be compared on the basis of suitably detailed national accident data. An earlier paper (Broughton 1995) showed, from theoretical considerations, that the most satisfactory safety index is the one currently used by the British Department of Transport (DOT) to measure the level of secondary safety (crashworthiness). This paper presents empirical tests using British accident data from 1989-92 which confirm its value. It also describes a modelling approach which yields the same index and thus provides a theoretical justification for the DOT index. The index declines linearly with mass of model; a second safety index is developed on the basis of this relation which allows models of widely differing masses to be compared directly.
Consequently, only a more limited goal is feasible. The most that can be achieved is to measure the level of secondary safety (crashworthiness) provided by each model, that is, the probability of an occupant being injured once a car has become involved in an accident. The earlier paper concluded, from theoretical considerations, that the most satisfactory safety index is the one which is used by the British Department of Transport (DOT) and hence can be described informally as “The British index for comparing the accident record of car models”. This paper presents various analyses of British accident data from 1989-92 that test its value empirically, it also investigates the relation between the DOT index and vehicle mass and derives an adjusted safety index which takes account of vehicle mass. The analyses are based on data from the “Stats19 database”, which contains statistical details of all road accidents reported to the police in Great Britain in which one or more people are injured. Injuries are classified as fatal, serious or slight, and all police forces supply data using a uniform report form, the “Stats19 form”. As only injury accidents are represented in the data, all empirical results relate to injury accidents. (N.B. many publications relate to the issues covered by this paper, only those referred to directly are listed among the References.)
INTRODUCTION In several countries, accident data are collected in sufficient detail and on a sufficient scale for it to be possible to assess the relative safety of different car models. Since 1989, the British Statsl9t accident reports have included the Vehicle Registration Mark of accident-involved vehicles, which enables details such as vehicle make and model to be extracted from files at the Driver and Vehicle Licensing Agency (DVLA). An earlier paper (Broughton 1996) has considered the theoretical basis for assessing the relative safety of different models, with particular reference to the data available from the Stats19 database. This paper presents more detailed results and develops the modelling further. The ideal basis for assessing the relative safety of any model can be stated simply. It is the ratio of the number of occupant casualties that occur in accidents involving that model relative to the number that would be expected if the accidents had instead involved cars of a “standard” model representing the current average. A sophisticated statistical model is required to achieve this ideal, and a candidate will be described. It is impossible to apply this model, however, as information about the accident exposure of different car models at the required level of detail is largely lacking.
THE DOT METHOD
*Crown Copyright 1994. The views expressed in this publication are not nec&a~ly those of the Department of Transport. tThe Stats19 form is used by all police forces in Great Britain to record details of any road a&dent involving human injury or death.
The latest DOT report dealing with car accident rates (Department of Transport, 1993) has two sets of tables, one relating to primary safety and the other 101
102
J. BROUGIWON
to secondary safety. Comparisons by model of car are only made for secondary safety, and the method used will be referred to as the DOT method. It is calculated using data from two-car accidents where at least one driver was injured, on the grounds that in such accidents both cars experience the same potential risks. The index is: number of drivers who are injured in these accidents D= number of drivers who are involved in these accidents A second index used in the report is the proportion of drivers involved in these accidents who are killed or seriously injured (ksi): DA=
Proportion of drivers of model m cars who are ksi when involved in two-car accidents where at least one driver is injured
but an earlier paper (Broughton 1996) has shown that an alternative index is preferable: DB=
Proportion of drivers cars who are ksi when involved in two-car accidents where at least one driver is ksi.
The restricted set of accidents used to evaluate the index is intended to standardize the risks faced by drivers, but the DOT method goes further by introducing factors which are likely to influence the likelihood of a driver being injured. Full details of the method are presented in an appendix to the DOT report and were summarized in the earlier paper. Briefly, a logistic regression model is used to represent the influence on the casualty proportion of: speed limit of road sex of driver
first point of impact age of driver
Clearly, speed limit is only a proxy for the variable of interest, accident severity. The earlier paper concluded from theoretical considerations that, once these influences have been taken into account, D and D, provide the most satisfactory means of comparing the secondary safety of different models of car. The analyses described below have been made to check practical aspects of the indices, based on the accidents recorded in the Stats19 files for 1989-92 in which:
(4 two cars were involved and at least one driver was injured; (W the Vehicle Registration Mark of at least one of the cars is known and has been matched in the DVLA records; (4 at least one of the models appears in the list in the DOT report which includes all models with more than 20,000 registered cars.
The range of “other” cars
The DOT index could be biased if the models studied are not in collision with a common range of ‘other’ cars. If, for example, a particular model is involved in relatively many accidents with large cars, then it is likely that more of its drivers will be injured than if these accidents had involved a typical range of cars, leading to an unfavourable value of D. As a first step in checking whether this happens in practice, models have been grouped according to size as specified in the DOT report: as an approximate guide, ‘small’ cars are 140-152 inches long, ‘small/medium’ cars are 153-167 inches long, ‘medium’ cars are 168-180 inches and ‘large’ cars are over 180 inches long. A subset of accidents is used for this analysis, since for each car in an accident the type of model must be known and must appear in the list from the DOT report; 187,695 accidents fulfil these extra requirements. As an example, 55,641 of these accidents involve either 1 or 2 small/medium cars, distributed as follows: Size of one car small/medium small/medium small/medium small/medium small/medium
Size of other car small small/medium medium large all
Number of accidents
Proportion
15786 20967 15131 3757 55641
0.298 0.374 0.267 0.061 1.000
Table 1 presents the distributions for the four size ranges (columns l-4) and each differs to some extent from the distribution for cars of all sizes (column 5). The differences which are significant (probability of the difference arising by chance < 0.05) are marked with *. While the table shows some significant differences between the size distributions, Table 2 shows that the indices change very little when they are adjusted to the common basis provided by the ‘all sizes’ distribution. The reason is probably that the differences have no clear pattern. If, for example, the table had instead shown that large cars tend to collide Table 1. The proportion of accidents which involve cars of size A which also involve cars of size B Size A Size B
Small
Small/med
Medium
Large
All sizes
Small Small/medium Medium Large
0.284* 0.377 0.272; 0.068*
0.298 0.374 0.267 0.061*
0.303* 0.375 0.261* 0.062
0.3188 0.362* 0.262 0.058*
0.296 0,374 0.266 0.063
All sizes
1.000
1.000
1.000
1.000
1.000
Note: * denotes a value which differs significantly (p~O.05) from the corresponding value in the “all sizes” distribution.
Accident record of car models
Table 2. Unadjusted
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and adjusted DOT indices, by size of car
ksi (Ds) Size of car Large Medium Small/medium Small
Unadjusted
Adjusted
0.328 0.494 0.594 0.139
0.332 0.496 0.595 0.736
Note: “adjusted” results use the common
All casualties (D) Increase
Unadjusted
Adjusted
0.399 0.514 0.598 0.728
0.403 0.516 0.599 0.725
1.1% 0.4 0.1 -0.4
Increase 1.0% 0.3 0.1 -0.3
basis provided by the “all sizes” distribution.
with large and small cars to collide with small, rather larger adjustments would presumably have been necessary. Similar conclusions emerge when the collisions involving the 24 models with the greatest number of accident involvements are studied in detail. Some models collide with other models more or less frequently than expected-for example, Nissan Bluebirds collided with other Bluebirds 73% more frequently than expected, while Renault 5’s and Rover 200’s collided 33% less frequently. These are extreme examples, however, and the collision distributions for the models most commonly involved in accidents (Ford Escorts and Fiestas) match the expected distributions fairly closely. Overall, differences from the expected values are slightly greater than would have arisen by chance. When the DOT indices are adjusted to allow for differences between the actual and expected collision distributions, the adjustments are small-almost all are less than l%, and all are well within the standard error for the estimated index. The same is found with the Folksam indices which were also studied in the earlier paper. Thus, although some models do differ significantly in the distribution of “other” cars with which they collide, the Folksam and DOT indices are not biased by ignoring the differences. Provided that the confidence intervals are interpreted properly, there is no need to adjust the indices to allow for differences between the distributions. The stability of the DOT index
Two main aspects of the stability of DOT index will be considered-are the indices calculated in separate years consistent, and do models with similar characteristics have similar indices? The indices presented in the Department of Transport report (1993) are based on data accumulated over successive years, in order to obtain the statistical benefits of analysing larger numbers of accidents. This is appropriate only if results calculated for individual years are consistent. This has been checked by calculating the indices with accident data from individual years, and comparing them with the indices calculated for the grouped data from 1989-92.
Some variations are inevitable, especially among the less common models, so the differences are compared with the standard errors for the indices: these indicate the range of variation that might be expected from purely random effects. Only 4.4% of variations exceeded 1 standard error for the casualty index D, and 6.4% for the ksi index DB, so it is likely that variations in individual years about the indices calculated for the grouped data have arisen purely by chance. This stability of the index over four years confirms that it is justified to accumulate data over several years to provide more reliable results. The earlier report showed, however, that the index is a relative measure which compares the safety of different models at the same time but cannot assess changes in safety over time as new models enter the car fleet. This means that there will be a limit to the number of years over which this can be done, which depends upon the rate of introduction of new models with improved secondary safety features and the average “lifetime” of a car, as shown by the following example. Suppose that a new model appears in year Y which has a better level of secondary safety than comparable contemporary models, so that its index will be below average. Suppose also that by year Y+ 10 most other models have been replaced by improved versions and its secondary safety is worse than the new average, so that its index will now be above average. The fact that D is a relative measure means that the average cannot change, so the model’s index must rise over the years. Hence, the value calculated from data accumulated over the decade will differ from the value calculated at the beginning or the end of the decade. No sign has been found of this occurring at present, but it may become necessary in future to base the index on data from only the most recent few years. Results achieved by statisticians from the DOT Statistics Directorate provide further evidence of the stability of the index. They compiled a list of variants of relatively common models which could be identified from the details supplied by DVLA, for example, high performance versions. Each “family” of variants would be expected to have the same index, since they
J. BROUGHTON
104
share the same protective features. The indices are indeed closely clustered and each family has in effect a common index, despite the different specifications of the variants. There are sound technical explanations for those few cases where an index differs significantly from the central value for the family.
measure the effect of these variables on the likelihood of becoming involved in such an accident, so h is directly comparable to the DOT index. Indeed, by rearranging (2):
=
AN ALTERNATIVE
MODEL
A modelling approach is now described which leads to the DOT index and so provides a theoretical derivation for it. The description includes only three explanatory factors, namely driver age, driver sex and road type (represented by speed limit), but can easily be extended to incorporate others if necessary. The model assumes a multiplicative relationship between the independent factors and the number of casualties: (1)
where C(u,s,r,m)=number of driver casualties of age a and sex s on roads of type r (as categorized by speed limit, for example) while driving cars of model m, X(u,s,r,m) =mileage of drivers of age a and sex s in cars of model m on roads of type r, F,G,H are factors to be determined, E is an error term, assumed to have zero mean and constant variance. The H-factors are of particular interest, as they represent the differences between the number of driver casualties expected with different car models: (1) is thus a model of primary safety. The F- and G-factors are of lesser interest, as they are included to eliminate bias arising from road type etc. In order to give reliable results, the model needs to be applied with fairly detailed mileage data X, so the results would have little value with the data currently available in Great Britain. An alternative that does not require mileage data can be developed by letting I(u,s,r,m) be the number of drivers of age a and sex s involved in two-car accidents on roads of type r while driving cars of model m, as recorded in the Stats19 data. I is analogous to the mileage data X but not a direct substitute, so the factors calculated using I would not match those calculated using (1) if suitable mileage data existed. The new model is: C(u,s,cm)=f(u,s)*g(r)*h(m)*Z(u,s,r,m)+~(u,s,r,m)
(2)
f, g and h measure the effect of the independent variables a, s, r and m on the likelihood of a driver
being injured when involved in a two-car accident: f and g represent the influence of non-vehicle factors while h represents the model-related factors. This is a model of secondary safety since J g and h do not
unadjusted DOT index
This operates in a very similar way to the logistic regression model of the DOT approach: starting from the basic casualty proportions, it calculates a safety index free (within the limits imposed by the available data) from the influence of non-vehicle factors. Thus, this modelling provides a theoretical justification for the DOT index. (2) is fitted by finding factors which minimize S = C .a’. A FORTRAN program has been developed which rapidly converges to the solution from any plausible initial values forfand g, although alternatively the factors could be calculated with a linear regression model and logarithmically transformed data. The model will also calculate either ksi index, D, or D,. C is restricted to drivers ksi with both; with the latter, Z is restricted to accidents in which at least one of the drivers is ksi. Results
When model (2) was fitted to the 1988-92 driver casualty data for the 91 models in two-car accidents, four age bands were used and two road types, builtup (speed limit at most 40 mph) and non built-up (speed limit over 40 mph). The effectiveness with which the model represents the variations in the driver casualty data can be judged by comparison with a simpler model which excludes the non-vehicle explanatory factors, i.e. it assumes that the casualty proportion for each model does not vary with type of road or driver: C(u,s,r,m)=h(m)*I(u,s,r,m)+&,s,r,m)
(3)
The following values of R* indicate the agreement between the actual and predicted casualty data C: model (2) model (3)
D
DB
0.998 0.978
0.988 0.977
DA
0.973 0.750
Thus, the explanatory factors improve the performance of the model significantly, confirming the case for the DOT’S relatively sophisticated statistical approach. There appears to be little scope for further improvement of the model of all casualties, but the ksi models may perhaps benefit from more detailed road type data. R2 values are higher for DB than for DA, presumably because D is more closely related to D, than to DA. The high R2 values achieved by model (2) show
Accident record of car models
that factors not included in the model can have very little influence on the driver casualty data, although they may well operate indirectly via the factors that are included. Thus, there is effectively no risk of D or DB being biased by exogenous factors and, within the statistical limits set by the number of cars of each model that are involved in accidents, the index will reliably compare secondary safety. The only drawbacks to its use are practical, and arise directly from the reliance on national accident data: large numbers of a new car model must be in use before its safety can be assessed accurately, and it is difficult to relate the assessment to specific features of the model. On the other hand, the index does measure how well the model protects its drivers in the range of accidents actually occurring on the roads of Great Britain, rather than in the simulated accidents used in crash testing. Turning now to the specific results obtained when fitting model (2), Table 3 shows the non-vehicle factors. The factor “road type” is the increased likelihood of injury for a driver involved in an accident on a non built-up road, relative to a built-up road; the eight driver-related factors have been adjusted to have a mean of 1. The pattern of the driver-related results agrees with general analyses of the casualty rates of British drivers (e.g. Broughton 1990), which find that rates are lowest around the age of 50 and begin to rise more rapidly after the age of 65, and that rates are higher for women than for men. The relatively small increases for the 55 age group compared with the 35-54 age group reflects the relatively low mileage of British drivers over 65 years old. By contrast, the value of the road type factor for D exceeds 1, implying greater risk of injury on non built-up roads, whereas driver casualty rates are lower on non built-up than on built-up roads. The explanation is that the factor is measuring the greater risk of a driver being injured Table 3. Driver- and road-related number of driver casualties
factors which influence [/and g in model (2)]
D
the
&I
Factor
Value
SE
Value
SE
Road type
1.121
0.012
1.156
0.040
Male driver 17-14 25-34 35-54 55-
0.829 0.832 0.850 0.939
0.011 0.011 0.010 0.013
0.834 0.834 0.881 1.078
0.031 0.031 0.035 0.040
Female driver 17-24 25-34 35-54 55-
1.181 1.148 1.146 1.169
0.015 0.015 0.014 0.024
1.076 1.089 1.089 1.187
0.043 0.051 0.036 0.065
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when involved in a two-car accident on a high-speed road, rather than the rate at which these accidents occur. THE EFFECT OF VEHICLE THE DOT INDICES
MASS ON
It is well known that larger cars tend to protect their occupants better than small cars, and it would be desirable to develop the DOT indices to allow for the effects of size. A method is described which is based on the adjusted values of D and D, that are obtained using model (2); it could equally well be applied with results from the DOT logistic regression approach. The mass of 87 of the 91 models was established from a commercial report (Glass’s Guide Service 1992); this could only be done approximately because the variants of models such as the Ford Sierra have a range of masses. Figure 1 shows that the adjusted casualty proportion falls steadily with increasing mass. Fitting a simple linear model to the data from 1989-92 yields the relation: D = 1.053 -O.O0045*mass
(R2=0.85, N=87, respectively.)
SE’s
are
0.013,
(4) 0.00002
A similar pattern is found with D,, the ksi index. The points are slightly more scattered and the fitted line is slightly steeper: D,= 1.118-O.O0055*mass
(5)
(R2=0.73,
N =87, SE’s are 0.024, 0.00004 respectively.) It is striking that these simple models explain such a high proportion of the variation in the casualty data. Note also that (4) implies that all drivers are injured when mass= 100 kg [210 kg for (5)]. Evans and Frick (1993) found that in two-car accidents the risk of death for the driver of the lighter car was p3.53 times the risk for the driver of the heavier car, where p is the ratio of the masses. This suggests that the relation between mass and adjusted proportion may be non-linear, at least in the case of fatal accidents, but the data do not support this for predominantly non-fatal accidents. When (4) is refitted with (mass)f in place of mass, the optimal model for D has c = 1.00. For D,, the optimal value of c = 0.85, but the marginal improvement in fit does not justify the addition of an extra term. Thus, the linear model is optimal in both cases. The mass-adjusted
safety index
Equation (4) establishes the typical proportion of driver casualties to be expected in a model of given mass, so actual values can be compared with these
J BROUGHTON
106
0.9 -
5 I .s
0.6 -
;
0.5 -
0.4 -
0.2 500
I
I
I
1000
1500
2000
Car mass (kg) Fig. 1.
expected values to see which models perform significantly better or worse than average. Models lying above the fitted line in Fig. 1 perform worse than average, those lying below perform better. Thus, the mass-adjusted safety index MS1 = D -( 1.053 - O.O0045*mass) compares the index of a particular model with the value expected for a typical model of the same mass. A model with negative MS1 has fewer driver casualties than expected, so it is relatively safe: a positive value indicates a relatively unsafe model. The points farthest below the fitted line denote the level of secondary safety achieved by the most successful current designs, subject to the confidence intervals for the estimates. When the model is re-fitted for the individual years 1989-92, very similar fitted lines and MSIvalues are found, so MS1 is a stable measure of secondary safety which represents model-specific effects. This is also consistent with the conclusion in the earlier paper that overall changes in secondary safety will not affect the general distribution of casualty proportions, although the period covered is too short to provide real confirmation. The regression which fitted (4) treated all casualty proportions equally, while some are actually more precise than others for statistical reasons related to the number of accidents in which each model is involved. A weighted regression allows for this, it yields a slightly steeper fitted line so slightly different mass-adjusted indices are produced on the basis of this line. These tend to favour the more popular models since the weighting of the regression emphasizes data from these models, so a different type of
bias is introduced. On balance, it seems preferable to treat each model equally, as was done when calculating (4). The ranking of models using the mass-adjusted index clearly differs greatly from the ranking using the original index. For example, the Citroen 2CV/Dyane ranks lowest using the original index because it has the greatest value of D; however, its MS1 is only slightly worse than average so it lies in the middle of the mass-adjusted ranking. Conversely, Jaguars have the lowest value of D but slightly more Jaguar drivers are injured than would be expected with a car of this mass, so they rank highest by the original index but below average by the massadjusted index. The two sets of indices have separate but complementary roles: (i) the unadjusted index is relevant to the car buyer who wishes to compare the safety of the models being considered, since their personal safety will be of especial concern to them; (ii) the mass-adjusted index is of interest to regulators and the motor industry, as it shows whether particular models achieve good safety records by added mass rather than by good design. The influence of mass and design
It has been claimed that (4) represents the influence of mass on the casualty proportion, but it might also be influenced by other aspects of vehicle design. These will influence the fitted line if safety-related features tend to be better designed in small models than in large, or vice versa. If small models are better
Accident record of car models
designed than large, then their casualty proportions will be somewhat lower than they would have been with uniform design standards and the casualty proportion of large models will be somewhat higher. Consequently, the fitted line in Fig. 1 would be less steep than it would have been if standards had been uniform, and it would under-represent the effect of mass. Equally, if large models were better designed than small, the fitted line in Fig. 1 would be too steep. However, if “good” and “bad” designs coexist in all size ranges, (4) will show the unalloyed effect of mass. It seems likely that in fact “good” and “bad” designs coexist in all size ranges, and that (4) is not influenced by design. This will be checked by studying popular models which have variants spanning a reasonably wide range of masses, to see whether the casualty proportion does vary systematically with mass. Three manufacturers have sold sufficient cars in Great Britain for their models to be compared in detail: Ford (5 models), Rover (5 models) and Vauxhall (4 models). The mass of any car that was identified in the accident data as being of one of these 14 models was extracted from a commercial report (Glass’s Guide Service 1992) on the basis of its engine capacity, body type and year of first registration. This provides vehicle mass with a fair degree of precision, although the published figures are less comprehensive for some models than for others. Also, a heavilyloaded car with four adult passengers and their luggage can weigh at least 300 kg more than the same car when it only carries its driver. Such variation should not bias the analysis, however, as the distribution of “loaded” weight of accident-involved cars relative to the published “unladen” weight is probably consistent for each model across the mass ranges, but these considerations do imply that mass ranges should not be too narrow. Accident-involved cars were assigned to mass ranges (generally of 50 kg, sometimes 100 kg where vehicle numbers were low). The values of D that were calculated are presented in Fig. 2 together with the fitted line (4); the masses of Rover 800’s proved in practice to be too closely clustered for the range to be sub-divided as intended, but the point is shown for completeness. The standard errors of most of the estimated indices are less than 0.02, although for 5 of the less common combinations of mass and model they exceed 0.04. For most Rover and Vauxhall models, the line segments are almost exactly parallel to the fitted line, so the variation with mass is almost exactly as shown by (4). The casualty proportion falls rather more steeply with Astra/Belmonts, although this may be linked to the replacement of the earlier model range
107
in October 1984 by heavier models: the steeper fall may indicate that the newer range has improved safety features. Several other Rover and Vauxhall models have also been redesigned to some extent, but it appears that any safety benefit has been largely in line with what would be expected from the increased mass. Three Ford models conform less well to the pattern found among Rover and Vauxhall models. The Sierra/Sapphire shows no decrease with mass, while the decrease for the Fiesta and Escort is lessthan expected: these results are probably robust as these three models are so numerous. The replacement of existing models by heavier designs may explain the non-conforming results for Fiestas and Escorts. Lighter Fiestas were predominantly registered before 1989, while the majority of the heavier Fiestas were registered in or after 1989; few of the lighter Escorts were registered after 1987, but three-quarters of the heavier Escorts were registered in or after 1987: the new designs may not have achieved, in full, the safety benefit to be expected from the increase in mass. There is no indication of such an explanation with the Sierra/Sapphire range; the lightest cars tend to be relatively old, but the other three mass ranges have similar age distributions. Thus, 9 of the 13 models studied support the proposition that (4) represents solely the effect of mass, one model shows no systematic variation with mass, and the replacement of existing designs confuses the interpretation of results from the other three models. On balance, this supporting evidence is reasonably convincing, but more homogeneous vehicle groups would be needed to achieve more conclusive results. The opportunity to do this is restricted, however, by the available sample sizes, so the frequency with which manufacturers redesign or replace their models makes it impracticable to take the analysis much further. CONCLUSIONS This paper has completed a study of the ways in which national accident data can be analysed to compare the safety of different car models. The study has been influenced by the data that are available in Great Britain, but the conclusions should be generally applicable. An earlier paper (Broughton 1996) has shown that, since there is virtually no information about the relative levels of exposure of different models, only indices of secondary or passive safety (crashworthiness) can be calculated at present. It concluded from theoretical considerations that the most satisfactory safety index is the one currently used by the British Department of Transport (DOT),
J. BROUGHTON
108
0.8
Rover
r
Ford
0.6
0.6
Rover 800 700
I
I
I
I
I
800
900
1000
1100
1200
I 1300
I 1400
0.4 700
I
I
I
I
I
800
900
1000
1100
1200
1300
0 1400
0.8 r
Vauxhall
0.4 700
I
I
I
I
I
I
I
800
900
1000
1100
1200
1300
1400
Fig. 2.
and this paper has presented various empirical tests of the index. It has also described an alternative modelling approach for deriving the DOT index which provides a theoretical justification for the index and could make use of detailed exposure data by car model if these become available. The fitted models reproduce the casualty data so well that it is unlikely that the index is biased by exogenous factors. One test of the stability of the index has compared results from the four years for which the necessary data have been collected in Great Britain. The values are very stable, which justifies the practice of accumulating data over several years to provide
more precise estimates. A second test of stability has consisted of comparing the indices of variants of relatively common models. These have proved to be closely clustered, so that each family has in effect a common index in spite of the different specifications of the variants; this is important because the variants have common protective features. It is well known that the risk of the driver being injured once a car is involved in an accident tends to reduce with the car’s size. An adjusted version of the DOT index has been described which relies on the very regular relation that exists between the index and car mass: on average, for every 100 kg added to the unladen mass of a car, the probability of its driver
Accident
record
being injured when involved in a two-car accident where one or other driver is injured falls by 0.045. Detailed analysis of accident data for several popular models tends to confirm that the reduction of the index is entirely the effect of mass, although the index does not appear to fall with increasing mass as expected among Ford Sierras and Sapphires. The range of the index among models of similar mass then shows the extent to which better driver protection can be achieved by improved design. The mass-adjusted DOT index allows the safety of cars of widely differing masses to be compared directly, thereby showing whether some models may be relatively safe because of extra mass rather than better design. This information is of interest to Government regulators and the car industry, while car buyers will probably be more concerned with the basic index.
of car models
109
Acknowledgement-The work described in this paper was carried out in the Safety and Environment Resource Centre of TRL.
REFERENCES Broughton, J. Casualty rates among car occupants, 1976-1986. Department of Transport, TRRL Report RR2441 Transport and Road Research Laboratory, Crowthome; 1990. Broughton, J. The theoretical basis for comparing the accident record of car models. Accid. Anal. and Prev. 28: 89-99; 1996. Department of Transport. Cars: make and model: injury accident and casualty rates: Great Britain: 1991. London: HMSO; 1993. Evans, L.; Frick, M. C. Mass ratio and relative driver fatality risk in two-vehicle crashes. Accid. Anal. and Prev. 25213-224; 1993. Glass’s Guide Service. Glass’s car check book 1992. 1992.
oool-4575(95)ooo49-6
THE BRITISH INDEX FOR COMPARING THE ACCIDENT RECORD OF CAR MODELS* JEREMY BROUGHTON Transport Research Laboratory, Crowthorne, Berkshire, RGll
6AU, U.K.
(Received 6 April 1994; accepted 18 July 1995) Abstract-This paper describes the second part of a study of the ways in which the accident records of different models of car can be compared on the basis of suitably detailed national accident data. An earlier paper (Broughton 1995) showed, from theoretical considerations, that the most satisfactory safety index is the one currently used by the British Department of Transport (DOT) to measure the level of secondary safety (crashworthiness). This paper presents empirical tests using British accident data from 1989-92 which confirm its value. It also describes a modelling approach which yields the same index and thus provides a theoretical justification for the DOT index. The index declines linearly with mass of model; a second safety index is developed on the basis of this relation which allows models of widely differing masses to be compared directly.
Consequently, only a more limited goal is feasible. The most that can be achieved is to measure the level of secondary safety (crashworthiness) provided by each model, that is, the probability of an occupant being injured once a car has become involved in an accident. The earlier paper concluded, from theoretical considerations, that the most satisfactory safety index is the one which is used by the British Department of Transport (DOT) and hence can be described informally as “The British index for comparing the accident record of car models”. This paper presents various analyses of British accident data from 1989-92 that test its value empirically, it also investigates the relation between the DOT index and vehicle mass and derives an adjusted safety index which takes account of vehicle mass. The analyses are based on data from the “Stats19 database”, which contains statistical details of all road accidents reported to the police in Great Britain in which one or more people are injured. Injuries are classified as fatal, serious or slight, and all police forces supply data using a uniform report form, the “Stats19 form”. As only injury accidents are represented in the data, all empirical results relate to injury accidents. (N.B. many publications relate to the issues covered by this paper, only those referred to directly are listed among the References.)
INTRODUCTION In several countries, accident data are collected in sufficient detail and on a sufficient scale for it to be possible to assess the relative safety of different car models. Since 1989, the British Statsl9t accident reports have included the Vehicle Registration Mark of accident-involved vehicles, which enables details such as vehicle make and model to be extracted from files at the Driver and Vehicle Licensing Agency (DVLA). An earlier paper (Broughton 1996) has considered the theoretical basis for assessing the relative safety of different models, with particular reference to the data available from the Stats19 database. This paper presents more detailed results and develops the modelling further. The ideal basis for assessing the relative safety of any model can be stated simply. It is the ratio of the number of occupant casualties that occur in accidents involving that model relative to the number that would be expected if the accidents had instead involved cars of a “standard” model representing the current average. A sophisticated statistical model is required to achieve this ideal, and a candidate will be described. It is impossible to apply this model, however, as information about the accident exposure of different car models at the required level of detail is largely lacking.
THE DOT METHOD
*Crown Copyright 1994. The views expressed in this publication are not nec&a~ly those of the Department of Transport. tThe Stats19 form is used by all police forces in Great Britain to record details of any road a&dent involving human injury or death.
The latest DOT report dealing with car accident rates (Department of Transport, 1993) has two sets of tables, one relating to primary safety and the other 101
102
J. BROUGIWON
to secondary safety. Comparisons by model of car are only made for secondary safety, and the method used will be referred to as the DOT method. It is calculated using data from two-car accidents where at least one driver was injured, on the grounds that in such accidents both cars experience the same potential risks. The index is: number of drivers who are injured in these accidents D= number of drivers who are involved in these accidents A second index used in the report is the proportion of drivers involved in these accidents who are killed or seriously injured (ksi): DA=
Proportion of drivers of model m cars who are ksi when involved in two-car accidents where at least one driver is injured
but an earlier paper (Broughton 1996) has shown that an alternative index is preferable: DB=
Proportion of drivers cars who are ksi when involved in two-car accidents where at least one driver is ksi.
The restricted set of accidents used to evaluate the index is intended to standardize the risks faced by drivers, but the DOT method goes further by introducing factors which are likely to influence the likelihood of a driver being injured. Full details of the method are presented in an appendix to the DOT report and were summarized in the earlier paper. Briefly, a logistic regression model is used to represent the influence on the casualty proportion of: speed limit of road sex of driver
first point of impact age of driver
Clearly, speed limit is only a proxy for the variable of interest, accident severity. The earlier paper concluded from theoretical considerations that, once these influences have been taken into account, D and D, provide the most satisfactory means of comparing the secondary safety of different models of car. The analyses described below have been made to check practical aspects of the indices, based on the accidents recorded in the Stats19 files for 1989-92 in which:
(4 two cars were involved and at least one driver was injured; (W the Vehicle Registration Mark of at least one of the cars is known and has been matched in the DVLA records; (4 at least one of the models appears in the list in the DOT report which includes all models with more than 20,000 registered cars.
The range of “other” cars
The DOT index could be biased if the models studied are not in collision with a common range of ‘other’ cars. If, for example, a particular model is involved in relatively many accidents with large cars, then it is likely that more of its drivers will be injured than if these accidents had involved a typical range of cars, leading to an unfavourable value of D. As a first step in checking whether this happens in practice, models have been grouped according to size as specified in the DOT report: as an approximate guide, ‘small’ cars are 140-152 inches long, ‘small/medium’ cars are 153-167 inches long, ‘medium’ cars are 168-180 inches and ‘large’ cars are over 180 inches long. A subset of accidents is used for this analysis, since for each car in an accident the type of model must be known and must appear in the list from the DOT report; 187,695 accidents fulfil these extra requirements. As an example, 55,641 of these accidents involve either 1 or 2 small/medium cars, distributed as follows: Size of one car small/medium small/medium small/medium small/medium small/medium
Size of other car small small/medium medium large all
Number of accidents
Proportion
15786 20967 15131 3757 55641
0.298 0.374 0.267 0.061 1.000
Table 1 presents the distributions for the four size ranges (columns l-4) and each differs to some extent from the distribution for cars of all sizes (column 5). The differences which are significant (probability of the difference arising by chance < 0.05) are marked with *. While the table shows some significant differences between the size distributions, Table 2 shows that the indices change very little when they are adjusted to the common basis provided by the ‘all sizes’ distribution. The reason is probably that the differences have no clear pattern. If, for example, the table had instead shown that large cars tend to collide Table 1. The proportion of accidents which involve cars of size A which also involve cars of size B Size A Size B
Small
Small/med
Medium
Large
All sizes
Small Small/medium Medium Large
0.284* 0.377 0.272; 0.068*
0.298 0.374 0.267 0.061*
0.303* 0.375 0.261* 0.062
0.3188 0.362* 0.262 0.058*
0.296 0,374 0.266 0.063
All sizes
1.000
1.000
1.000
1.000
1.000
Note: * denotes a value which differs significantly (p~O.05) from the corresponding value in the “all sizes” distribution.
Accident record of car models
Table 2. Unadjusted
103
and adjusted DOT indices, by size of car
ksi (Ds) Size of car Large Medium Small/medium Small
Unadjusted
Adjusted
0.328 0.494 0.594 0.139
0.332 0.496 0.595 0.736
Note: “adjusted” results use the common
All casualties (D) Increase
Unadjusted
Adjusted
0.399 0.514 0.598 0.728
0.403 0.516 0.599 0.725
1.1% 0.4 0.1 -0.4
Increase 1.0% 0.3 0.1 -0.3
basis provided by the “all sizes” distribution.
with large and small cars to collide with small, rather larger adjustments would presumably have been necessary. Similar conclusions emerge when the collisions involving the 24 models with the greatest number of accident involvements are studied in detail. Some models collide with other models more or less frequently than expected-for example, Nissan Bluebirds collided with other Bluebirds 73% more frequently than expected, while Renault 5’s and Rover 200’s collided 33% less frequently. These are extreme examples, however, and the collision distributions for the models most commonly involved in accidents (Ford Escorts and Fiestas) match the expected distributions fairly closely. Overall, differences from the expected values are slightly greater than would have arisen by chance. When the DOT indices are adjusted to allow for differences between the actual and expected collision distributions, the adjustments are small-almost all are less than l%, and all are well within the standard error for the estimated index. The same is found with the Folksam indices which were also studied in the earlier paper. Thus, although some models do differ significantly in the distribution of “other” cars with which they collide, the Folksam and DOT indices are not biased by ignoring the differences. Provided that the confidence intervals are interpreted properly, there is no need to adjust the indices to allow for differences between the distributions. The stability of the DOT index
Two main aspects of the stability of DOT index will be considered-are the indices calculated in separate years consistent, and do models with similar characteristics have similar indices? The indices presented in the Department of Transport report (1993) are based on data accumulated over successive years, in order to obtain the statistical benefits of analysing larger numbers of accidents. This is appropriate only if results calculated for individual years are consistent. This has been checked by calculating the indices with accident data from individual years, and comparing them with the indices calculated for the grouped data from 1989-92.
Some variations are inevitable, especially among the less common models, so the differences are compared with the standard errors for the indices: these indicate the range of variation that might be expected from purely random effects. Only 4.4% of variations exceeded 1 standard error for the casualty index D, and 6.4% for the ksi index DB, so it is likely that variations in individual years about the indices calculated for the grouped data have arisen purely by chance. This stability of the index over four years confirms that it is justified to accumulate data over several years to provide more reliable results. The earlier report showed, however, that the index is a relative measure which compares the safety of different models at the same time but cannot assess changes in safety over time as new models enter the car fleet. This means that there will be a limit to the number of years over which this can be done, which depends upon the rate of introduction of new models with improved secondary safety features and the average “lifetime” of a car, as shown by the following example. Suppose that a new model appears in year Y which has a better level of secondary safety than comparable contemporary models, so that its index will be below average. Suppose also that by year Y+ 10 most other models have been replaced by improved versions and its secondary safety is worse than the new average, so that its index will now be above average. The fact that D is a relative measure means that the average cannot change, so the model’s index must rise over the years. Hence, the value calculated from data accumulated over the decade will differ from the value calculated at the beginning or the end of the decade. No sign has been found of this occurring at present, but it may become necessary in future to base the index on data from only the most recent few years. Results achieved by statisticians from the DOT Statistics Directorate provide further evidence of the stability of the index. They compiled a list of variants of relatively common models which could be identified from the details supplied by DVLA, for example, high performance versions. Each “family” of variants would be expected to have the same index, since they
J. BROUGHTON
104
share the same protective features. The indices are indeed closely clustered and each family has in effect a common index, despite the different specifications of the variants. There are sound technical explanations for those few cases where an index differs significantly from the central value for the family.
measure the effect of these variables on the likelihood of becoming involved in such an accident, so h is directly comparable to the DOT index. Indeed, by rearranging (2):
=
AN ALTERNATIVE
MODEL
A modelling approach is now described which leads to the DOT index and so provides a theoretical derivation for it. The description includes only three explanatory factors, namely driver age, driver sex and road type (represented by speed limit), but can easily be extended to incorporate others if necessary. The model assumes a multiplicative relationship between the independent factors and the number of casualties: (1)
where C(u,s,r,m)=number of driver casualties of age a and sex s on roads of type r (as categorized by speed limit, for example) while driving cars of model m, X(u,s,r,m) =mileage of drivers of age a and sex s in cars of model m on roads of type r, F,G,H are factors to be determined, E is an error term, assumed to have zero mean and constant variance. The H-factors are of particular interest, as they represent the differences between the number of driver casualties expected with different car models: (1) is thus a model of primary safety. The F- and G-factors are of lesser interest, as they are included to eliminate bias arising from road type etc. In order to give reliable results, the model needs to be applied with fairly detailed mileage data X, so the results would have little value with the data currently available in Great Britain. An alternative that does not require mileage data can be developed by letting I(u,s,r,m) be the number of drivers of age a and sex s involved in two-car accidents on roads of type r while driving cars of model m, as recorded in the Stats19 data. I is analogous to the mileage data X but not a direct substitute, so the factors calculated using I would not match those calculated using (1) if suitable mileage data existed. The new model is: C(u,s,cm)=f(u,s)*g(r)*h(m)*Z(u,s,r,m)+~(u,s,r,m)
(2)
f, g and h measure the effect of the independent variables a, s, r and m on the likelihood of a driver
being injured when involved in a two-car accident: f and g represent the influence of non-vehicle factors while h represents the model-related factors. This is a model of secondary safety since J g and h do not
unadjusted DOT index
This operates in a very similar way to the logistic regression model of the DOT approach: starting from the basic casualty proportions, it calculates a safety index free (within the limits imposed by the available data) from the influence of non-vehicle factors. Thus, this modelling provides a theoretical justification for the DOT index. (2) is fitted by finding factors which minimize S = C .a’. A FORTRAN program has been developed which rapidly converges to the solution from any plausible initial values forfand g, although alternatively the factors could be calculated with a linear regression model and logarithmically transformed data. The model will also calculate either ksi index, D, or D,. C is restricted to drivers ksi with both; with the latter, Z is restricted to accidents in which at least one of the drivers is ksi. Results
When model (2) was fitted to the 1988-92 driver casualty data for the 91 models in two-car accidents, four age bands were used and two road types, builtup (speed limit at most 40 mph) and non built-up (speed limit over 40 mph). The effectiveness with which the model represents the variations in the driver casualty data can be judged by comparison with a simpler model which excludes the non-vehicle explanatory factors, i.e. it assumes that the casualty proportion for each model does not vary with type of road or driver: C(u,s,r,m)=h(m)*I(u,s,r,m)+&,s,r,m)
(3)
The following values of R* indicate the agreement between the actual and predicted casualty data C: model (2) model (3)
D
DB
0.998 0.978
0.988 0.977
DA
0.973 0.750
Thus, the explanatory factors improve the performance of the model significantly, confirming the case for the DOT’S relatively sophisticated statistical approach. There appears to be little scope for further improvement of the model of all casualties, but the ksi models may perhaps benefit from more detailed road type data. R2 values are higher for DB than for DA, presumably because D is more closely related to D, than to DA. The high R2 values achieved by model (2) show
Accident record of car models
that factors not included in the model can have very little influence on the driver casualty data, although they may well operate indirectly via the factors that are included. Thus, there is effectively no risk of D or DB being biased by exogenous factors and, within the statistical limits set by the number of cars of each model that are involved in accidents, the index will reliably compare secondary safety. The only drawbacks to its use are practical, and arise directly from the reliance on national accident data: large numbers of a new car model must be in use before its safety can be assessed accurately, and it is difficult to relate the assessment to specific features of the model. On the other hand, the index does measure how well the model protects its drivers in the range of accidents actually occurring on the roads of Great Britain, rather than in the simulated accidents used in crash testing. Turning now to the specific results obtained when fitting model (2), Table 3 shows the non-vehicle factors. The factor “road type” is the increased likelihood of injury for a driver involved in an accident on a non built-up road, relative to a built-up road; the eight driver-related factors have been adjusted to have a mean of 1. The pattern of the driver-related results agrees with general analyses of the casualty rates of British drivers (e.g. Broughton 1990), which find that rates are lowest around the age of 50 and begin to rise more rapidly after the age of 65, and that rates are higher for women than for men. The relatively small increases for the 55 age group compared with the 35-54 age group reflects the relatively low mileage of British drivers over 65 years old. By contrast, the value of the road type factor for D exceeds 1, implying greater risk of injury on non built-up roads, whereas driver casualty rates are lower on non built-up than on built-up roads. The explanation is that the factor is measuring the greater risk of a driver being injured Table 3. Driver- and road-related number of driver casualties
factors which influence [/and g in model (2)]
D
the
&I
Factor
Value
SE
Value
SE
Road type
1.121
0.012
1.156
0.040
Male driver 17-14 25-34 35-54 55-
0.829 0.832 0.850 0.939
0.011 0.011 0.010 0.013
0.834 0.834 0.881 1.078
0.031 0.031 0.035 0.040
Female driver 17-24 25-34 35-54 55-
1.181 1.148 1.146 1.169
0.015 0.015 0.014 0.024
1.076 1.089 1.089 1.187
0.043 0.051 0.036 0.065
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when involved in a two-car accident on a high-speed road, rather than the rate at which these accidents occur. THE EFFECT OF VEHICLE THE DOT INDICES
MASS ON
It is well known that larger cars tend to protect their occupants better than small cars, and it would be desirable to develop the DOT indices to allow for the effects of size. A method is described which is based on the adjusted values of D and D, that are obtained using model (2); it could equally well be applied with results from the DOT logistic regression approach. The mass of 87 of the 91 models was established from a commercial report (Glass’s Guide Service 1992); this could only be done approximately because the variants of models such as the Ford Sierra have a range of masses. Figure 1 shows that the adjusted casualty proportion falls steadily with increasing mass. Fitting a simple linear model to the data from 1989-92 yields the relation: D = 1.053 -O.O0045*mass
(R2=0.85, N=87, respectively.)
SE’s
are
0.013,
(4) 0.00002
A similar pattern is found with D,, the ksi index. The points are slightly more scattered and the fitted line is slightly steeper: D,= 1.118-O.O0055*mass
(5)
(R2=0.73,
N =87, SE’s are 0.024, 0.00004 respectively.) It is striking that these simple models explain such a high proportion of the variation in the casualty data. Note also that (4) implies that all drivers are injured when mass= 100 kg [210 kg for (5)]. Evans and Frick (1993) found that in two-car accidents the risk of death for the driver of the lighter car was p3.53 times the risk for the driver of the heavier car, where p is the ratio of the masses. This suggests that the relation between mass and adjusted proportion may be non-linear, at least in the case of fatal accidents, but the data do not support this for predominantly non-fatal accidents. When (4) is refitted with (mass)f in place of mass, the optimal model for D has c = 1.00. For D,, the optimal value of c = 0.85, but the marginal improvement in fit does not justify the addition of an extra term. Thus, the linear model is optimal in both cases. The mass-adjusted
safety index
Equation (4) establishes the typical proportion of driver casualties to be expected in a model of given mass, so actual values can be compared with these
J BROUGHTON
106
0.9 -
5 I .s
0.6 -
;
0.5 -
0.4 -
0.2 500
I
I
I
1000
1500
2000
Car mass (kg) Fig. 1.
expected values to see which models perform significantly better or worse than average. Models lying above the fitted line in Fig. 1 perform worse than average, those lying below perform better. Thus, the mass-adjusted safety index MS1 = D -( 1.053 - O.O0045*mass) compares the index of a particular model with the value expected for a typical model of the same mass. A model with negative MS1 has fewer driver casualties than expected, so it is relatively safe: a positive value indicates a relatively unsafe model. The points farthest below the fitted line denote the level of secondary safety achieved by the most successful current designs, subject to the confidence intervals for the estimates. When the model is re-fitted for the individual years 1989-92, very similar fitted lines and MSIvalues are found, so MS1 is a stable measure of secondary safety which represents model-specific effects. This is also consistent with the conclusion in the earlier paper that overall changes in secondary safety will not affect the general distribution of casualty proportions, although the period covered is too short to provide real confirmation. The regression which fitted (4) treated all casualty proportions equally, while some are actually more precise than others for statistical reasons related to the number of accidents in which each model is involved. A weighted regression allows for this, it yields a slightly steeper fitted line so slightly different mass-adjusted indices are produced on the basis of this line. These tend to favour the more popular models since the weighting of the regression emphasizes data from these models, so a different type of
bias is introduced. On balance, it seems preferable to treat each model equally, as was done when calculating (4). The ranking of models using the mass-adjusted index clearly differs greatly from the ranking using the original index. For example, the Citroen 2CV/Dyane ranks lowest using the original index because it has the greatest value of D; however, its MS1 is only slightly worse than average so it lies in the middle of the mass-adjusted ranking. Conversely, Jaguars have the lowest value of D but slightly more Jaguar drivers are injured than would be expected with a car of this mass, so they rank highest by the original index but below average by the massadjusted index. The two sets of indices have separate but complementary roles: (i) the unadjusted index is relevant to the car buyer who wishes to compare the safety of the models being considered, since their personal safety will be of especial concern to them; (ii) the mass-adjusted index is of interest to regulators and the motor industry, as it shows whether particular models achieve good safety records by added mass rather than by good design. The influence of mass and design
It has been claimed that (4) represents the influence of mass on the casualty proportion, but it might also be influenced by other aspects of vehicle design. These will influence the fitted line if safety-related features tend to be better designed in small models than in large, or vice versa. If small models are better
Accident record of car models
designed than large, then their casualty proportions will be somewhat lower than they would have been with uniform design standards and the casualty proportion of large models will be somewhat higher. Consequently, the fitted line in Fig. 1 would be less steep than it would have been if standards had been uniform, and it would under-represent the effect of mass. Equally, if large models were better designed than small, the fitted line in Fig. 1 would be too steep. However, if “good” and “bad” designs coexist in all size ranges, (4) will show the unalloyed effect of mass. It seems likely that in fact “good” and “bad” designs coexist in all size ranges, and that (4) is not influenced by design. This will be checked by studying popular models which have variants spanning a reasonably wide range of masses, to see whether the casualty proportion does vary systematically with mass. Three manufacturers have sold sufficient cars in Great Britain for their models to be compared in detail: Ford (5 models), Rover (5 models) and Vauxhall (4 models). The mass of any car that was identified in the accident data as being of one of these 14 models was extracted from a commercial report (Glass’s Guide Service 1992) on the basis of its engine capacity, body type and year of first registration. This provides vehicle mass with a fair degree of precision, although the published figures are less comprehensive for some models than for others. Also, a heavilyloaded car with four adult passengers and their luggage can weigh at least 300 kg more than the same car when it only carries its driver. Such variation should not bias the analysis, however, as the distribution of “loaded” weight of accident-involved cars relative to the published “unladen” weight is probably consistent for each model across the mass ranges, but these considerations do imply that mass ranges should not be too narrow. Accident-involved cars were assigned to mass ranges (generally of 50 kg, sometimes 100 kg where vehicle numbers were low). The values of D that were calculated are presented in Fig. 2 together with the fitted line (4); the masses of Rover 800’s proved in practice to be too closely clustered for the range to be sub-divided as intended, but the point is shown for completeness. The standard errors of most of the estimated indices are less than 0.02, although for 5 of the less common combinations of mass and model they exceed 0.04. For most Rover and Vauxhall models, the line segments are almost exactly parallel to the fitted line, so the variation with mass is almost exactly as shown by (4). The casualty proportion falls rather more steeply with Astra/Belmonts, although this may be linked to the replacement of the earlier model range
107
in October 1984 by heavier models: the steeper fall may indicate that the newer range has improved safety features. Several other Rover and Vauxhall models have also been redesigned to some extent, but it appears that any safety benefit has been largely in line with what would be expected from the increased mass. Three Ford models conform less well to the pattern found among Rover and Vauxhall models. The Sierra/Sapphire shows no decrease with mass, while the decrease for the Fiesta and Escort is lessthan expected: these results are probably robust as these three models are so numerous. The replacement of existing models by heavier designs may explain the non-conforming results for Fiestas and Escorts. Lighter Fiestas were predominantly registered before 1989, while the majority of the heavier Fiestas were registered in or after 1989; few of the lighter Escorts were registered after 1987, but three-quarters of the heavier Escorts were registered in or after 1987: the new designs may not have achieved, in full, the safety benefit to be expected from the increase in mass. There is no indication of such an explanation with the Sierra/Sapphire range; the lightest cars tend to be relatively old, but the other three mass ranges have similar age distributions. Thus, 9 of the 13 models studied support the proposition that (4) represents solely the effect of mass, one model shows no systematic variation with mass, and the replacement of existing designs confuses the interpretation of results from the other three models. On balance, this supporting evidence is reasonably convincing, but more homogeneous vehicle groups would be needed to achieve more conclusive results. The opportunity to do this is restricted, however, by the available sample sizes, so the frequency with which manufacturers redesign or replace their models makes it impracticable to take the analysis much further. CONCLUSIONS This paper has completed a study of the ways in which national accident data can be analysed to compare the safety of different car models. The study has been influenced by the data that are available in Great Britain, but the conclusions should be generally applicable. An earlier paper (Broughton 1996) has shown that, since there is virtually no information about the relative levels of exposure of different models, only indices of secondary or passive safety (crashworthiness) can be calculated at present. It concluded from theoretical considerations that the most satisfactory safety index is the one currently used by the British Department of Transport (DOT),
J. BROUGHTON
108
0.8
Rover
r
Ford
0.6
0.6
Rover 800 700
I
I
I
I
I
800
900
1000
1100
1200
I 1300
I 1400
0.4 700
I
I
I
I
I
800
900
1000
1100
1200
1300
0 1400
0.8 r
Vauxhall
0.4 700
I
I
I
I
I
I
I
800
900
1000
1100
1200
1300
1400
Fig. 2.
and this paper has presented various empirical tests of the index. It has also described an alternative modelling approach for deriving the DOT index which provides a theoretical justification for the index and could make use of detailed exposure data by car model if these become available. The fitted models reproduce the casualty data so well that it is unlikely that the index is biased by exogenous factors. One test of the stability of the index has compared results from the four years for which the necessary data have been collected in Great Britain. The values are very stable, which justifies the practice of accumulating data over several years to provide
more precise estimates. A second test of stability has consisted of comparing the indices of variants of relatively common models. These have proved to be closely clustered, so that each family has in effect a common index in spite of the different specifications of the variants; this is important because the variants have common protective features. It is well known that the risk of the driver being injured once a car is involved in an accident tends to reduce with the car’s size. An adjusted version of the DOT index has been described which relies on the very regular relation that exists between the index and car mass: on average, for every 100 kg added to the unladen mass of a car, the probability of its driver
Accident
record
being injured when involved in a two-car accident where one or other driver is injured falls by 0.045. Detailed analysis of accident data for several popular models tends to confirm that the reduction of the index is entirely the effect of mass, although the index does not appear to fall with increasing mass as expected among Ford Sierras and Sapphires. The range of the index among models of similar mass then shows the extent to which better driver protection can be achieved by improved design. The mass-adjusted DOT index allows the safety of cars of widely differing masses to be compared directly, thereby showing whether some models may be relatively safe because of extra mass rather than better design. This information is of interest to Government regulators and the car industry, while car buyers will probably be more concerned with the basic index.
of car models
109
Acknowledgement-The work described in this paper was carried out in the Safety and Environment Resource Centre of TRL.
REFERENCES Broughton, J. Casualty rates among car occupants, 1976-1986. Department of Transport, TRRL Report RR2441 Transport and Road Research Laboratory, Crowthome; 1990. Broughton, J. The theoretical basis for comparing the accident record of car models. Accid. Anal. and Prev. 28: 89-99; 1996. Department of Transport. Cars: make and model: injury accident and casualty rates: Great Britain: 1991. London: HMSO; 1993. Evans, L.; Frick, M. C. Mass ratio and relative driver fatality risk in two-vehicle crashes. Accid. Anal. and Prev. 25213-224; 1993. Glass’s Guide Service. Glass’s car check book 1992. 1992.