American Journal of Epidemiology Advance Access originally published online on November 23, 2005
American Journal of Epidemiology 2006 163(2):188-195; doi:10.1093/aje/kwj015
Practice of Epidemiology |
Comparison between Two Quasi-Induced Exposure Methods for Studying Risk Factors for Road Crashes
1 Department of Preventive Medicine and Public Health, Faculty of Pharmacy, University of Granada, Granada, Spain
2 Department of Preventive Medicine and Public Health, Faculty of Medicine, University of Granada, Granada, Spain
3 Department of Statistics, Faculty of Medicine, University of Granada, Granada, Spain
Correspondence to Pablo Lardelli-Claret, Departamento de Medicina Preventiva y Salud Pública, Facultad de Farmacia, Campus de Cartuja s/n, 18071 Granada, Spain (e-mail: lardelli{at}ugr.es).
Received for publication February 8, 2005. Accepted for publication August 4, 2005.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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This study was designed to compare estimates from two quasi-induced exposure methods of the effects of driver- and vehicle-related conditions on the risk of causing a road crash for drivers of vehicles with four or more wheels. From the Spanish register of road crashes with victims, the authors selected, for 1993–2002, all 755,329 drivers of
4-wheeled vehicles involved in single-vehicle crashes or in two-vehicle collisions in which only one of the drivers was considered responsible. Multinomial and logistic regression models were used to obtain the odds ratio for each driver- and vehicle-related variable. Construction of these models was based on the assumptions of classical quasi-induced exposure methods and on the method (a paired-by-collision analysis of responsible and nonresponsible drivers) proposed by Perneger and Smith (Am J Epidemiol 1991;134:1138–45). The main driver-dependent conditions for any type of crash were psychophysical circumstances (alcohol use and sleepiness). The effect of most driver- and vehicle-related characteristics was higher for single-vehicle crashes than for two-vehicle collisions. Furthermore, both classical and paired-by-collision analyses yielded similar estimates and can be considered equally useful alternatives for assessing the effect of driver and vehicle characteristics on the risk of causing a collision between two vehicles.
accidents, traffic; automobile driving; epidemiologic methods; risk factors; vehicles
Abbreviations: OR, odds ratio; RAIR, relative accident involvement ratio
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Since the publication of Thorpe's work (1
), quasi-induced exposure methods have been used regularly to study factors associated with the risk of causing road crashes (2–5). The aim of these methods is to estimate the increase in risk of being involved in a road crash associated with different driver- or vehicle-related characteristics, when no direct measurements of the intensity of exposure are available for these characteristics. Reviews of the development of induced and quasi-induced exposure methods have been published by Cuthbert (6), Rice et al. (7), and Stamatiadis and Deacon (8). Briefly, the quasi-induced exposure method, as described by the latter authors, is based on the following principles (8): First, only two-vehicle collisions in which only one of the two drivers involved was considered responsible for the crash ("clean collisions") are selected for the analysis; second, nonresponsible drivers involved in collisions may be considered an approximately random sample of the road-user population; and third, the former assumption means that estimating the risk of involvement in a collision for a certain type of driver or vehicle (i) requires simply comparing the frequency of this particular driver's or vehicle's appearing in the population of responsible drivers with the frequency of the same driver's or vehicle's appearing in the sample of nonresponsible drivers. This is known as the relative accident involvement ratio i (RAIRi). For collisions between two vehicles (RAIRi/m), the equation used to estimate risk is
 | (1) |
If the intensity of exposure to the risk of involvement in a crash is the same for single-vehicle crashes and crashes involving two vehicles, the relative propensity to cause a single-vehicle crash can also be estimated for type i drivers or vehicles (RAIRi/s) by comparing the frequency of appearance of a given driver in the population of drivers involved in single-vehicle crashes with the frequency of appearance of the same type of driver in the sample of nonresponsible drivers:
 | (2) |
If we define a reference driver (or vehicle) k, the quotient of RAIRi divided by RAIRk expresses the factor by which the risk for driver i is higher than the risk for driver k. Because the variable that provides information regarding responsibility for any given type of driver is dichotomous ("responsible" vs. "nonresponsible"), this quotient can be considered the odds ratio (OR) of being responsible for type i drivers compared with type k drivers. For example, for multiple-vehicle crashes,
 | (3) |
The OR for single-vehicle crashes (ORi/s) is calculated in a similar manner:
 | (4) |
Transforming the RAIRi values into ORi values facilitates the use of unconditional multivariate logistic regression models to obtain ORi estimates adjusted for the confounding effect of all other variables used as independent terms in the model. This is particularly important if we wish to control for the confounding effect of environmental circumstances on the risk associated with driver characteristics, since the intensity of exposure for each type of driver is known to vary markedly with the driving environment (8, 9).
The quasi-induced exposure method described above has two important methodological limitations: 1) the potential lack of validity for identifying responsibility for each driver involved in a collision and 2) the possibility that nonresponsible drivers involved in clean collisions may not provide a good estimate of the distribution of drivers on the road, and hence of the intensity of exposure to the risk of causing a crash (8).
In 1991, Perneger and Smith (10) published the results of a matched case-control study of clean collisions, where cases were defined as the drivers responsible for the collisions. For each responsible driver, the nonresponsible driver involved in the same collision was used as the matched control. Although the original study did not clarify this point explicitly, this approach is simply a variant of the quasi-induced exposure method, with the advantage that the matched case-control design makes it possible to control simultaneously for practically all environment-dependent confounding factors. In this model, given that responsible and nonresponsible drivers are matched, ORi/m can be calculated with conditional logistic regression analyses, which take into account the "natural" matching of the two groups of drivers.
To our knowledge, no studies have compared the results of these two methods using data from a single source. Such a comparison is valuable, because it can help to validate some theoretical assumptions of quasi-induced exposure methods and can provide empirical arguments in favor of one approach or the other, although both share the same limitation: the lack of a direct measure of the intensity of exposure for each type of driver. The aim of the present study was to compare estimates of the effects of driver- and vehicle-related conditions on the risk of causing a crash for vehicles with four or more wheels (4-wheeled vehicles). We compared the original quasi-induced exposure method as described by Stamatiadis and Deacon (8) with the modified approach described by Perneger and Smith (10) to analyze data on road crashes obtained from a single database.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Study design and variables
The source of information for this study was the Spanish register of road crashes with victims, which is maintained by the Spanish Dirección General de Tráfico (Madrid, Spain). The characteristics of the register have been described elsewhere (11
). Two variables recorded by Spanish police at the scene of a crash and included in the Dirección General de Tráfico database are 1) the specific infraction committed by each driver involved in the crash (classified in 20 categories) and 2) the commission of speed-related infractions (classified in five categories) (see appendix table 1). The rationale of the study was that in two-vehicle collisions in which only one driver committed an infraction, this driver can be considered to have caused the collision and is thus defined as the responsible driver. The other (noninfractor) driver involved in the collision is assumed to have been passively involved. Therefore, the group of noninfractor drivers involved in these collisions can be considered a representative sample of all drivers on the road at the time of the crash (12, p. 262). The biases that may have been introduced into the estimates by our use of commission of an infraction by the driver as a surrogate indicator of responsibility were discussed extensively in previous articles (11–13).
On the basis of the foregoing criteria, we studied 755,329 drivers of 4-wheeled vehicles who were involved in road crashes with victims that were recorded in Spain between 1993 and 2002. All crashes satisfied the following requirements: No pedestrians were involved; no more than two vehicles were involved; at least one 4-wheeled vehicle was involved; and, for collisions between two vehicles, only one of the two drivers committed an infraction on the list of possible traffic infractions (see appendix table 1).
For each driver of a 4-wheeled vehicle, we obtained information from the register on the following variables.
Driver characteristics.
Driver characteristics studied included age (18–24, 25–34, 35–44, 45–54, 55–64, 65–74, or >74 years or unknown), sex (male, female, unknown), nation of origin (Spain, Portugal, France, Morocco, Germany, Great Britain, Italy, other, unknown), psychophysical circumstances surrounding the crash (none, driving under the influence of alcohol without a breath test, driving under the influence of alcohol as documented by a positive breath test, sudden illness, sleepiness/drowsiness, other, unknown), years in possession of a driver's license (0–1, 2–3, 4–5, 6–7, 8–9, or >9 years or unknown), administrative infractions (none, driving without a license, driving with an expired license, driving a vehicle that had not passed inspection, other, unknown), type of driver (private, professional, other, unknown), use of safety belts (no, yes, unknown), and hours of driving without a break prior to the crash (<1, 1–3, >3–5, or >5 or unknown).
Vehicle characteristics.
Vehicle characteristics considered included the type of vehicle (passenger car, ambulance, tractor or machinery, van, truck weighing 
3,500 kg, truck weighing >3,500 kg, articulated vehicle, bus), the number of years since vehicle registration (<5, 5–9, 10–14, >14, unknown), and mechanical defects existing prior to the crash (none, worn tires, tire blowout, brakes in poor condition, other defects, unknown).
Type of crash.
Crashes were divided into two types: single-vehicle crashes and collisions between two vehicles.
Environmental circumstances.
Environmental circumstances comprised year, month, day of the week, type of day (working day, day before a holiday, holiday, day after a holiday), time of day, zone (location of crash) (open road, urban road, through road), type of road (conventional highway; interstate or expressway; secondary, service, or connecting road; other), visibility (good, limited), condition of the road surface (normal, altered), meteorologic conditions (good, poor), other dangerous circumstances (absent, present), and traffic density (smooth, dense, traffic jam).
Statistical analysis
Table 1 shows the distribution of drivers according to type of crash, responsibility, and analyses performed. For the "classical" quasi-induced exposure models (8), we defined the reference group as consisting of 281,560 drivers of 4-wheeled vehicles involved in clean collisions between two vehicles who had not committed any infraction (other than an administrative infraction). The characteristics of these drivers and their vehicles were compared with those of two other groups of drivers: 1) those 302,452 drivers of 4-wheeled vehicles involved in a clean collision between two vehicles who had committed an infraction other than an administrative infraction and 2) those 171,317 drivers involved in single-vehicle crashes. These two groups of drivers were considered responsible for the crashes they were involved in. A multinomial logistic regression model was used for these comparisons. In this model, the dependent variable was the type of driver, with three categories: not responsible (the reference category), responsible for single-vehicle crashes, and responsible for collisions between two vehicles. For each category i of each variable included in the model, we estimated two separate ORs (and corresponding 95 percent confidence intervals), one for each type of crash (14). The significance of the differences between the two ORs was determined with two-sided chi-squared tests. In the first step, we constructed a model that included only driver and vehicle characteristics. In the second step, we added variables for the environmental circumstances surrounding the crash.
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In the restricted (paired-by-collision) analysis for collisions between two
4-wheeled vehicles (10), we studied only the 200,589 clean collisions (collisions in which only one of the drivers committed a traffic infraction) involving two 4-wheeled vehicles; single-vehicle crashes and collisions between a 4-wheeled vehicle and a two-wheeled vehicle were excluded. Conditional logistic regression analysis was used to compare the characteristics of each of the 200,589 infractor drivers with the characteristics of their corresponding control drivers (the noninfractor driver involved in the same collision). Because environmental factors were the same for both drivers involved in the collision, the paired analysis made it possible to control fully for confounding biases arising from environmental circumstances. To quantify the degree to which the paired-by-collision analysis removed this source of bias, we subjected the sample of drivers to two complementary analyses. First, we carried out unconditional logistic regression analysis from which we excluded environmental characteristics. This removed the control for the confounding influence of environmental circumstances. Then we conducted unconditional logistic regression analysis in which we included in the model all variables for environmental circumstances. This compensated in part for the loss of control for environmental circumstances resulting from the loss of the "natural" matching.
These three models allowed us to again obtain, for each category i of each variable included in the model, its corresponding OR and 95 percent confidence interval (15).
All analyses were done with the Stata (version 8.0) statistical software package (16).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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Table 2 presents the results of "classical" quasi-induced exposure analysis for a selection of driver- and vehicle-related variables, performed in two multinomial logistic regression analyses: one that excluded environmental variables from the model and one that included such variables. (Results from the complete set of models are presented in Web table 1 on the Journal's website (www.aje.oxfordjournals.org).) The results obtained with the two analyses were similar in broad terms; that is, the inclusion of environmental factors in the multivariate models did not greatly change the OR estimates. This was especially true for two-vehicle collisions, for which the two estimates were almost exactly the same. For single-vehicle crashes, some differences were found between unadjusted and adjusted OR estimates. The slightly protective effect of female sex observed in the unadjusted analysis (OR = 0.86) disappeared after adjustment (OR = 0.99), and the adjusted ORs for all psychophysical circumstances (with the exception of sudden illness) were lower than their corresponding unadjusted estimates. Regarding the type of vehicle, the protective association with the risk of causing a single-vehicle crash was stronger in the adjusted analysis than in the unadjusted analysis for tractors/machinery, trucks, and articulated vehicles. The risk increased appreciably for buses in the adjusted analysis (OR = 1.68) but not in the unadjusted one (OR = 1.10).
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The results shown in table 2 allowed us to compare the magnitudes of the ORs for single-vehicle crashes and two-vehicle collisions in the unadjusted and adjusted multinomial models. Although the patterns of association were similar for both types of crashes, differences in the magnitudes of some ORs were clear. In the adjusted model, the increases in risk of causing a crash related to the age group 18–24 years, all psychophysical circumstances (except driving under the influence of alcohol as documented by a positive breath test), and number of hours of driving without a break were higher for single crashes than for two-vehicle collisions. In contrast, higher ages (>55 years) were more strongly associated with the risk of causing two-vehicle collisions than with the risk of single crashes. The protective effect of number of years in possession of a driver's license was stronger for single crashes than for two-vehicle collisions. Regarding the type of vehicle, a lower risk of causing a crash was found for tractors/machinery, trucks, and articulated vehicles, although this association was again stronger for single crashes than for two-vehicle collisions. Ambulances showed an increased risk for two-vehicle collisions (adjusted OR = 1.73) but not for single crashes (adjusted OR = 0.99). For buses, we found an increase in risk for single crashes (adjusted OR = 1.68) but the opposite effect for two-vehicle collisions (adjusted OR = 0.36).
Table 3 shows, for the same selected group of variables as described in table 2 (results from the complete set of models are presented in Web table 2 (www.aje.oxfordjournals.org)), results obtained from the three logistic regression models for clean collisions between two 4-wheeled vehicles (one conditional logistic regression model for the paired analysis and two unconditional logistic regression models (unadjusted and adjusted for environmental conditions) for the unpaired analysis). The ORs obtained with the latter two models were almost the same. In other words, as in the classical analysis, inclusion of environmental factors in the model did not modify the OR estimates. The ORs obtained with the paired analysis were also similar to those obtained with the unpaired models. The OR estimates were higher with the paired analysis than with the unpaired analyses only for psychophysical conditions.
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When we compared the results from the classical analysis for two-vehicle collisions (adjusted for environmental variables) (table 2) with those obtained from the paired analysis of collisions between two
4-wheeled vehicles (table 3), the two series of OR estimates were similar for almost all driver- and vehicle-related factors. The only remarkable differences were for psychophysical conditions: ORs for these variables in the paired analysis were substantially higher (by more than 10 percent) than corresponding ORs in the classical analysis. |
DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONReferences |
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The main conclusion that can be drawn from our findings is that both classical quasi-induced exposure methods applied to collisions between two vehicles and the paired-by-collision method proposed by Perneger and Smith (10
) yield similar results, and therefore can be considered equally useful alternatives for assessing the effects of driver- and vehicle-related variables on the risk of causing a collision. Because our aim in this study was to compare results obtained with two quasi-induced exposure strategies, we will not discuss here the patterns of association that the two approaches yielded for the driver- and vehicle-related variables. In most cases, they were consistent with earlier studies (10, 17–20), and a fuller discussion of the associations can be found in our previous publications (11–13). Theoretically, the paired analysis offers better control than the classical analysis of the confounding bias introduced by the physical environment, since the former is able to control both measured and unmeasured environment-related factors. However, our results suggest that the magnitude of this bias is quite small for the risk of causing collisions between two vehicles. Only large OR estimates such as those obtained for psychophysical conditions changed appreciably depending on the type of analysis (classical or paired). Nonetheless, this minor advantage of the paired analysis is counterbalanced by the fact that the classical method makes it possible to estimate the effect of risk factors for causing single crashes, not only collisions between vehicles.
The results obtained with the classical analysis show that the pattern of causality for single-vehicle crashes is different from that for two-vehicle crashes. In general, driver-dependent factors had a greater influence on the risk of causing a single-vehicle crash than on the risk of causing a two-vehicle collision. Furthermore, the effect of older age was more pronounced for the risk of causing two-vehicle collisions, whereas younger age was related to a higher risk of causing single crashes. This differential effect of age on single- and multiple-vehicle crashes was described in several earlier studies (8, 21–24). However, the estimates obtained with the classical quasi-induced exposure method for single-vehicle crashes should be interpreted with caution, for two reasons: First, the distributions of drivers and vehicles responsible for causing single-vehicle crashes and multiple-vehicle crashes differed, so we might suspect differences in the distributions of drivers and vehicles exposed to the risk of causing either type of crash. Accordingly, the use of the same reference population (nonresponsible drivers in clean collisions) to estimate ORs for both types of crashes might have biased the estimates for single-vehicle crashes. Second, unlike the situation for two-vehicle collisions, adjustment for environmental factors modified some of the OR estimates for the risk of causing single crashes in comparison with the corresponding figures in the unadjusted analysis. Because the environmental factors included in the multivariate models may not have accounted for all of the confounding influence of physical environment on the risk of causing single crashes, the OR estimates for single crashes may have been affected by some degree of residual confounding.
From the above discussion, it seems clear that estimates of risk obtained with quasi-induced exposure methods applied to the analysis of collisions between vehicles should not be generalized to other types of crashes.
In this study, we could not truly assess the validity of each type of quasi-induced exposure method, because both were quasi-induced exposure methods. In other words, no gold-standard method was used for comparison that could have provided a direct, unbiased measure of risk exposure. What our analysis did provide is a comparison of the two methods that may help other researchers choose the most appropriate approach for their own data. Nevertheless, at present, there is no perfect method for obtaining an unbiased estimate of the risk-exposure rate for every type of driver in the general population of road users in every type of driving environment (25, 26).
Like other quasi-induced exposure methods, the present analysis had the advantages and disadvantages that characterize all such studies and that have been discussed in detail elsewhere (8, 11, 12, 25). An additional problem which should be taken into account in the present study is the treatment of missing values. When we repeated the analyses after excluding drivers with missing values, the sample size was greatly reduced (from 755,329 to 275,825 in the multinomial model), but the resulting OR estimates did not change appreciably, although their confidence intervals widened. Therefore, we decided to include missing values for each independent variable as a separate category, assuming that the magnitude of the resulting bias, if any, would not be so large as to distort the patterns of association.
In conclusion, our results suggest that the effects of driver- or vehicle-related factors on the risk of causing a road crash differ between single-vehicle crashes and two-vehicle collisions. Both classical and paired-by-collision quasi-induced exposure methods can be considered equally useful alternatives for assessing the effect of driver- and vehicle-related variables on the risk of causing a two-vehicle collision.
APPENDIX TABLE 1. Traffic infractions recorded by the Spanish Dirección General de Tráfico
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ACKNOWLEDGMENTS |
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This study was financed by the Fondo de Investigaciones Sanitarias (project FIS 02/0707) and the Fondo Europeo de Desarrollo Regional (European Union).
The authors thank K. Shashok for translating the original manuscript into English and the Dirección General de Tráfico of Spain for allowing access to their database.
Conflict of interest: none declared.
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