A New Holistic Crashes Prediction Model based on Zero-Truncated Data for Intercity Four-Lane Highways Curves

Document Type : Research Paper


1 Ph.D. candidate, Department of Civil Engineering, Faculty of civil and earth resources engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Professor, Department of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran

3 Assistant Professor, Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran


This study aimed at exploring the effect of consistent design and self-explanatory the horizontal curves on crash frequency in four-lane highways using Zero-Truncated Crashes data. The present study has considered the related variables for 45 curves of four-lane intercity highways in the three-year (2018-2020). The standard Poisson distribution is a benchmark for modeling equi-dispersed count data and could not express under-dispersed Zero-Truncated data. Modeling was performed using Poisson, Negative Binomial, Zero-Truncated Poisson, Zero-Truncated Negative Binomial, and Conway-Maxwell Poisson (COM-Poisson) regression. The results revealed that the COM-Poisson regression distribution could effectively fit the model under-dispersed Zero-Truncated Crashes data. According to the results, the ratio of the curve radius to the average radius of the adjacent curves (as the alignment consistency variable), the difference between the expected and the existing superelevation (as the vehicle stability consistency variable), and the variables of the total self-explaining index and heavy vehicle percentage have significant relationships with crash frequency. As a result, increasing the self-explanatory features of curves is an efficient and prioritized policy for safety improvement on the intercity four-lane highways.


- Akaike, H.(1974). A new look at the statistical model identification. IEEE
Transactions on Automatic Control. 19(6):716–772.
- Al-Masaeid, H. R., Hamed, M., Aboul-Ela, M., & Ghannam, A. G. (1994). Consistency of horizontal alignment for different vehicle classes. Transp. Res. Rec. 1500, Transportation Research Board, Washington, D.C., 178–183.
- Al-Sahili, K., Dwaikat, M. (2019). Modeling geometric Design Consistency and Road Safety for Two-Lane  Rural Highway in the West Bank, Palestine. Arabian Journal for Science and Engineering, 44(10), 4895-4909.
- Anderson, I.B., Bauer, K.M., Harwood, D.W.,& Fritzpatrick, L.(1999). Relationship to the safety of geometric design consistency measures for rural two-lane highways.J. Transp. Res. Board 1658, 43–51.
- Bargh, J. A., & Ferguson, M. J. (2000). Beyond behaviorism: On the automaticity of higher mental processes. Psychological Bulletin, 126(6), 925–945.
- Cafiso, S., Di Graziano, A., Di Silvestro, G., La Cava, G.,& Persaud, B., 2010. Development of comprehensive accident models for two-lane rural highways using exposure,geometry, consistency, and context variables. Accid. Anal. Prev. 42, 1072–1079.
- Cafiso, S., La Cava, G., & Montella, A.(2007). Safety index for evaluation of two-lane rural highways. Transportation Research Record, 2019(1), 136-145.
- Charlton, S. G., & Starkey, N. J. (2013). Driving on familiar roads: Automaticity and inattention blindness. Transportation Research Part F: Traffic Psychology and Behaviour, 19, 121–133.
- Cohen, A.C. (1960). Estimating the parameter in a conditional Poisson distribution. Biometrics, vol. 16, no. 2, 203–211.
- Conway, R.W.,& Maxwell, W.L.A.(1962). Queuing Model with State-Dependent Service Rates. Journal of Industrial Engineering. 12, 132-136.
- Conway, R.W.,& Maxwell, W.L.A.(1962). Queuing Model with State-Dependent Service Rates. Journal of Industrial Engineering. 12, 132-136.
- Cox, D.R. and E.J. Snell.(1989). Analysis of Binary Data. Second Edition. Chapman & Hall.
- Cummings, P.(2009). Methods for estimating adjusted risk ratios, The Stata Journal. Vol. 9, No. 2, 2009, 175–196.
- De Ona, J.D., and Garach, L.,Calvo ,F., & Garcia-Munoz,T.(2013).Relationship between predicted speed reduction on horizontal curves and  safety on two-lane rural roads   in Spain. Journal of Transportation Engineering,140(3),04013015.
- Dhahir, B., & Hassan, Y. (2017). Relationship between traffic safety and speed differential on horizontal curves based on naturalistic driving studies, In Proc. Road Safety & Simulation International Conference, Paper (Vol. 58).
- Eenink, R., Reurings, M., Elvik, R., Cardoso, J., Wichert, S.,& Stefan, C., (2007).Accident prediction models and road safety impact assessment: recommendations for using these tools. Report RI-SWOV-WP2-D2-F. SWOV Institute for Road Safety Research, Leidschendam,4p.
- Fitzpatrick,K., Elefteriadou,L., Harwood., ,D.W,Collins,J.M.,McFadden.J.,Anderson,I.B.,Krammes,R.A., Irizarry,N., Parma,K.D., Bauer,K.M., &Passetti, K .(2000a). Speed Prediction for Two-Lane Rural Highways. Federal Highway Administration, Report FHWA-RD-99-171, Springfield, Virginia.
- Fitzpatrick, K., M. Wooldridge, O. Tsimoni, J. Collins, P. Green, K.Bauer, K. Parma, R. Koppa, D. Harwood, I. Anderson, R. Krammes, & B. Poggioli. (2000b)Alternative Design Consistency Rating Methods for Two-Lane Rural Highways. FHWA Report FHWA-RD-99-172. Springfield,Va.
- Global status report on road safety.(2018).World Health Organization.
-Gooch, J. P., Gayah, V. V., & Donnell, E. T. (2016).Quantifying the safety effects of horizontal curves on two-way, two-lane rural roads. Accident Analysis  and Prevention, 92, 71-81.
- Greene, W. (2008) Functional forms for the negative binomial model for count data, Economics Letters.Vol. 99, 585–590.
- Hamilton, I., Himes, S., Porter, R.J., & Donnell. (2019).Safety Evaluation of Horizontal Alignment Design Consistency on Rural Two-Lane Highways. Transportation Research Record,1-9.
- Hassan, Y., T. Sayed, & P. Tabernero. (2001). Establishing a Practical Approach for Design Consistency. Evaluation. Journal of Transportation Engineering, Vol. 127, No. 4, 295–302.
- Hills, B. L. (1980). Vision, visibility, and perception in driving. Perception, 9,183–216.
- Johnson, N. L., Kemp, A. W., & Kotz, S. (2005). Univariate discrete distributions.Wiley.
- Khan, G., Bill, A. R., Chitturi, M., & Noyce, D. A. (2012). “Horizontal curves, signs, and safety”, Transportation research record, 2279(1), 124-131.
- Krammes, R. A., Rao, K. S., & Oh, H. (1995). Highway geometric design consistency evaluation software. Transp. Res. Rec. 1500, Transportation Research Board, Washington, D.C., 19–24.
- Lamm, R., Choueiri, E.M., & Mailaender, T.(1991).Side Friction Demand Versus Side Friction Assumed for Curve Design on Two-Lane Rural Highways. Transportation Research Record, 1303: 11-21.
- Lamm, R., Psarianos, B., & Mailaender, T. (1999). Highway design and traffic safety engineering handbook, McGraw-Hill, New York.
- Liopis-Castello, D., Bella, F., Camacho-Torregrosa, F.J., & Garcia, A.(2018). New Consistency Model Based on Inertial Operating Speed Profiles for Road Safety Evaluation. Journal of Transportation Engineering, Part A: Systems, 144(4).
- Luque, R.,& Castro,M. (2018). Highway geometric  design consistency speed models and local or global assessment.Int.J.Civ.Eng. 14(6),347-355.
- Martens, M. H., & Fox, M. R. J. (2007). Do familiarity and expectations change perception? Drivers glances and responses to changes. Transportation Research Part F, 10, 476–492.
- Miller, I., & Freund, J.E.(1977) Probability and Statistics for Engineers, 2nd ed. Prentice-Hall, Englewood Cliffs, N.J.
- Ng, J. & Sayed, T. (2004). Effect of geometric design consistency on road safety. Canadian Journal of Civil Engineering, 31(2), 218-227.
- NHTSA.(2016). Traffic Safety Facts. National Highway Traffic Safety Administration, National Center for Statistics and Analysis, U.S. Department of Transportation, Washington, DC 20590.
- Nicholson, A. (1998). Superelevation, side friction, and roadway consistency. J.Transp.Engrg.,ASCE,124(5),411- 418.
- Oh , J., Lyon ,C., Washington ,SP., Persaud ,BN., & Bared, J.(2003). Validation of the FHWA crash models for rural intersections: Lessons learned. Transportation Research Record 1840,41–49.
- PIARC.(2016). Human Factors Guidelines for a safer Man-Road Interface. Technical Committee C.2 Design and Operation of Safer Road Infrastructure.
- PIARC.(2019). Road Safety Evaluation Based on Human Factors Method Technical Committee C.2 Design and Operation of Safer Road Infrastructure.
- Polus, A.(1980). The Relationship of Overall Geometric Characteristics to the Safety Level of Rural Highways. Eno Transportation Foundation, Traffic Quarterly, 34(4): 575-585.
- Saffarzadeh,M., Shabani,S., & Azarmi,A. (2007). Accident prediction model in two-way two-lane highway curves, Bulletin of Transportation (Pajouheshnameh Haml va Naghl,IR), 4(3),213-221.
- Sawalha, Z. & Sayed, T.(2006). Traffic accident modeling: some statistical issues. Can. J. Civ. Eng. 33(9), 1115–1123
- Schneider, W. H. , Savolainen, P. T. & Moore, D. N.(2010).Effects of horizontal curvature on single-vehicle motorcycle crashes along rural two-lane highways. Transportation Research Record: Journal of the Transportation Research Board , vol. 2194 , no. 1, 91-98.
- Schneider, W. H. , Zimmerman, K. , Van Boxel, D.  & Vavilikolanu, S.(2009). Bayesian analysis of the effect of horizontal curvature on truck crashes using training and validation data sets. Transportation Research Record: Journal of the Transportation Research Board , vol. 2096, no. 1, 41-46.
- Sellers, K.F.,& Shmueli,G.(2010). A Flexible Regression Model for Count Data.The Annals of Applied Statistics. 4, Issue 2, 943-961.
- Sellers,K.F.,& Shmueli, G.(2013). Data Dispersion: Now you see it...Now you don't, Communication in Statistics: Theory and Methods. 42, Issue 17, 3134-47.
- Senders, J. W. The Estimation of Operator Workload in Complex Systems.In Systems Psychology, McGraw-Hill, New York.(1970). 207–216.
- Shmueli,G., Minka, T.P., Kadane, J.B.,  Borle, S.,& Boatwright, P.(2005). A Useful Distribution for Fitting Discrete Data: Revival of the Conway–Maxwell–Poisson Distribution, Journal of The Royal Statistical Society. Series C (Applied Statistics). 54, Issue 1, 127-142.
- Sivak, M. (1996). The information that drivers use: Is it indeed 90% visual? Perception, 25, 1081–1089.
- Stadtler, T.(1998). Lexikon der Psychologie. Alkfred Kroner Verlag. Stuttgart.
- Taylor,j.R.,(1982).An introduction to error analysis university science books.
- Theeuwes, J., & Godthelp, H.(1995). Self-Explaining Roads. Safety Science, Vol. 19, No. 2–3, 217–225.
- Treat, J. R., Tumbas, N. S., McDonald, S. T., Shinar, D., Hume, R. D., Mayer, R. E.,Stanisfer, R. L., & Castellan, N. J.(1977). Tri-level study of the causes of traffic accidents. Report No. DOT-HS-034-3-535-77(TAC).
- Wimmer, G.& Altmann, G. (1999). Thesaurus of univariate discrete probability distributions. Stamm.