A space–time multivariate Bayesian model to analyse road traffic accidents by severity

Journal of the Royal Statistical Society. Series A: Statistics in Society

Volumn 180, Issue 1, 2017, Pages 119-139

  Boulieri, Areti ^a   Liverani, Silvia ^a,b,c   de Hoogh, Kees ^a,d   Blangiardo, Marta ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b BRUNEL UNIVERSITY   (United Kingdom)

^c MRC BIOSTATISTICS UNIT   (United Kingdom)

^d SWISS TROPICAL AND PUBLIC HEALTH INSTITUTE   (Switzerland)

Author keywords

Bayesian hierarchical models; Multivariate modelling; Probability maps; Road traffic accidents; Space time correlation

Indexed keywords

EID: 84956620253     PISSN: 09641998     EISSN: 1467985X     Source Type: Journal    
DOI: 10.1111/rssa.12178     Document Type: Article

References (74)

1. Ackaah, W. and Salifu, M. (2011) Crash prediction model for two-lane rural highways in the Ashanti region of Ghana. IATSS Res., 35, 34–40.
2. Aguero-Valverde, J. (2011) Direct spatial correlation in crash frequency models. 3rd Int. Conf. Road Safety and Simulation, Indianapolis.
3. Aguero-Valverde, J. and Jovanis, P. (2006) Spatial analysis of fatal and injury crashes in Pennsylvania. Accidnt Anal. Prevn, 38, 618–625.
4. Aguero-Valverde, J. and Jovanis, P. P. (2007) Identifying road segments with high risk of weather-related crashes using full Bayesian hierarchical models. 86th A. Meet. Transportation Research Board, Washington DC.
5. Aguero-Valverde, J. and Jovanis, P. (2009) Bayesian multivariate Poisson lognormal models for crash severity modeling and site ranking. J. Transportn Res. Bd, 2136, 82–91.
6. Al-Osh, M. A. and Alzaid, A. A. (1987) First-order integer-valued autoregressive (INAR(1)) process. J. Time Ser. Anal., 8, 261–275.
7. Beelen, R., Hoek, G., Vienneau, D., Eeftens, M., Dimakopoulou, K., Pedeli, X., Tsay, M.-Y., Künzli, N., Schikowski, T., Marcon, A., Eriksen, K. T., Raaschou-Nielsen, O., Stephanou, E., Patelarou, E., Lanki, T., Yli-Tuomi, T., Declercq, C., Falq, G., Stempfelet, M., Birk, M., Cyrys, J., von Klot, S., Nádor, G., Varr, M. J., Dédelé, A., Grauleviien, R., Mölter, A., Lindley, S., Madsen, C., Cesaroni, G., Ranzi, A., Badaloni, C., Hoffmann, B., Nonnemacher, M., Krämer, U., Kuhlbusch, T., Cirach, M., de Nazelle, A., Nieuwenhuijsen, M., Bellander, T., Korek, M., Olsson, D., Strömgren, M., Dons, E., Jerrett, M., Fischer, P., Wang, M., Brunekreef, B. and de Hoogh, K. (2013) Development of NO2 and NOx land use regression models for estimating air pollution exposure in 36 study areas in Europe—the ESCAPE project. Atmosph. Environ., 72, 10–23.
8. Bernardinelli, L., Clayton, D., Pascutto, C., Montomoli, C., Ghislandi, M. and Songini, M. (1995) Bayesian analysis of space-time variation in disease risk. Statist. Med., 14, 2433–2443.
9. Besag, J. (1974) Spatial interaction and the statistical analysis of lattice systems (with discussion). J. R. Statist. Soc. B, 36, 192–236.
10. Besag, J., York, J. and Mollié, A. (1991) Bayesian image restoration, with two applications in spatial statistics. Ann. Inst. Statist. Math., 43, 1–20.
11. Best, N., Richardson, S. and Thomson, A. (2005) A comparison of Bayesian spatial models for disease mapping. Statist. Meth. Med. Res., 14, 35–59.
12. Bijleveld, F. D. (2005) The covariance between the number of accidents and the number of victims in multivariate analysis of accident related outcomes. Accidnt Anal. Prevn, 37, 591–600.
13. Bijleveld, F., Commandeur, J., Koopman, S. J. and van Montfort, K. (2010) Multivariate non-linear time series modelling of exposure and risk in road safety research. Appl. Statist., 59, 145–161.
14. Box, G. E. and Jenkins, G. M. (1976) Time Series Analysis: Forecasting and Control, revised edn. San Francisco: Holden-Day.
15. Brijs, T., Karlis, D., Van den Bossche, F. and Wets, G. (2007) A Bayesian model for ranking hazardous road sites. J. R. Statist. Soc. A, 170, 1001–1017.
16. Christiansen, C., Morris, C. and Pendleton, O. (1992) A hierarchical Poisson model with beta adjustments for traffic accident analysis. Technical Report 103. Center for Statistical Sciences, University of Texas at Austin, Austin.
17. Clayton, D. and Bernardinelli, L. (1992) Bayesian methods for mapping disease risk. In Geographical and Environmental Epidemiology: Methods for Small Area Studies (eds P. Elliott, J. Cuzick, D. English and R. Stern). Oxford: Oxford University Press.
18. Department for Transport (2010) Road Accident Statistics Branch, road accident data, 2009. Technical Report. UK Data Archive, Colchester.
19. Durbin, J. and Koopman, S. J. (2012) Time Series Analysis by State Space Methods. Oxford: Oxford University Press.
20. Eeftens, M., Tsai, M.-Y., Ampe, C., Anwander, B., Beelen, R., Bellander, T., Cesaroni, G., Cirach, M., Cyrys, J., de Hoogh, K., Nazelle, A. D., de Vocht, F., Declercq, C., Dédelé, A., Eriksen, K., Galassi, C., Gražulevičiené, R., Grivas, G., Heinrich, J., Hoffmann, B., Iakovides, M., Ineichen, A., Katsouyanni, K., Korek, M., Krämer, U., Kuhlbusch, T., Lanki, T., Madsen, C., Meliefste, K., Mölter, A., Mosler, G., Nieuwenhuijsen, M., Oldenwening, M., Pennanen, A., Probst-Hensch, N., Quass, U., Raaschou-Nielsen, O., Ranzi, A., Stephanou, E., Sugiri, D., Udvardy, O., Vaskövi, E., Weinmayr, G., Brunekreef, B. and Hoek, G. (2012) Spatial variation of PM2.5, PM10, PM2.5 absorbance and PMcoarse concentrations between and within 20 European study areas and the relationship with NO2—results of the ESCAPE project. Atmosph. Environ., 62, 303–317.
21. Eksler, V.,Lassarre, S. and Thomas, I.(2008) Belgian regions: Federated or divided in road fatality risk evolution? (Available from http://www.ekf.vsb.cz/export/sites/ekf/projekty/cs/weby/esf0116/databazeprispevku/clanky__ERSA__2008/139.pdf.)
22. Fahrmeir, L. and Lang, S. (2001) Bayesian inference for generalized additive mixed models based on Markov random field priors. Appl. Statist., 50, 201–220.
23. Fridstrom, L., Ifver, J., Ingebrigtsen, S., Kulmala, R. and Thomsen, L. K. (1995) Measuring the contribution of randomness, exposure, weather, and daylight to the variation in road accident counts. Accidnt Anal. Prevn, 27, 1–20.
24. Gaudry, G., Long, R. and Qian, T. (1993) A martingale proof of L2 boundedness of Clifford-valued singular integrals. Ann. Mat. Pura Appl., 165, 369–394.
25. Gelman, A. (2006) Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Baysn Anal., 1, 515–534.
26. Gelman, A., Carlin, J. B., Stern, H. S. and Rubin, D. B. (2003) Bayesian Data Analysis. Boca Raton: Chapman and Hall–CRC.
27. Ghosh, M., Natarajan, K., Stroud, T. W. F. and Carlin, B. P. (1998) Generalized linear models for small-area estimation. J. Am. Statist. Ass., 93, 273–282.
28. Ghosh, M. and Rao, J. N. K. (1994) Small area estimation: an appraisal. Statist. Sci., 9, 55–76.
29. Goh, B. H. (2005) The dynamic effects of the Asian financial crisis on construction demand and tender price levels in Singapore. Build. Environ., 40, 267–276.
30. Graham, D. J. and Glaister, S. (2003) Spatial variation in road pedestrian casualties: the role of urban scale, density and land-use mix. Urb. Stud., 40, 1591–1607.
31. de Hoogh, K., Wang, M., Adam, M., Badaloni, C., Beelen, R., Birk, M., Cesaroni, G., Cirach, M., Declercq, C., Dédelé, A., Dons, E., de Nazelle, A., Eeftens, M., Eriksen, K., Eriksson, C., Fischer, P., Grauleviien, R., Gryparis, A., Hoffmann, B., Jerrett, M., Katsouyanni, K., Iakovides, M., Lanki, T., Lindley, S., Madsen, C., Mölter, A., Mosler, G., Ndor, G., Nieuwenhuijsen, M., Pershagen, G., Peters, A., Phuleria, H., Probst-Hensch, N., Raaschou-Nielsen, O., Quass, U., Ranzi, A., Stephanou, E., Sugiri, D., Schwarze, P., Tsai, M.-Y., Yli-Tuomi, T., Varr, M. J., Vienneau, D., Weinmayr, G., Brunekreef, B. and Hoek, G. (2013) Development of land use regression models for particle composition in twenty study areas in Europe. Environ. Sci. Technol., 47, 5778–5786.
32. Houston, D. J. and Richardson, L. E. (2002) Traffic safety and the switch to a primary seat belt law: the California experience. Accidnt Anal. Prevn, 34, 743–751.
33. Jones, A. P., Haynes, R., Kennedy, V., Harvey, I. M., Jewell, T. and Lea, D. (2008) Geographical variations in mortality and morbidity from road traffic accidents in England and Wales. Hlth Place, 14, 519–535.
34. Jovanis, P. P. and Chang, H.-L. (1986) Modeling the relationship of accidents to miles traveled. J. Transportn Res. Bd, 1068, 42–51.
35. Kass, R. E. and Natarajan, R. (2006) A default conjugate prior for variance components in generalized linear mixed models (comment on article by Browne and Draper). Baysn Anal., 3, 535–542.
36. Kelsall, J. and Wakefield, J. (1999) Discussion of Bayesian models for spatially correlated disease and exposure data, by Best et al. Baysn Statist., 6, 151.
37. Kim, K. and Yamashita, E. (2002) Motor vehicle crashes and land use: empirical analysis from Hawaii. J. Transportn Res. Bd, 1784, 73–79.
38. Knorr-Held, L. (2000) Bayesian modelling of inseparable space-time variation in disease risk. Statist. Med., 19, 2555–2567.
39. Knorr-Held, L. and Besag, J. (1998) Modelling risk from a disease in time and space. Statist. Med., 17, 2045–2060.
40. Li, G., Best, N., Hansell, A. L., Ahmed, I. and Richardson, S. (2012) BaySTDetect: detecting unusual temporal patterns in small area data via Bayesian model choice. Biostatistics, 13, 695–710.
41. Lunn, D., Jackson, C., Best, N., Thomas, A. and Spiegelhalter, D. (2012) The BUGS Book: a Practical Introduction to Bayesian Analysis. Boca Raton: Chapman and Hall–CRC.
42. Ma, J. and Kockelman, K. (2006) Bayesian multivariate Poisson regression for models of injury count, by severity. J. Transportn Res. Bd, 1950, 24–34.
43. Ma, J., Kockelman, K. M. and Damien, P. (2008) A multivariate Poisson-lognormal regression model for prediction of crash counts by severity, using Bayesian methods. Accid. Anal. Prevn, 40, 964–975.
44. MacNab, Y. C. (2004) Bayesian spatial and ecological models for small-area accident and injury analysis. Accid. Anal. Prevn, 36, 1019–1028.
45. MacNab, Y. C. and Dean, C. B. (2001) Autoregressive spatial smoothing and temporal spline smoothing for mapping rates. Biometrics, 57, 949–956.
46. MacNab, Y. C. and Dean, C. B. (2002) Spatio-temporal modelling of rates for the construction of disease maps. Statist. Med., 21, 347–358.
47. Maiti, T. (1998) Hierarchical Bayes estimation of mortality rates for disease mapping. J. Statist. Planng Inf., 69, 339–348.
48. Mardia, K. V. (1988) Multi-dimensional multivariate Gaussian Markov random fields with application to image processing. J. Multiv. Anal., 24, 265–284.
49. McKenzie, E. (1985) Some simple models for discrete variable time series. Wat. Resour. Bull., 21, 645–650.
50. Miaou, S. P. (1994) The relationship between truck accidents and geometric design of road sections: Poisson versus Negative Binomial regressions. Accidnt Anal. Prevn, 26, 471–482.
51. Miaou, S. P. and Lum, H. (1993) Modeling vehicle accidents and highway geometric design relationships. Accidnt Anal. Prevn, 25, 689–709.
52. Miaou, S. P. and Song, J. J. (2005) Bayesian ranking of sites for engineering safety improvements: decision parameter, treatability concept, statistical criterion, and spatial dependence. Accidnt Anal. Prevn, 37, 699–720.
53. Miaou, S. P., Song, J. J. and Mallick, B. K. (2003) Roadway traffic crash mapping: a space-time modeling approach. J. Transportn Statist., 6, no. 1.
54. Miranda-Moreno, L. F., Fu, L., Saccomanno, F. F. and Labbe, A. (2005) Alternative risk models for ranking locations for safety improvement. J. Transportn Res. Bd, 1908, 1–8.
55. Noland, R. B. and Quddus, M. A. (2004) A spatially disaggregate analysis of road casualties in England. Accidnt Anal. Prevn, 36, 973–984.
56. Park, E. S. and Lord, D. (2007) Multivariate Poisson lognormal models for jointly modeling crash frequency by severity. J. Transportn Res. Bd, 2019, 1–6.
57. Qin, X., Ivan, J. N. and Ravishanker, N. (2004) Selecting exposure measures in crash rate prediction for two-lane highway segments. Accidnt Anal. Prevn, 36, 183–191.
58. Quddus, M. A. (2008a) Modelling area-wide count outcomes with spatial correlation and heterogeneity: an analysis of London crash data. Accidnt Anal. Prevn, 40, 1486–1497.
59. Quddus, M. A. (2008b) Time series count data models: an empirical application to traffic accidents. Accid. Anal. Prevn, 40, 1732–1741.
60. Richardson, S., Abellan, J. J. and Best, N. (2006) Bayesian spatio-temporal analysis of joint patterns of male and female lung cancer risks in Yorkshire (UK). Statist. Meth. Med. Res., 15, 385–407.
61. Richardson, S., Thomson, A., Best, N. and Elliott, P. (2004) Interpreting posterior relative risk estimates in disease-mapping studies. Environ. Hlth Perspect., 112, 1016–1025.
62. Schlüter, P. J., Deely, J. J. and Nicholson, A. J. (1997) Ranking and selecting motor vehicle accident sites by using a hierarchical Bayesian model. Statistician, 46, 293–316.
63. Shankar, V., Mannering, F. and Barfield, W. (1995) Effect of roadway geometrics and environmental factors on rural freeway accident frequencies. Accidnt Anal. Prevn, 27, 371–389.
64. Song, J. J., Ghosh, M., Miaou, S. and Mallick, B. (2006) Bayesian multivariate spatial models for roadway traffic crash mapping. J. Multiv. Anal., 97, 246–273.
65. Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002) Bayesian measures of model complexity and fit (with discussion). J. R. Statist. Soc. B, 64, 583–639.
66. Tegnér, G. and Loncar-Lucassi, V. (1997) Demand for road use, accidents and their gravity in Stockholm: measurement and analysis of the Dennis package. Transek, Stockholm.
67. Torre, G. L., Beeck, E. V., Quaranta, G., Mannocci, A. and Ricciardi, W. (2007) Determinants of within-country variation in traffic accident mortality in Italy: a geographical analysis. Int. J. Hlth Geog., 23, no. 6, 49.
68. Tunaru, R. (2002) Hierarchical Bayesian models for multiple count data. Austrian J. Statist., 31, 221–229.
69. Van den Bossche, F., Wets, G. and Brijs, T. (2006) Predicting road crashes using calendar data. Transportation Research Board 85th A. Meet., no. 06-2016.
70. Wakefield, J., Best, N. and Waller, L. (2000) Bayesian approaches to disease mapping. In Spatial Epidemiology (eds P. Elliott, J. Wakefield, N. Best and D. Briggs), pp. 104–127. Oxford: Oxford University Press.
71. Waller, L. A., Carlin, B. P., Xia, H. and Gelfand, A. E. (1997) Hierarchical spatio-temporal mapping of disease rates. J. Am. Statist. Ass., 92, 607–617.
72. Wang, Y. and Kockelman, K. M. (2013) A Poisson-lognormal conditional autoregressive model for multivariate spatial analysis of pedestrian crash counts across neighborhoods. Accidnt Anal. Prevn, 60, 71–84.
73. Wang, C., Quddus, M. A. and Ison, S. G. (2011) Predicting accident frequency at their severity levels and its application in site ranking using a two-stage mixed multivariate model. Accidnt Anal. Prevn, 43, 1979–1990.
74. Wolfe, A. C. (1982) The concept of exposure to the risk of a road traffic accident and an overview of exposure data collection methods. Accidnt Anal. Prevn, 14, 337–340.