Comparison of univariate and two-stage approaches for estimating crash frequency by severity-Case study for horizontal curves on two-lane rural roads.

The Highway Safety Manual (HSM) procedures apply specific safety performance functions (SPFs) and crash modification factors (CMFs) appropriate for estimating the safety effects of design and operational changes to a roadway. Although the applicability of the SPFs and CMFs may significantly vary by crash severity, they are mainly based on total crash counts, with different approaches for estimation of crashes by crash severity. The variety of approaches in the HSM and in the literature in general suggests that there may be no one best approach for all situations, and that there is a need to develop and compare alternative approaches for each potential application. This paper addresses this need by demonstrating the development and comparison of alternative approaches using horizontal curves on two-lane roads as a case study. This site type was chosen because of the high propensity for severe crashes and the potential for exploring a wide range of variables that affect this propensity. To facilitate this investigation, a two-stage modeling approach is developed whereby the proportion of crashes for each severity level is estimated as a function of roadway-specific factors and traffic attributes and then applied to an estimate of total crashes from an SPF. Using Highway Safety Information System (HSIS) curve data for Washington state, a heterogeneous negative binomial (HTNB) regression model is estimated for total crash counts and then applied with severity distribution functions (SDFs) developed by a generalized ordered probit model (GOP). To evaluate the performance of this two-stage approach, a comparison is made with predictions directly obtained from estimated univariate SPFs for crash frequency by severity and also from a fixed proportion method that has been suggested in the HSM. The results revealed that, while the two-stage SDF approach and univariate approach adopt different procedures for model estimation, their prediction accuracies are similar, and both are superior to the fixed proportion method. In short, this study highlights the potential of the two-stage SDF approach in accounting for crash frequency variations by severity levels, at least for curved two-lane road sections, and especially for the all too frequent cases where samples are too small to estimate viable univariate crash severity models.