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Highlights • The bivariate framework examines geometry effects on safety across the road classes. • Three crash frequency models were estimated by crash severity level and road class. • The sensitivity of crash frequency to each geometric factor was investigated. • Results can help highway engineers to evaluate current design standards and policy. Abstract This paper examined the accident risk factors associated with highway traffic and roadway design, for each of three highway classes in the United States using a bivariate modeling framework involving two levels of accident severity. With regard to the highest class (Interstates), the results suggest that, compared to no-casualty accidents, casualty accidents are more sensitive to traffic volume and average vertical grade, but less sensitive to the inside shoulder width and the median width. For US Roads, it was determined that, compared to no-casualty accidents, casualty accidents are more sensitive to traffic volume, outside shoulder width, pavement condition, and median width but less sensitive to the average vertical grade. For the relatively lowest-class roads (State Roads), it was determined that, compared to no-casualty accidents, casualty accidents are more sensitive to the traffic volume, lane width, outside shoulder width, and pavement condition. Compared to the relatively lower-class highways, accidents at higher-class highways are more sensitive to: changes in traffic volume, average vertical grade, median width, inside shoulder width, and the pavement condition (no-casualty accidents only); but less sensitive to changes in lane width, pavement condition (casualty accidents only), and the outside shoulder width. This variation in sensitivity across the different road classes could be attributed to the differences in road geometry standards across the road classes, as the results seem to support the hypothesis that these standards strongly influence accident occurrence. It is hoped that the developed bivariate negative binomial models can help highway engineers to evaluate their current design standards and policy, and to assess the safety consequences of changes in these standards in each road class. [ABSTRACT FROM AUTHOR]