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First published online January 1, 2010

Modeling Injury Severity of Multiple Occupants of Vehicles: Copula-Based Multivariate Approach

Abstract

Research to date on crash injury severity has focused on the driver of the vehicle or the most severely injured occupant. Though useful, these studies have not provided injury profiles of all occupants in crash-involved vehicles. This lack of a comprehensive picture has limited the ability to devise measures that enhance the safety and reduce the severity of the injury sustained by all vehicular occupants. Moreover, such studies ignore the possible presence of correlated, unobserved factors that may simultaneously affect the injury severity levels of multiple occupants. This paper aims to fill the gap by presenting a simultaneous model of injury severity to apply to crashes that involve any number of occupants. A copula-based methodology, which could be used to estimate such complex model systems, was applied to a data set of crashes drawn from the 2007 General Estimates System in the United States. The model estimation results provide strong evidence of the presence of correlated unobserved factors that affect injury severity levels of vehicle occupants. The correlation exhibited heterogeneity across vehicle types, with a greater level of interoccupant dependency in heavy SUVs and pickup trucks. The study also sheds light on how numerous exogenous factors—including occupant, vehicle, and crash characteristics; environmental factors; and roadway attributes—affect the injury severity levels of occupants in different seat positions. The findings confirm that rear-seat passengers are less vulnerable to severe injuries than front-row passengers and point to the need to enhance vehicular design features that promote front-row occupant safety.

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References

1. Global Status Report on Road Safety. World Health Organization, Geneva, Switzerland, 2009.
2. NHTSA. 2008 Traffic Safety Annual Assessment—Highlights. Traffic Safety Facts. National Center for Statistics and Analysis, Washington, D.C., 2009.
3. O'Donnell C. J., and Connor D. H. Predicting the Severity of Motor Vehicle Accident Injuries Using Models of Ordered Multiple Choice. Accident Analysis and Prevention, Vol. 28, No. 6, 1996, pp. 739–753.
4. Khattak A. J., Kantor P., and Council F. M. Role of Adverse Weather in Key Crash Types on Limited-Access Roadways: Implications for Advanced Weather Systems. In Transportation Research Record 1621, TRB, National Research Council, Washington, D.C., 1998, pp. 10–19.
5. Ulfarsson G. F., and Mannering F. L. Differences in Male and Female Injury Severities in Sport-Utility Vehicle, Minivan, Pickup and Passenger Car Accidents. Accident Analysis and Prevention, Vol. 36, No. 2, 2004, pp. 135–147.
6. Eluru N., and Bhat C. R. A Joint Econometric Analysis of Seat Belt Use and Crash-Related Injury Severity. Accident Analysis and Prevention, Vol. 39, No. 5, 2007, pp. 1037–1049.
7. Hutchinson T. P. Statistical Modelling of Injury Severity, with Special Reference to Driver and Front Seat Passenger in Single-Vehicle Crashes. Accident Analysis and Prevention, Vol. 18, No. 2, 1986, pp. 157–167.
8. Yamamoto T., and Shankar V. N. Bivariate Ordered-Response Probit Model of Driver's and Passenger's Injury Severities in Collisions with Fixed Objects. Accident Analysis and Prevention, Vol. 36, No. 5, 2004, pp. 869–876.
9. Lennon A., Siskind V., and Haworth N. Rear Seat Safer: Seating Position, Restraint Use and Injuries in Children in Traffic Crashes in Victoria, Australia. Accident Analysis and Prevention, Vol. 40, No. 2, 2008, pp. 829–834.
10. Lund U. J. The Effect of Seating Location on the Injury of Properly Restrained Children in Child Safety Seats. Accident Analysis and Prevention, Vol. 37, No. 3, 2005, pp. 435–439.
11. Berg M. D., Cook L., Corneli H., Vernon D. D., and Dean J. M. Effect of Seat Position and Restraint Use on Injuries to Children in Motor Vehicle Crashes. Pediatrics, Vol. 105, No. 4, 2000, pp. 831–835.
12. Braver E. R., Whitfield R., and Ferguson S. A. Seating Position and Children's Risk of Dying in Motor Vehicle Crashes. Injury Prevention, Vol. 4, No. 3, 1998, pp. 181–187.
13. Evans L., and Frick M. Seating Position in Cars and Fatality Risk. American Journal of Public Health, Vol. 78, No. 11, 1988, pp. 1456–1458.
14. Smith K. M., and Cummings P. Passenger Seating Position and the Risk of Passenger Death or Injury in Traffic Crashes. Accident Analysis and Prevention, Vol. 36, No. 2, 2004, pp. 257–260.
15. Smith K. M., and Cummings P. Passenger Seating Position and the Risk of Passenger Death in Traffic Crashes: A Matched Cohort Study. Injury Prevention, Vol. 12, No. 2, 2006, pp. 83–86.
16. Wang X., and Kockelman K. M. Use of Heteroscedastic Ordered Logit Model to Study Severity of Occupant Injury: Distinguishing the Effects of Vehicle Weight and Type. In Transportation Research Record: Journal of the Transportation Research Board, No. 1908, Transportation Research Board of the National Academies, Washington, D.C., 2005, pp. 195–204.
17. Claret P. L., Jimenez-Moleon J. J., Luna-Del-Castillo J. de D., and Bueno-Cavanillas A. Individual Factors Affecting the Risk of Death for Rear-Seated Passengers in Road Crashes. Accident Analysis and Prevention, Vol. 38, No. 3, 2006, pp. 563–566.
18. Mayrose J., and Priya A. The Safest Seat: Effect of Seating Position on Occupant Mortality. Journal of Safety Research, Vol. 39, No. 4, 2008, pp. 433–436.
19. Bhat C. R. A Multi-Level Cross-Classified Model for Discrete Response Variables. Transportation Research Part B, Vol. 34, No. 7, 2000, pp. 567–582.
20. Bottai M., Salvati N., and Orsini N. Multilevel Models for Analyzing People's Daily Movement Behavior. Journal of Geographical Systems, Vol. 8, No. 1, 2006, pp. 97–108.
21. Czado C., and Prokopenko S. Modeling Transport Mode Decisions Using Hierarchical Binary Spatial Regression Models with Cluster Effects. Statistical Modeling, Vol. 8, No. 4, 2008, pp. 315–345.
22. Bhat C. R., and Eluru N. A Copula-Based Approach to Accommodate Residential Self-Selection Effects in Travel Behavior Modeling. Transportation Research Part B, Vol. 43, No. 7, 2009, pp. 749–765.
23. Trivedi P. K., and Zimmer D. M. Copula Modeling: An Introduction for Practitioners. Foundations and Trends in Econometrics, Vol. 1, No. 1, 2007, pp. 1–110.
24. Genest C., and MacKay R. J. Copules Archimediennes et Familles de Lois Bidimensionnelles Dont les Marges Sont Donnees. Canadian Journal of Statistics, Vol. 14, No. 2, 1986, pp. 145–159.
25. Sklar A. Random Variables, Joint Distribution Functions, and Copulas. Kybernetika, Vol. 9, 1973, pp. 449–460.
26. Nelsen R. B. An Introduction to Copulas, 2nd ed. Springer-Verlag, New York, 2006.
27. Clayton D. G. A Model for Association in Bivariate Life Tables and Its Application in Epidemiological Studies of Family Tendency in Chronic Disease Incidence. Biometrika, Vol. 65, No. 1, 1978, pp. 141–151.
28. Gumbel E. J. Bivariate Exponential Distributions. Journal of the American Statistical Association, Vol. 55, No. 292, 1960, pp. 698–707.
29. Frank M. J. On the Simultaneous Associativity of F(x, y) and x + y - F(x, y). Aequationes Mathematicae, Vol. 19, No. 1, 1979, pp. 194–226.
30. Joe H. Parametric Families of Multivariate Distributions with Given Marginals. Journal of Multivariate Analysis, Vol. 46, No. 2, 1993, pp. 262–282.
31. Joe H. Multivariate Models and Dependence Concepts. Chapman and Hall, London, 1997.
32. McKelvey R. D., and Zavoina W. A Statistical Model for the Analysis of Ordinal Level Dependent Variables. Journal of Mathematical Sociology, Vol. 4, 1975, pp. 103–120.
33. Quinn C. The Health-Economic Applications of Copulas: Methods in Applied Econometric Research. Health, Econometrics and Data Group Working Paper 07/22. Department of Economics, University of York, United Kingdom, 2007.
34. Paleti R., Eluru N., and Bhat C. R. Examining the Influence of Aggressive Driving Behavior on Driver Injury Severity in Traffic Crashes. Technical paper. Department of Civil, Architectural, and Environmental Engineering, University of Texas at Austin, August 2009.
35. Greene W. Econometric Analysis, 6th ed. Prentice Hall, Upper Saddle River, N.J., 2008.

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Article first published online: January 1, 2010
Issue published: January 2010

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© 2010 National Academy of Sciences.
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Authors

Affiliations

Naveen Eluru
Department of Civil, Architectural, and Environmental Engineering, University of Texas at Austin, 1 University Station C1761, Austin TX 78712-0278.
Rajesh Paleti
Department of Civil, Architectural, and Environmental Engineering, University of Texas at Austin, 1 University Station C1761, Austin TX 78712-0278.
Ram M. Pendyala
School of Sustainable Engineering and the Built Environment, Room ECG252, Arizona State University, Tempe, AZ 85287-5306.
Chandra R. Bhat
Department of Civil, Architectural, and Environmental Engineering, University of Texas at Austin, 1 University Station C1761, Austin TX 78712-0278.

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