Ezra Hauer

Estimating Safety by the Empirical Bayes Method: A Tutorial

The empirical Bayes (EB) method addresses two problems of safety estimation: it increases the precision of estimates beyond what is possible when one is limited to the use of a 2- to 3-year accident history, and it corrects for the regression-to-mean bias. The increase in precision is important when the usual estimate is too imprecise to be useful. The elimination of the regression-to-mean bias is important whenever the accident history of the entity is in some way connected with the reason why its safety is estimated. The theory of the EB method is well developed. It is now used in the Interactive Highway Safety Design Model and will be used in the Comprehensive Highway Safety Improvement Model. The time has come for the EB method to be the standard and staple of professional practice. The study’s goal is to facilitate the transition from theory into practice.

Identification of Sites with Promise

Procedures for the identification of black spots, or hazardous locations, are attempts to select some sites out of many to improve safety. These are sites with promise. The historical and conceptual development of such procedures is reviewed. On the basis of this review, an attempt is made to create some order in the thinking. Suggestions are made to improve identification. It is noted that the status of the stage that follows identification, the stage of site safety diagnosis and remediation, is underdeveloped.

Safety Effectiveness of Intersection Left- and Right-Turn Lanes

The results of research involving a well-designed before-and-after evaluation of the safety effects of providing left- and right-turn lanes for at-grade intersections are presented. Geometric design, traffic control, traffic volume, and traffic accident data were gathered for a total of 280 improved intersections as well as 300 similar intersections that were not improved during the study period. The types of improvement projects evaluated included installation of added left-turn lanes, added right-turn lanes, and extension of the length of existing left- or right-turn lanes. An observational before-and-after evaluation of these projects was performed by using several alternative evaluation approaches. Three contrasting approaches to before-and-after evaluation were used: the yoked comparison or matched-pair approach, the comparison group approach, and the empirical Bayes approach. The research not only evaluated the safety effectiveness of left- and right-turn lane improvements but also compared the performances of these three alternative approaches in making such evaluations. The research developed quantitative safety effectiveness measures for installation design improvements involving added left-turn lanes and added right-turn lanes. The research concluded that the empirical Bayes method provides the most accurate and reliable results. Further use of this method is recommended.

Accidents, overtaking and speed control

ACCIDENT INVOLVEMENT RATES ARE OBSERVED TO BE HIGHER AT SLOW AND FAST TRAVEL SPEEDS THAN AT INTERMEDIATE VELOCITIES. THE HYPOTHESIS IS ADVANCED THAT ACCIDENT INVOLVEMENT IS RELATED TO OVERTAKINGS. IT IS SHOWN THAT THE TOTAL NUMBER OF OVERTAKINGS VARIES WITH SPEED IN A MANNER WHICH IS SIMILAR TO THAT OF THE ACCIDENT INVOLVEMENT RATE. SOME IMPLICATIONS OF THE RATE OF OVERTAKING ON THE SPEED SELECTION BY THE DRIVER ARE EXPLORED. THE EFFECT OF VARIOUS COLLECTIVE SPEED CONTROL STRATEGIES ON THE TOTAL AMOUNT OF OVERTAKING IS INVESTIGATED. /AUTHOR/

Statistical Road Safety Modeling

The hope is that statistical models fitted to historical data can be used to estimate the effect of road design elements on safety. Whether this can be done is not clear. A sign of trouble is that models based on diverse data sets tend not to yield similar results. Suggestions are made on how to increase the chance of success in this quest. Emphasis is on three questions: Which variables should serve in the model? What mathematical function should represent their influence? How does one check whether the representation of the influence of a variable is appropriate?

Screening the road network for sites with promise

Network screening is the first step in the site safety improvement process. The product of network screening is a list of sites that are ranked by priority for the conduct of detailed engineering studies. In turn, cost-effective projects are formulated from the studies. With the purpose of laying the foundation for improved network screening, the role of network screening is clarified, and how project cost and safety benefit can be anticipated at the time of screening is examined. The strengths and weaknesses of alternative assumptions on which the anticipation of safety benefit can be based are discussed. A way to guard against misallocation of resources due to the randomness of accident counts is suggested, and a method for finding peak sites within road sections is proposed.

Speed enforcement and speed choice

Abstract A rational appraoch to practical problems of speed enforcement requires an understanding of the manner in which enforcement affects speed choice. In this report, four experiments are described. Each experiment consisted of measuring speeds of vehicles before, during and after enforcement took place, accompanied by a control section to which no speed enforcement was applied. The four experiments differ in the number of days of enforcement. During experiments 1 and 2 considerable attrition of data occurred. Therefore, conclusions are based mainly on data obtained during experiments 3 and 4. The data base contains some 116,000 speed observations. For some experiments, the license plate record of vehicles was coded. This allows the tracing of the same vehicle day after day. Analysis leads to several conclusions. When enforcement is in place, the average speed of the traffic stream is reduced at the site of enforcement, upstream and downstream of it. At the site of speed limit enforcement, the average speed of the traffic stream is around the posted speed limit. This reduction in average speed decays (exponentially) with distance downstream. There is a distinct time halo effect. That is, the average speed is depressed from its pre-enforcement level after enforcement has been removed. For a single application of enforcement, the effect seems to vanish after 3 days. When the speed limit at a site is enforced for 5 consecutive days, the average speed remains depressed at least for 6 days after the last day of enforcement. In two of the experiments, enforcement was related to a reduction in the “width” of the speed distribution. In one experiment no such reduction occurred. When individual vehicles are traced day after day, it appears that repeated exposure to enforcement does not induce larger reductions in the speed of travel. It is also found that habitually fast and habitually slow drivers reduced their speed somewhat more than those driving at the average traffic stream speed.

Speed and Safety

The speed at which people elect to travel is affected by vehicle and road design; by limits to speed and enforcement of those limits; by traffic control, signs, and markings; and so forth. The speed at which people travel, in turn, affects road safety. In this context two questions arise: (a) How is the evolution of speed over time and space affected by what drivers do? (b) How does speed affect safety? This paper reviews what is known, notes the gaps in knowledge, and describes where opinions differ and why. Unfortunately, despite decades of speed measurement and monitoring, the evolution of speed over time is poorly documented, and the understanding of what drives the evolution is largely missing. It is known that speeds evolve over time, but not why; it is known that there is some spillover of the change from one road to another, but its size or extent cannot be predicted. This is a neglected field of inquiry. More is known in answer to Question b. There can be no reasonable doubt that if speed increases while other conditions (vehicles, roads, medical services) remain unchanged, the accidents that occur will tend to be more severe. However, the prevalent and strongly held belief that the greater the speed, the higher is the probability that accidents will occur is, at present, not well supported by research. Even so, given a change in mean speed, one can predict the consequences in injuries and fatalities and this paper discusses how to do so.

Two Problems of Averaging Arising in the Estimation of the Relationship Between Accidents and Traffic Flow

A function linking the expected accident frequency to traffic flow is called a safety performance function (SPF). SPFs are estimated from data for various facilities and accident types. Typically, accident counts over a period of a year or more, and estimates of average flow for such periods, serve as data. The ideal is for SPFs to represent cause-effect regularities. However, because accident counts are for a long time period and because average flows are used, two issues of averaging arise. First, the cause-effect relationship is between accidents and the flows prevailing near the time of accident occurrence. Therefore, ideally, these should be the argument of the SPF. In practice, however, either because of lack of detail or difficulties of estimation, average flows are used for estimation. The question is what problems arise when average flows, such as annual average daily traffic, instead of the flows at the time of the accident are used as the argument of the SPF. This is the argument averaging problem. Second, there are at least two (daytime and nighttime) and perhaps many more cause-effect SPFs that prevail in the course of a year. Ideally, each relationship should be estimated separately. The question is what problems arise if one joint SPF is estimated when two or more separate functions should have been used. This is the function averaging problem. After analysis, how to account and how to correct for the argument averaging problem are shown. At this time, avoiding the function averaging problem by estimating daytime and nighttime SPFs separately can be the only recommendation.

Bias-by-selection: Overestimation of the effectiveness of safety countermeasures caused by the process of selection for treatment

Abstract The effectiveness of safety countermeasures is often estimated from “before” and “after” accident histories of systems on which the countermeasure has been implemented. Due to practical reasons, systems are at times selected for treatment on the basis of their poor safety performance. This process of selection will ensure that on the average a reduction in the number of accidents will be observed even if the countermeasure has no effect. In this paper a robust and simple method for the estimation of this bias-by-selection is obtained. It allows elimination of the bias from research results. The dependence of the bias-by-selection on the duration of the accident history available and on the severity of the selection criterion, is explored.