Skip to main content
Log in

A hierarchical Bayes approach to adjust for selection bias in before–after analyses of vision zero policies

  • Original paper
  • Published:
Computational Statistics Aims and scope Submit manuscript


American cities devote significant resources to the implementation of traffic safety countermeasures that prevent pedestrian fatalities. However, the before–after comparisons typically used to evaluate the success of these countermeasures often suffer from selection bias. This paper motivates the tendency for selection bias to overestimate the benefits of traffic safety policy, using New York City’s Vision Zero strategy as an example. The NASS General Estimates System, Fatality Analysis Reporting System and other databases are combined into a Bayesian hierarchical model to calculate a more realistic before–after comparison. The results confirm the before–after analysis of New York City’s Vision Zero policy did in fact overestimate the effect of the policy, and a more realistic estimate is roughly two-thirds the size.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others


  • American Association of State Highway and Transportation Officials (2001) Policy on geometric design of highways and streets. 1 (990):158.

  • Amjadi R, Martinez W (2021) The 2016 data challenge of the American Statistical Association. Comput Stat.

  • Berger JO (2013) Statistical decision theory and Bayesian analysis. Springer, Berlin

    Google Scholar 

  • Davis GA (2000) Accident reduction factors and causal inference in traffic safety studies: a review. Accid Anal Prev 32(1):95–109

    Article  MathSciNet  Google Scholar 

  • Efron B, Trevor H (2016) Computer age statistical inference, vol 5. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Freedman D, Robert P, Roger P (1998) Statistics, vol 4. WW Norton & Company, New York

    MATH  Google Scholar 

  • Friedman M (1992) Do old fallacies ever die? J Econ Lit 30(4):2129–2132

    Google Scholar 

  • Gelman A (2005) Analysis of variance—why it is more important than ever. Ann Stat 33(1):1–53

    Article  MathSciNet  Google Scholar 

  • Gelman Andrew, Hill Jennifer (2006) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Gelman Andrew, Little Thomas C (1997) Poststratification into many categories using hierarchical logistic regression. Surv Methodol 23(2):127–35

    Google Scholar 

  • Good IJ (1953) The population frequencies of species and the estimation of population parameters. Biometrika 40:237–264

    Article  MathSciNet  Google Scholar 

  • Goodwin AH, Libby JT, William LH, Mary ET (2010) Countermeasures that work: a highway safety countermeasure guide for state highway safety offices

  • Greenwood M, Yule GU (1920) An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or of repeated accidents. J R Stat Soc 83(2):255–79

    Article  Google Scholar 

  • Hauer E (2005) Cause and effect in observational cross-section studies on road safety. Unpublished Manuscript

  • Imbens GW, Donald BR (2015) Causal inference in statistics, social, and biomedical sciences. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Johansson R (2009) Vision Zero—implementing a policy for traffic safety. Saf Sci 47(6):826–31

    Article  Google Scholar 

  • Leaf WA, Preusser DF (1999) Literature review on vehicle travel speeds and pedestrian injuries. US Department of Transportation, National Highway Traffic Safety Administration

  • Mokdad AH, James SM, Donna FS, Julie LG (2004) Actual causes of death in the United States, 2000. JAMA 291(10):1238–1245

    Article  Google Scholar 

  • National Highway Traffic Safety Administration (2016) Traffic Safety Facts: Research Note, Dot Hs 812 260.

  • National Research Council (US) Transportation Research Board, Committee for Guidance on Setting, and Enforcing Speed Limits (1998) Managing speed: review of current practice for setting and enforcing speed limits, vol 254. Transportation Research Board

  • New York City Vision Zero Taskforce (2017) Vision Zero: year three report.

  • Robbins H (1955) An empirical Bayes approach to statistics. In: Proceedings of Third Berkeley Symposium Mathematics Statistics and Probability, vol 1(1). University of California Press, Berkeley, pp 157–164

  • Robbins H, Cun-Hui Z (1988) Estimating a treatment effect under biased sampling. Proc Natl Acad Sci 85(11):3670–3672

    Article  MathSciNet  Google Scholar 

  • Robbins H, Cun-Hui Z (2000) Efficiency of the U, V method of estimation. Proc Natl Acad Sci 97(24):12976–12979

    Article  MathSciNet  Google Scholar 

  • Rosén E, Ulrich S (2009) Pedestrian fatality risk as a function of car impact speed. Accid Anal Prev 41(3):536–542

    Article  Google Scholar 

  • Rosenbaum Paul R (2017) Observation and experiment: an introduction to causal inference. Harvard University Press, Cambridge

    Book  Google Scholar 

  • Stan Development Team (2016) RStan: the R interface to stan (version 2.14.1).

  • Stigler SM (2016) The seven pillars of statistical wisdom. Harvard University Press, Cambridge

    Book  Google Scholar 

  • Yajuan S, Pillai NS, Gelman A (2015) Bayesian nonparametric weighted sampling inference. Bayesian Anal 10(3):605–625

    MathSciNet  MATH  Google Scholar 

  • Shelton T (1991) National accident sampling system general estimates system. Technical Note, 1988 to 1990.

  • The Swedish Trade & Investment Council and Government Offices of Sweden. “Vision Zero.”

  • Tingvall C, Narelle H (2000) Vision Zero: an ethical approach to safety and mobility. In: 6th Ite international conference road safety & traffic enforcement: beyond, vol 1999

  • U.S. Department of Transportation (2016) Revised departmental guidance on valuation of a statistical life in economic analysis.

  • Xu J, Sherry LM, Kenneth DK, Brigham AB (2016) National vital statistics reports. National Vital Statistics Reports, vol 64(2)

Download references


We would like to thank Roya Amjadi, Wendy Martinez, Stas Kolenikov and the American Statistical Association’s Government Statistics Section for their encouragement. We would also like to thank Michael Sobel, Owen Ward and members of New York City Community Board 7, especially Richard Robbins and Catherine DeLazzero for their knowledge and expertise.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Jonathan Auerbach.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Auerbach, J., Eshleman, C. & Trangucci, R. A hierarchical Bayes approach to adjust for selection bias in before–after analyses of vision zero policies. Comput Stat 36, 1577–1604 (2021).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: