Application of the Induced Exposure Method to Compare Risks of Traffic Crashes among Different Types of Drivers under Different Environmental Conditions

José Luis Redondo-Calderón1, Juan de Dios Luna-del-Castillo2, José Juan Jiménez-Moleón3, Miguel García-Martín3, Pablo Lardelli-Claret3 and Ramón Gálvez-Vargas3

1 Delegación Provincial de Salud, E-14004 Cordoba, Spain.
2 Departamento de Estadística e Investigación Operativa, Universidad de Granada, Granada, Spain.
3 Departamento de Medicina Preventiva y Salud Pública, Universidad de Granada, Granada, Spain.


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
The authors used the induced exposure method to compare risks of traffic crashes among different types of Spanish drivers under different environmental conditions. The authors analyzed traffic crashes recorded by the Spanish Dirección General de Tráfico for the years 1991 and 1992 to compare proportions of drivers in different age/sex categories who were involved in single-vehicle and multivehicle crashes under different psychological and physical conditions. Crash risk was 1.42- to 2.35-fold greater in men than in women, depending on driver category and environmental factors. Risk was also significantly higher in the 18- to 24-year-old age group (1.75- to 2.87-fold greater than in drivers aged 25–49 years) and under abnormal psychological-physical conditions (1.69- to 4.10-fold greater among drivers under the influence of alcohol). Twilight and night driving, driving in urban areas, and driving on weekends and legal holidays were also associated, though nonsignificantly, with a slightly higher traffic crash risk. These findings are consistent with earlier reports, and they support the usefulness of the induced exposure method as an easy and economical tool with which to analyze data contained in traffic crash records.

accidents, traffic; automobile driving; epidemiologic methods; risk

Abbreviations: DGT, Dirección General de Tráfico.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
For comparison of traffic crash risks between different types of drivers, exposure rates in each group must be estimated (1GoGoGo–4Go). Investigators disagree as to the best estimate of exposure (number of trips, driving time, distance traveled, etc.) (1Go, 3GoGo–5Go). The information needed is not usually available, so it is often obtained through telephone surveys or other ad hoc procedures (2Go, 5Go, 6Go). This raises a number of well-known problems (lack of validity and reliability of information sources, high cost, and difficulties in estimating exposure rates for different driver and environmental conditions) (1GoGo–3Go, 7Go, 8Go) that limit the usefulness of the traffic crash registers available in most developed countries.

To help overcome this problem, Thorpe proposed what is known as the induced exposure method for obtaining indirect estimates of exposure from traffic crash registers (see Stamatiadis and Deacon (2Go)). Related methods can now be divided into two groups. The quasi-induced exposure method is based on the distinction between responsible drivers and nonresponsible drivers, and it considers the latter group a representative sample of all drivers on the road (2Go, 9Go, 10Go). The main problem with this approach is that the identity of the typical responsible driver remains unclear (8Go). The second group comprises methods that do not require identification of responsible drivers but instead are based on comparisons between categories of drivers involved in different types of crashes. This group includes the method proposed by Cuthbert (11Go) in 1994, which compares the proportions of drivers in each category involved in single-vehicle crashes (excluding cases in which a pedestrian was struck by a vehicle) and multivehicle crashes. The robustness of the theoretical foundations of this model, the possibility of comparing risks adjusted for environmental conditions at the time of the crash, and the extreme simplicity of the mathematical formulas make this method an especially attractive option for analyzing data available from traffic crash registers.

Using Cuthbert's induced exposure method, we compared traffic crash risks between different categories of Spanish drivers under different environmental conditions. We then compared our results with those of earlier studies that used conventional methods.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
This study can be considered to comprise a case series, although our analysis of the data resembles methods more typical of those of case-control studies. The case series was constructed from the register of traffic crashes resulting in injury or death (excluding accidents involving pedestrians) recorded by the Spanish Dirección General de Tráfico (DGT) during 1991 and 1992. This register contains information from the accident reports that Spanish police are required to file for every traffic crash involving victims.

For each crash, we recorded 1) type of crash (single-vehicle or multivehicle), 2) type of day (workday or weekend day/legal holiday), 3) surface conditions (dry or altered (i.e., shaded, wet, icy, snowy, muddy, gravelly, oily, or macadamized)), 4) light conditions (daylight, twilight, or night), and 5) traffic zone (open highway, thruway (section of a highway within city limits), or urban street). Light conditions at the time of the crash were determined post hoc, considering the hours of sunrise and sunset in Spain (40°N latitude) on any given date. The categories "thruway" and "urban" were combined in order to simplify the analysis, since no significant differences were found between the two.

For each driver, we recorded age, sex, and psychological-physical condition. Age was stratified into four categories: <18, 18–24, 25–49, and >49 years. Driver's psychological-physical condition originally contained 11 categories: 1, normal; 2, normal-appearing, driving nonstop for up to 3 hours; 3, normal-appearing, driving nonstop for 3–5 hours; 4, normal-appearing, driving nonstop for more than 5 hours; 5, under the influence of alcohol, no alcoholemia test given; 6, under the influence of alcohol, with positive alcoholemia test; 7, under the influence of drugs; 8, inattentive or distracted; 9, sick, having experienced sudden illness; 10, asleep or drowsy; and 11, worried. To ensure that the sample size in each category was large enough, we recategorized this variable into four groups, as follows: normal driving (categories 1 and 2); prolonged nonstop driving (categories 3 and 4); driving under the influence of alcohol (categories 5 and 6); and other circumstances (categories 7–11).

Analysis
In the induced exposure method proposed by Cuthbert (11Go), the crash rate for a given type of driver (per unit of exposure and under specific environmental conditions) is the sum of two components, one driver-dependent and the other determined by the rate of exposure of the type of driver concerned under certain environmental conditions. The latter is a random component which can be small for some types of crashes but large for others. When this component is large, the distribution of involved drivers will approach the general distribution of all drivers under those environmental conditions; in contrast, when the random component is small, the distribution of involved drivers will be a representative sample of all drivers on the road under those environmental conditions, weighted by each type of driver's intrinsic risk of having a crash. This situation is typical of single-vehicle crashes (excluding accidents involving pedestrians) involving a single responsible driver. Multivehicle crashes represent the opposite situation: A good number of the drivers involved can be assumed to be nonresponsible; therefore, the group of involved drivers is more likely to reflect a sample of all drivers on the road at the time of the crash. According to this reasoning, under given environmental conditions, the ratio of the number of drivers of a given type who are involved in single-vehicle crashes to those who are involved in multivehicle crashes correlates directly with the magnitude of intrinsic risk for this type of driver. This ratio divided by the ratio for a different type of driver (a reference type) yields an odds ratio.

The mathematical formulas used to derive induced exposure are straightforward. If xij is the rate of exposure of type i drivers under environmental condition j, the mean numbers of drivers involved in single-vehicle and multivehicle crashes are

and

where:

The quotient Rij is expressed by the equation


This ratio is dependent not on the exposure rate but mainly on the type of driver, if this effect is large. If we consider a reference type of driver designated k, with a low risk of traffic crashes, the quotient of Rij divided by Rkj provides information on the multiple of increase in the ratio of single-vehicle crashes to multivehicle crashes for type i drivers with respect to type k drivers. This can be considered an odds ratio (Oij), expressed by the following equation:

Because all variables are Poisson variables, a Taylor series can be used to derive the logarithm of Oij. Using the first term, we obtain the equation

The resulting multiplicative model expresses the logarithm of the odds ratio as the product of two components: si - sk estimates the increase in risk associated with a type i driver in comparison with a reference type (type k) driver, and {alpha}j quantifies the effect of environmental factor j on the increase in risk. This model thus makes it possible to estimate the effect of type of driver on Oij while controlling for environmental conditions, and vice versa.

On the basis of the theoretical foundations described above, this model can be considered valid as long as the random component for multivehicle crashes is greater than the component for single-vehicle crashes, as will be the case whenever {alpha}j is greater than 0. To estimate both the driver-dependent and environment-dependent components in the model, we need a second reference category for type of driver, which we will call sw. This gives the equation

Adding the values of log(O) for all environmental categories gives

for type i drivers and

for type w drivers. Dividing the first expression by the second yields

The second term in the model was estimated in this study from data in the traffic crash register:


Therefore, the estimates of relative risk can be interpreted as the increases in risk for type i drivers relative to type k drivers, expressed in relation to the increase in risk for type w drivers relative to type k drivers (conventionally assumed to have a magnitude of 1, a standard increase in risk). Once the values for si - sk are estimated (rescaled in relation to sw - sk), {alpha}j is estimated by summing across all categories of drivers:

which yields

The confidence intervals for the parameters in the model can be calculated from the estimate of the variance of log(Oij). Because nij, mij, nkj, and mkj are Poisson variables, the variance can be estimated as follows:

The standard error of each estimator can be calculated from the square root of the sum of the variances of log(Oij) for each estimation.

In the present study, the small sample size for some of the combinations of driver and environmental factors made it impossible to estimate risk of traffic crashes for all driver and environmental conditions together. Therefore, to estimate increases in risk associated with type of driver, we constructed six models that combined all three driver-dependent factors with all possible pairs of environmental factors. To estimate increases in risk associated with environmental factors, we designed a model for each factor separately that also included all three driver factors.

Men aged >49 years driving under normal psychological-physical conditions were considered the reference type of driver (type k) in all models. This was the category with the largest sample size and the smallest value of R for any given environmental factor. To rescale the values of si - sk, we used type w drivers as the second reference group: women between 25 and 49 years of age driving under normal psychological-physical conditions. Therefore, in all models, we assigned a value of 1 to sw - sk, which expresses the difference in risk between these two categories of drivers.

All statistical analyses were carried out with the Data Manager program of the BMDP Dynamic statistical software package (12Go).


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
During the 2-year study period, the DGT database collected information on 151,364 traffic crashes with victims (excluding pedestrians): 47,358 single-vehicle crashes and 104,006 multiple-vehicle crashes. Data were missing from 6,125 register entries (4 percent), so the final sample consisted of 145,239 traffic crashes involving 253,050 drivers. Table 1 shows how crashes and drivers were distributed according to the different variables. A noteworthy finding was the low proportion (3 percent) of drivers reported to be under the influence of alcohol.


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TABLE 1. Percentage distributions of crashes and involved drivers according to environmental and individual variables in a study of automobile accidents, Spain, 1991 and 1992

 
Table 2 shows the models adjusted for each of the six combinations of pairs of environmental factors. The absolute magnitude of the rescaled estimators of si - sk differed between models, but increases in relative risk estimated separately for each driver factor from the ratios between the coefficients obtained with the models (table 3) were much more homogeneous. Therefore, results are reported below in terms of the ratios of rescaled si - sk estimators for each driver variable, specifically for those estimators that were statistically significant.


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TABLE 2. Estimated effects of individual factors (si - sk rescaled) in an induced exposure model of automobile accidents, adjusted by pairs of environmental factors, Spain, 1991 and 1992

 

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TABLE 3. Ratios between coefficients for driver-dependent variables, according to other variables, in a study of automobile accidents, Spain, 1991 and 1992

 
Under normal psychological-physical conditions, the risk of being involved in a crash for drivers aged 25–49 years was 1.52- to 2.35-fold higher in men than in women, depending on the model (table 3). Among drivers aged 18–24 years, the increases in risk were slightly smaller. The excess risk for men in comparison with women was modified under psychological-physical conditions other than normal. For example, in the category "inebriated," the increases ranged from 1.29-fold to 1.37-fold in the 25- to 49-year-old group and from 1.19-fold to 1.32-fold in the 18- to 24-year-old group. Interestingly, in the category of prolonged nonstop driving, the increases in risk for drivers aged 25–49 years were 1.28- to 1.45-fold greater for women than for men.

When we compared age groups under normal psychological-physical conditions, the risk was greater among drivers aged 18–24 years than among drivers aged 25–49 years. The magnitude of the increase was always slightly larger in women (from 2.00-fold to 2.87-fold) than in men (from 1.75-fold to 2.08-fold). No estimates could be calculated for drivers older than 49 years; among men, this group was used as the reference group (type k), and among women the sample was too small.

Under psychological-physical conditions other than normal, the increase in risk among drivers aged 18–24 years was attenuated considerably. The risks for men older than 49 years were consistently lower than those for men aged 25–49 years, with a small margin of variation: 0.82–0.90 for prolonged driving, 0.62–0.74 for driving under the influence of alcohol, and 0.63–0.72 for other conditions.

Of the three driver-related factors, psychological-physical conditions contributed the greatest increases in risk of traffic crashes. Among men aged 25–49 years, inebriated driving increased the risk of traffic crashes 2.37- to 2.45-fold over the risk under normal conditions. Among men aged 18–24 years, the increase in risk was slightly smaller (from 1.69-fold to 1.85-fold). The effect of alcohol on risk of traffic crashes was even greater in women than in men: 2.93- to 4.10-fold for women aged 25–49 years and 1.91- to 2.48-fold for women aged 18–24 years. Prolonged driving also significantly increased the risk of traffic crashes, especially among women.

Table 4 shows the estimates of {alpha}j for the effect of each environmental factor, adjusted for driver factors. None of the coefficients differed significantly from 0. The largest coefficients were found for traffic zone. The increases in risk were greatest under twilight conditions (1.42-fold greater than during daylight driving) and for urban zones and thruways (1.39-fold greater than for open highways).


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TABLE 4. Coefficients for environmental factors ({alpha}j) in an induced exposure model of automobile accidents, Spain, 1991 and 1992

 

    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
A prime methodological consideration in this study is the degree to which the data in the DGT register can be considered exhaustive, or at least representative of all traffic crashes with victims that occurred in Spain during the period investigated. Some types of crashes are known to be underreported, particularly those that cause no deaths or serious injuries, those involving a single driver, and those that occur in urban areas (13Go, 14Go). The validity of the information on environmental conditions and driver age and sex seemed acceptable (15Go), but information on psychological-physical conditions might not have been as accurate. Despite the many studies that have implicated alcohol drinking in a large percentage (as many as 50 percent) of traffic crashes (16Go), this factor appeared in only 3 percent of the crashes in the DGT register—a result that clearly indicates underreporting. It is a disturbing fact that alcohol level is not measured among all drivers involved in crashes in Spain. This undoubtedly raises serious questions about the validity of these variables. It is likely that the reference category (normal) was "contaminated" by the inclusion of drivers with low to moderate levels of alcohol-induced impairment; this would have resulted in underestimation of the effect of alcohol drinking.

The small sample size for some categories forced us to regroup some variables. As in other studies (2Go, 17Go, 18Go), we included subjects up to 24 years of age in the group of young drivers. However, because the minimum legal driving age in Spain is 18 years, we used this as the lower cutoff point to distinguish young drivers of automobiles from adolescent drivers of mopeds, scooters, or motorcycles. The particular characteristics of drivers under 18 years of age and the small sample size make the results for this age group difficult to interpret. With regard to drivers aged 25 years or older, the small sample sizes meant that only two subgroups could be created. We therefore used a cutoff age of 50 years to distinguish between young adult drivers and older drivers.

The psychological-physical categories we used were designed to distinguish inebriated drivers from all other drivers. We were forced to use the category designated "other" by the small sample sizes of the different subgroups comprising this category; the result was a heterogeneous group of drivers that, not surprisingly, did not yield useful findings. With regard to prolonged driving, the DGT recommends a rest after 3 hours of nonstop driving, and we used this amount of time as the cutoff point for the variable. Small sample sizes forced us to amalgamate crashes that occurred in urban zones and those that occurred on thruways and to combine crashes that occurred under all surface conditions other than normal. Despite these reclassifications, the final analysis was based on 1,536 cells, many of which contained only a few drivers, if any. This led to two problems. First, it was not possible to estimate risk for some subgroups of drivers, especially for women and for the youngest and oldest age groups. Second, variances were large, especially for environmental factors. Because of the large variance for some extreme categories, none of the estimators of {alpha}j were statistically significant. Nevertheless, we believe that this lack of significance was mainly the result of a very conservative estimation of the variance of {alpha}j (the sum of the variances of each log(Oij)), and several combinations of driver conditions had very small sample sizes.

The intrinsic validity of the induced exposure model is supported by the robust theoretical assumptions that form the basis of this approach. The strong point of the model, as Cuthbert noted (11Go), is its capacity to adjust individual risk estimates on the basis of environmental conditions. Few studies based on conventional methods allow for this adjustment, since they do not stratify exposure on the basis of these conditions (2Go, 8Go). A weak point of this approach, however, is that the model assumes that all drivers of a certain type have the same likelihood of being involved in single-vehicle crashes and multivehicle crashes. Some investigators (2Go) maintain that the type of crash (single- or multivehicle) is in fact driver-dependent. If this is so, in the equations we used to estimate risk, we would have had to add a term to model the different likelihoods; if the value were large, this would lead to overestimation of the risk. However, the estimates of the different likelihoods are generally small (2Go), and they are rarely large enough to seriously distort our estimates.

Because a proportion of the drivers involved in multi-vehicle crashes represented the drivers responsible for these events, this sample cannot be considered entirely representative of the population of drivers on the road. However, this contamination of our "control" group (nonresponsible drivers) would be expected to produce bias toward the null hypothesis—i.e., underestimation of the increase in risk. Nonetheless, a significantly higher risk was in fact detected for the main categories of interest (i.e., male sex, age 18–24 years, and psychological-physical conditions other than normal).

Extrinsic validity depends on the extent to which the estimates given by the model are biologically plausible and consistent with those obtained with more conventional methods. Unfortunately, the lack of estimates of rate of exposure by type of driver makes it impossible to compare our results with those of other studies that analyzed the same data. We compared our results with estimates obtained using conventional methods in studies conducted in other countries and estimates obtained by Cuthbert with the induced exposure method. Our findings are basically consistent with those reported by Cuthbert, who found a lower risk associated with older age and higher risks for the 17- to 22-year-old group (11Go). In comparison with drivers aged 23–30 years, the increase in risk for younger drivers yielded values quite similar to those we found when we compared the 18- to 24-year-old and 25- to 49-year-old groups. The increase in risk attributable to alcohol drinking was slightly higher among Cuthbert's subjects than among ours, probably because alcohol levels were tested in all drivers in Cuthbert's study. In both studies, the effect of drinking was lowest in the age group with the highest risk for traffic crashes. As regards the influence of sex, among the 17- to 24-year-old drivers in Cuthbert's study, the risk of traffic crashes was slightly lower in women (0.85 compared with men) (11Go); this value was slightly lower than the risk of traffic crashes among young female drivers in our study.

Our results are consistent with earlier findings based on other methods. Several reports found a higher risk in men than in women (5Go, 19Go). Massie et al. (8Go) noted that the higher risk among men was only for fatal crashes; when all crashes were considered together, the risk was higher among women. In the present study, accidents in urban zones that caused nonserious injuries were probably underrepresented; this would account for the excess risk among male drivers.

Like most other investigators (5Go, 8Go, 10Go, 17Go), we found that risk was clearly greater among young drivers (aged 18–24 years). However, the U-shaped curve typically found when risk of traffic crashes is plotted against age (4Go, 8Go, 10Go) was not apparent in our subjects, probably because we could not stratify subjects for age above 49 years. Most previous investigators found that risk increased in drivers aged 65–70 years (2Go, 5Go, 8Go), but in Spain the number of drivers (especially women) older than 70 years is very small, and this makes it difficult to estimate risks specifically for this age group.

The relation between alcohol drinking and increased risk of traffic crashes, especially fatal crashes, has been widely documented (10Go, 16Go, 20Go, 21Go). Our findings confirmed this association, although the magnitude of the increase in risk was slightly lower than that reported by other researchers (10Go, 21Go), probably because classification bias tended to underestimate the proportion of drivers who were under the influence of alcohol in our study.

We found no statistically significant associations between environmental factors and risk of traffic crashes, although the pattern of associations was similar to that reported in earlier studies: greater risk (regardless of severity) in urban areas, during twilight, and on weekends and legal holidays (8Go, 22GoGo–24Go). In general, the magnitude of the increases in risk associated with environmental factors was much lower than that of the risks estimated for any of the driver-related factors. This result supports the theoretical basis of the model.

In general, we found that the effect of any given variable on the risk of traffic crashes was reduced in a constant manner in the presence of other risk factors. For example, the increase in risk associated with male sex was attenuated in age groups with the highest risk and under psychological-physical conditions other than normal. Our results also show that the effect of driver-dependent factors was modified considerably by environmental conditions, an effect also reported by Stamatiadis and Deacon (2Go).

The increased risks associated with driver characteristics and environmental factors were estimated for all types of traffic crashes. It would clearly be valuable to stratify the estimates on the basis of type and seriousness of the crash, using a larger database that contained more information.

In conclusion, direct determinations of rates of exposure for each category of driver would probably yield more valid and precise estimates of the risk of being involved in an accident than would the induced exposure method. However, the latter approach provides estimates with an acceptable degree of validity and has the advantage of being much simpler and more economical, since all analyses are carried out using data from traffic crash registers, which are now available in most developed countries. These characteristics of the induced exposure method make it potentially applicable as a routine approach to the extraction of information from traffic databases. Many of such databases may contain information that can be considered more valid or reliable than the information we obtained from the DGT register.


    ACKNOWLEDGMENTS
 
This study was partially financed by the Fondo de Investigacion Sanitaria (grant 00/0072) from the Spanish Ministry of Health and Consumer Services.

The authors thank the Spanish Dirección General de Tráfico for providing data from the traffic crash register, Antonio Galiano for help with conversion of the register data to the BMDP format, and Karen Shashok for translating the original manuscript into English.


    NOTES
 
Correspondence to Dr. Pablo Lardelli-Claret, Departamento de Medicina Preventiva y Salud Pública, Facultad de Farmacia, Campus de Cartuja s/n, Universidad de Granada, E-18071 Granada, Spain (e-mail: lardelli{at}goliat.ugr.es).


    REFERENCES
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 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 

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Received for publication February 2, 2000. Accepted for publication August 16, 2000.





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