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19 the analyses. Because all but two of the analyses conducted in treatment period to produce an estimate of before-treatment this project utilized EB analyses, the following section pro- crash frequency that is adjusted for regression to the mean. vides a brief description of that general methodology. A more Using the SPF to control for AADT growth and the time trend comprehensive description is provided in Appendix B. factor, this adjusted before-treatment-period estimate is then projected to predict what would happen in each year of the after-treatment period if the treatment had not been imple- Overview of the Empirical Bayes mented. The sum of these predictions (i.e., what would hap- (EB) Methodology pen without treatment in the entire after-treatment period) is The general analysis methodology used in many of the compared to the observed crashes during that period (with the following evaluations was the empirical Bayes (EB) before- treatment implemented) to produce an estimate of the effect after analysis as described by Hauer (7), which has become of the treatment. The procedure also calculates the standard the standard of practice in recent years. This methodology deviation of this effect estimate, which makes it possible to does the following: determine if the measured effect is statistically significant or not at a specified level of significance. · Properly accounts for regression to the mean, · Overcomes the difficulties of using crash rates in normal- Installation of a Rural Traffic Signal izing for volume differences between the before-treatment and after-treatment periods, Description of Treatment and Crash Types · Reduces the level of uncertainty in the estimates of safety of Interest effect, This analysis examined the safety impacts of converting · Provides a foundation for developing guidelines for rural intersections from stop-controlled operation to signal- estimating the likely safety consequences of the contem- controlled. The basic objective was to estimate the change in plated implementation of the evaluated treatment, and crashes. Target crash types considered included the following: · Properly accounts for differences in crash experience and reporting practice in amalgamating data and results from · All crash types, diverse jurisdictions. · Right-angle (side-impact) crashes, · Left-turn-opposing (one-vehicle-oncoming) crashes, and To accomplish this, the EB analysis requires before- · Rear-end crashes. treatment and after-treatment crash and AADT data on the treatment sites and on a reference group of similar untreated The change in crash frequency was analyzed as well as the sites. The similarity of untreated sites is determined on the changes in overall economic costs, recognizing that different basis of the geometrics of the sites (e.g., rural, four-leg, stop- crash types and severity levels have different economic costs. controlled intersections and non-intersection locations on Appendix B provides the details associated with this evaluation. urban, undivided, four-lane, non-freeways), on similar AADT ranges, and on crash history in the before-treatment period. Using the reference group, a safety performance function Data Used (SPF) is developed--a regression equation that predicts an Geometric, traffic-volume, and accident data for treatment outcome variable (e.g., total crashes per year or injury right- and reference sites were acquired from HSIS for the states of angle crashes per year) based on either AADT only or on California (19932002) and Minnesota (19912002) to facil- AADT plus other site descriptors (e.g., lane width or presence itate the analysis. In addition, the Iowa DOT provided a of a left-turn lane). (In the studies conducted for this project, dataset of high-speed rural intersections in Iowa that were generalized linear modeling was used to estimate model coef- converted from stop-controlled to signal-controlled. The ficients in the regression equations using the SAS software Iowa DOT also provided a reference group of similar sites. package and assuming a negative binomial error distribution, Because these data were limited, the time trend necessary to practices consistent with the state of research in developing conduct an EB analysis could not be developed, but the results these models.) A "time trend factor" based on the reference from a cursory analysis of the Iowa data were used to reaffirm group data was also developed for each year in the before- the results from the analysis of California and Minnesota data. treatment and after-treatment periods and is typically re- flected as an SPF multiplier. This multiplier is used to account Methodology for annual effects due to variations in weather, demography, crash reporting, and so forth, across the study period. The SPF The general analysis methodology used was the EB before- outputs are combined with the observed crashes in the before- after analysis, as previously described. The evaluation not
20 only included analysis of the effects of the treatment on crash Table 5. Number of sites for treatment and reference frequencies for different accident types and severities indi- groups. vidually; it also included analysis of the effects on the overall State economic cost (or "crash harm") of crashes before and after Intersection Type California Minnesota the treatment. Since different crash types are characterized by Three leg -- 2 treatment 522 reference different severities (e.g., rear-end crashes are often less severe Three leg, two lanes on major road 4 treatment -- than angle crashes), the economic cost of a crash can be as- 1,405 reference signed based on crash type and severity using type/severity Four leg -- 15 treatment 736 reference economic costs from a recent FHWA study (72). Then, using Four leg, two lanes on major road 14 treatment -- an EB method that parallels the method described above for 742 reference crash frequencies, the overall estimate of treatment effect Four leg, four lanes on major road 10 treatment -- 183 reference when all crash types and severities are combined can be cal- -- = no sites. culated. A much more detailed statistical description of the EB method for both crash frequency and economic costs is found in Appendix B. provides a type of "AMF function," allowing the engineer to The analyses attempted to develop AMFs for two crash- input specific before- and after-conversion AADTs to estimate severity levels (i.e., injury versus no-injury) within each of the the expected effects. This procedure is documented in four crash types (i.e., total, right-angle, left-turn-opposing, Appendix B. and rear-end) within three types of stop-controlled (before- treatment) intersections. This was not possible in both states. Results The intersection types and the treatment and reference group sample sizes are noted in Table 5. Iowa data included a total of The initial EB evaluation of crash frequency by crash types 19 treatment sites and 59 reference sites (three- and four-leg indicated a significant effect of signal installation on angle, left- combined). turn and rear-end crashes. Table 6 shows the individual and In addition to providing data on these stop-controlled sites, combined results of the California and Minnesota analyses-- California and Minnesota provided data on other intersec- the AMFs and their standard deviation. tions that were signalized throughout the entire before- As shown in Table 6, the Iowa results are similar to those treatment and after-treatment period (63 four-legged sites from the other two states, providing some validation for from California, 21 four-leg sites from Minnesota). These data those results. The best overall estimate of effect is shown in were used in two ways. First, the signalized intersection the bottom row where the California and Minnesota results datasets were used to verify that the treated intersections in the are combined. There, for all intersection types combined, sig- after-treatment period performed similarly to intersections nal installation is expected to reduce total crashes by 44 per- that were already signalized during the after-treatment period. cent, right-angle crashes by 77 percent, left-turn crashes by 60 In general, the treated intersections did perform similarly, in- percent, and increase rear-end crashes by 58 percent. The dicating that the treated sites were not an unusual group of analyses conducted indicated that while there were slight dif- intersections. This similar performance helps validate the cal- ferences in effects for the different intersection types and culated crash-related AMF. Second, the data on intersections crash severities, these differences were not statistically signif- that were signalized throughout the entire before-treatment icant. Thus, the overall AMFs shown above are appropriate and after-treatment period were used to develop a more de- for all rural site types. tailed procedure for assessing whether a contemplated signal However, the significant increase in rear-end crashes raises installation is warranted at a given location. In one sense, the questions concerning how much of the angle and left-turn initial EB analysis produces an AMF for each target crash type, savings are negated by this rear-end increase. An examination but the AMF does not vary with AADT. The procedure of the economic costs of the changes based on an aggregation Table 6. Crash frequency AMFs (and standard deviations) by crash type for rural signalization. State Total Crashes Right-Angle Left-Turn Rear-End (RA) (LT) (RE) California 0.778 (0.061) 0.221 (0.036) 0.433 (0.065) 2.474 (0.373) Minnesota 0.488 (0.027) 0.228 (0.019) 0.374 (0.063) 1.300 (0.141) Iowa 0.950 (0.085) 0.265 (0.053) n/a 2.075 (0.323) California + 0.559 (0.025) 0.227 (0.017) 0.401 (0.047) 1.579 (0.142) Minnesota