Development of a Procedure for Estimating the Expected Safety Effects of a Contemplated Traffic Signal Installation

Persaud, McGee, Lyon & Lord 1 Development of a Procedure for Estimating the Expected Safety Effects of a Contemplated Traffic Signal Installation Bhagwant Persaud Professor Department of Civil Engineering, Ryerson University 350 Victoria Street, Toronto, Canada M5B 2K3 Phone: 416-979-5000, Ext. 6464; Fax: 416-979-5122; e-mail: bpersaud@ryerson.ca Hugh McGee Principal BMI, 8330 Boone Blvd., Suite 700, Vienna, VA 22182 Phone: 703-847-3071; Fax: 703-847-0298; email: hmcgee@bmiengineers.com Craig Lyon Research Associate Department of Civil Engineering, Ryerson University 350 Victoria Street, Toronto, Canada M5B 2K3 Phone: 416-979-5000, Ext. 6464; Fax: 416-979-5122; e-mail: craig.lyon@rogers.com Dominique Lord Associate Research Scientist Texas Transportation Institute, Texas A&M University System 3135 TAMU, College Station, TX, 77843-3135 Phone: 979-458-1218; Fax: 979-845-4872; e-mail: d-lord@tamu.edu ABSTRACT The Manual of Uniform Traffic Control Devices (MUTCD) contains warrants for traffic signal installation but cautions that satisfying a warrant does not in itself justify the decision to install a signal and that one should not be installed unless an engineering study indicates that this will improve the overall safety and/or operation of the intersection. The paper reports on the development of an easily implementable procedure, which is intended to be part of an engineering study, for estimating the expected safety effects of a contemplated signal installation. These effects can then be considered in conjunction with other impacts in a conventional economic evaluation. The development of the procedure using a multi-jurisdiction database is described and a detailed illustration presented. Use is made of the empirical Bayes methodology that has of late been recognized as state of the art in safety estimation and of the most recent advances in that methodology. The paper places substantial focus on the application of that methodology and on the development of the accident prediction models required to support that application. The development of the procedure is part of a National Cooperative Highway Research Program project (NCHRP 17-16) that aims to improve the safety warrant for signal installation and, more generally, how safety is considered in the decision to install or not install a signal. Word Count: 5345 text words plus 8 tables = 7345 total Submission Date: November 15, 2002 Key Words: Safety Evaluation, Accident Analysis, Traffic Signal Warrants, Accident Models

Persaud, McGee, Lyon & Lord 2 INTRODUCTION The fundamental objective of NCHRP Project 17-16 Accident Warrant for Traffic Signals on which this paper is based was to improve the procedure in the Manual on Uniform Traffic Control Devices (MUTCD) (1) for making decisions on traffic signal installation at existing twoway stop-controlled intersections in urban and suburban areas. New intersections are outside the scope of the research although some of the results could be adapted for use in that context. To achieve the fundamental objective, there were two principal questions that this study sought to answer: How can we estimate the change in accident frequency expected with the installation of a traffic signal? How can we use the knowledge on the safety impact of traffic signal installation to make decisions on where signals might be justified? To effectively answer these questions required the undertaking of three fundamental analytical tasks as proposed by Persaud (2): a) Development of accident prediction models for stop and signal controlled intersections. b) A study of the safety effect of signals already installed. c) The use of the results of a) and b) to develop decision-making tools. These tasks required the assembly of an extensive database consisting of traffic volume, geometric and accident data for several years for three sets of intersections: (i) those converted from stop to signal control; (ii) a reference group of signalized intersections; and (iii) a reference group of stop-controlled intersections. Accident prediction models were then estimated and an empirical Bayes procedure (3) was used in the development of the decision-making tools. Fundamental to the development of the tools is the estimation of the change in safety at a stop-controlled intersection if it were to be signalized. The proposed approach consists of 3 parts as follows: 1) Use the accident counts and traffic volumes for a recent period to estimate the expected number of accidents of various affected types that would occur if the intersection were not signalized. Prediction models for Stop-controlled intersections would be used here in the empirical Bayes procedure. 2) Estimate the expected number of accidents that would happen after, should the intersection be signalized, using prediction models for signal-controlled intersections. 3) Estimate the expected change in safety as the difference between estimates 1) and 2). The approach to part 2) is a departure from another recent one (4) in which an accident modification factor is applied to the estimate from part 1) to obtain the expected number of accidents in the after period in the absence of the treatment. It is convenient, in that a comprehensive set of accident modification factors, which would be required for a large number of conditions, is simply not available and is difficult to obtain. The proposed approach, however, required a fundamental assumption that the safety of a newly signalized intersection can be estimated from a prediction model developed on the basis of the general population of signalized intersections. This assumption was untested, so the conduct of a before-after study of signal installations was essential to ensure that the expected change in safety estimated for an installation in part 3) of the suggested approach would be consistent with that from a before-after study. This corroboration exercise was a fundamental aspect of this project. Conversations with practitioners and informal presentations and sharing of ideas developed during the course of the project have confirmed the need for, and acceptability of the

Persaud, McGee, Lyon & Lord 3 proposed approach. Dissemination to practitioners is vital to its success and has been already been facilitated by two recent Institute of Transportation Engineers (ITE) conference papers (5, 6) that have presented the rudiments of what has been proposed for NCHRP 17-16. This paper formally documents the analytical aspects of this large scale study that aimed to develop and test the proposed approach using empirical data specially collected for this purpose. First, the vital statistics on the data assembled are summarized. This is followed by a section on the accident prediction models developed. Next are the results of the retrospective before-after study of signals installed. The final section presents and illustrates the suggested procedure for estimating the safety impact of a contemplated signal installation as part of an engineering study. DATA SUMMARY Data were collected from several cities in the United States, and from Toronto, Canada, for intersections converted from two-way stop to signal control and also for reference groups of unconverted signalized and two-way stop-controlled intersections. Data for the unconverted intersections served for developing accident prediction models to be used in estimating the safety effects of conversion and in the engineering study procedure developed. Data were collected for each accident in the analysis period as well as for a wide variety of intersection characteristics. Field visits supplemented data already available from the jurisdiction. At a late stage of the study, data from the Highway Safety Information Service (HSIS) for California became available and were assembled for unconverted urban intersections. This data set was used to explore the development of improved prediction models for application in the engineering study procedure. Table 1 provides summary information on traffic volumes and injury accidents for the data assembled for this project. As can be seen, the reference group of unconverted intersections appears to be fairly representative, in terms of AADT ranges, of the converted intersections. The treatment and reference group data are seen to be dominated by Toronto intersections. However, as is shown later, the results for intersections in Toronto are reasonably consistent with those for intersections in the US jurisdictions. It is also seen that the dataset consists mainly of 4-legged intersections, the ones of primary interest in signal installation decisions. However, as will be seen later, the 3-legged intersection numbers were still sufficient to obtain useful results. DEVELOPMENT OF ACCIDENT PREDICTION MODELS Accident prediction models were required for use in the before-after study and in the development of the proposed engineering study procedure. Development of the models involved determining which explanatory variables should be used, whether and how variables should be grouped and how variables should enter into the model, i.e., the best model form. Variables such as area type, intersecting volumes, sight distance, presence of turn lanes etc., were explored for their relevance in explaining accident occurrence. Generalized linear modeling (7) was used to estimate model coefficients using the software package GENSTAT (8) and assuming a negative binomial error distribution, all consistent with the state of research in developing these models. In specifying a negative binomial error structure, a parameter, K, which relates the mean and variance of the regression estimate is iteratively estimated from the model and the data. The value of K, which is the inverse of the overdispersion parameter of the negative binomial distribution, is such that the larger the value of K is the better a model is for a given set of data. The conduct of the before-after study of converted intersections required the development of prediction models for unconverted stop-controlled intersections. These models would also be used in the procedure for conducting the engineering study. Models for unconverted signalized intersections were also developed for use in the engineering study procedure. Models were calibrated for rear-end, right angle and all accident types combined.

Persaud, McGee, Lyon & Lord 4 Based on experience with the quality of property damage accident data, a decision was taken early in the project that the development of models and all subsequent analysis would be based on injury (fatal plus non-fatal) accidents. In so doing, it was expected that difficulties that arise from the transferability of the models and the procedure across jurisdictions and over time would be minimized. This is because injury accidents are much less likely than property damage ones to exhibit significant reporting differences across time and space. Even so, the models can be recalibrated if such differences exist and are not unduly substantial. A procedure for doing so is presented by Harwood et al. (4) and is summarized later in this paper. Table 1 Data Summary State Group Legs Sites Years Major AADT Minor AADT Injury Accidents * MIN MAX MIN MAX ALL RE RA Stops 3 2 94-97 22953 24111 1056 1081 10 2 0 Signals 3 1 94-97 25109 25109 2697 2697 4 1 0 California Converts 3 2 94-97 25230 37300 1645 2523 16 8 0 Stops 4 11 94-97 5788 39275 69 2556 62 11 20 Signals 4 16 94-97 4512 27097 866 25314 147 28 44 Converts 4 20 94-97 5721 42300 384 9384 110 30 19 Stops 3 2 93-98 13755 28992 514 2016 26 7 4 Signals 3 3 93-98 16434 37935 1426 4738 82 40 1 Converts 3 1 93-98 42046 42046 1911 1911 18 10 0 Florida Stops 4 15 93-98 12376 34155 625 3723 130 22 18 Signals 4 5 93-98 13165 28988 2523 21541 180 55 15 Converts 4 13 93-98 4335 27716 1116 4202 223 53 39 Stops 3 3 89-98 12526 39873 256 1870 57 7 13 Signals 3 0 n/a n/a n/a n/a n/a n/a n/a n/a Maryland Converts 3 2 89-98 8902 19302 1510 2735 19 7 2 Stops 4 18 89-98 8251 48791 316 3000 234 51 46 Signals 4 5 89-98 20144 38946 1869 6200 219 58 28 Converts 4 10 89-98 6447 24586 1212 4392 124 17 57 Stops 3 3 90-97 15443 34740 458 4426 32 13 0 Signals 3 2 90-97 22776 22963 2587 5075 42 17 21 Virginia Converts 3 5 90-97 10118 37364 871 3587 75 30 14 Stops 4 15 90-97 3843 53489 254 2917 100 16 40 Signals 4 11 90-97 8980 30772 940 13457 194 64 37 Converts 4 10 90-97 9284 37280 1232 10061 142 29 42 Stops 3 2 88-96 32141 32254 1950 2015 36 7 14 Signals 3 0 88-96 n/a n/a n/a n/a n/a n/a n/a Converts 3 2 88-96 11158 28379 3233 4671 76 30 3 Wisconsin Stops 4 30 88-96 6079 43442 1081 7683 450 89 164 Signals 4 30 88-96 4959 33026 2435 17943 854 249 147 Converts 4 21 88-96 4981 43030 1931 6811 473 102 200 Stops 3 87 89-95 5227 52269 37 6962 451 156 110 Signals 3 13 89-95 18866 45240 647 2869 162 52 37 Toronto Converts 3 10 89-95 13949 55735 201 4650 80 38 11 Stops 4 109 89-95 5021 49775 146 10194 766 178 324 California HSIS Signals 4 29 89-95 6562 60276 1144 8393 481 166 130 Converts 4 26 89-95 7255 48465 789 22267 362 97 126 Stops 3 939 91-98 5073 99870 100 21800 5148 1811 588 Stops 4 479 91-98 5000 69333 100 16570 4275 1083 1221 Signals 3 170 91-98 9257 80500 100 25001 2632 1373 185 Signals 4 629 91-98 6303 78500 101 43000 14481 6634 2333 * RE = rear-end; RA = right-angle; LT = left-turning injury accidents

Persaud, McGee, Lyon & Lord 5 Models for Unconverted Two-Way Stop-Controlled Intersections Reference group data were used to develop prediction models for stop-controlled intersections. The inclusion of variables such as sight distance and approach speed did not significantly affect the fit. This is not surprising given the relatively little variation in these factors and the reality, as previous research has confirmed, that much of the variation in accident experience is explained by the volume of traffic entering an intersection. The calibrated models, which are presented in Table 2, were used in the before-after study of the converted intersections. While better models may be needed for other purposes, such as examining the effects of causal factors on accident occurrence, our experience is that bare-bones models such as are presented in Table 2 are adequate for the intended purposes in this research. TABLE 2 Models for Injury Accidents per Year at Stop-Controlled Intersections [based on 99 3-legged intersections (87 in Toronto) and 198 4-legged intersections (109 in Toronto)] ALL RIGHT-ANGLE REAR-END Model Form α(f1) b (F2) c α(f1) b (F2) c α(f1+f2) d # of Legs 4-leg 3-leg 4-leg 3-leg 4-leg 3-leg K 2.30 6.10 1.40 2.20 1.50 2.90 Ln(α) (US) Ln(α) (Toronto) b c d -7.76 (1.14) -8.04 (1.15) 0.499 (0.088) 0.430 (0.082) -13.33 (1.45) -13.84 (1.46) 0.968 (0.124) 0.558 (0.078) -9.01 (1.62) -8.91 (1.63) 0.218 (0.122) 0.799 (0.118) -15.69 (2.84) -15.91 (2.86) 1.012 (0.239) 0.582 (0.152) -8.99 (1.48) -14.62 (2.31) -14.73 (2.33) 0.763 (0.148) Table Legend: F1, F2 = entering AADT on major, minor road, respectively; K is the calibrated parameter relating the mean and variance of the prediction. 1.337 (0.224) The results, specifically the estimated value of the coefficient α, indicate that there is little or no difference between models for US sites taken together and the Toronto sites. While there was an indication that there were some differences among US sites, those differences were statistically insignificant, likely due to the small sample sizes. The California HSIS data were used to develop alternate models for stop-controlled intersections. This attempt to calibrate better models for stop controlled intersections failed in that the models were deemed to be no better than those already calibrated from the reference data. Therefore the stop-controlled models from Table 2 were adopted. Models for Unconverted Signalized Intersections Reference group data, consisting of intersections that were signalized throughout the data period, were used to develop regression models for signalized intersections. Again, the inclusion of variables such as sight distance and approach speed did not significantly affect the fit. In the models presented in Table 3, the dependent variable is injury accidents per year, and F1, F2 and K are defined as before. The number of 3-leg intersections was relatively small, which meant that the datasets had to be combined. An attempt was made to estimate a different constant (α) for 3 and 4-leg intersections using the number of legs as a dummy variable (0 and 1 for 3 and 4 leg). However,

Persaud, McGee, Lyon & Lord 6 the constant term (α) was almost identical for the two intersection types; therefore a single constant term was calibrated, although separate K values were calculated. TABLE 3 Models for Injury Accidents per Year at Signalized Intersections [based on 19 3-legged intersections and 96 4-legged intersections] ALL RIGHT-ANGLE REAR-END Model Form α(f1) b (F2) c α(f1) b (F2) c α(f1+f2) d K (3-legged) 1.7 0.6 1.1 K (4-legged) 3.2 3.7 2.1 ln(α) -10.82 (1.69) -7.06 (2.15) -11.25 (2.30) b 0.719 (0.140) 0.346 (0.178) c 0.562 (0.080) 0.368 (0.102) d 1.070 (0.221) Once again, the California HSIS data were used in an attempt to improve the models. The best models are shown in Table 4. Attempts at including other explanatory variables did not improve the models sufficiently for these variables to be included. α(f1) b (F2) c α(f1+f2) d Table 4 Models for Injury Accidents per Year at California HSIS Signalized Intersections ALL RIGHT-ANGLE REAR-END Model α(f1) b (F2) c α(f1+f2) d Form (F2/(F1+F2)) e # of Legs 4-leg 3-leg 4-leg 3-leg 4-leg 3-leg K 3.1 3.0 1.7 1.4 2.4 2.3 ln(α) (s..e) -5.75 (0.54) -7.51 (1.30) -3.77 (0.87) -11.94 (2.77) -10.99 (0.70) -9.79 (1.60) b 0.491 (0.052) 0.637 (0.124) 0.807 (0.262) c 0.198 (0.023) 0.190 (0.041) 0.190 (0.087) d 0.329 (0.082) 1.059 (0.066) 0.927 (0.152) e 0.245 (0.041) Based on a comparison between the reference group models in Table 3 and the California HSIS models in Table 4 of the standard errors and the K values, and considering that separate models could now be calibrated for 3 and 4-legged intersections, it was decided to adopt the California signalized intersection models for the purposes of this research. Application of Signalized Intersection Models to the Conversion Sample The conversion dataset consisted of 122 intersections with 386.68 site-years of data for which signals were in place. The number of accidents for these site-years was compared to that predicted by applying the California HSIS models in Table 4 to these intersections. The purpose was to test if converted intersections in the sample behaved similarly after conversion to other signalized intersections in the general population in terms of the relationship between accidents and traffic volume.

Persaud, McGee, Lyon & Lord 7 The results, shown in Table 5, are mixed. Excellent results are obtained for total and right angle injury accidents and on this basis it could be concluded with caution is ample indication that converted intersections in the sample behave similar to other signalized intersections in terms of the relationship between injury accidents and traffic volume. It was therefore decided that the California HSIS signalized intersection models were adequate for the procedure for conducting an engineering study to assess whether or not a contemplated signal installation is warranted. Similarly, these models could also be used in developing the crash experience warrant, a task that was also a part of the research. TABLE 5 Accidents at Signalized Intersections that were Converted Injury Accident Type Basis for after period accidents After period accidents (and standard deviation) Observed 120 Right angle Estimated by California model 123.1 (10.3) Observed 210 Rear-end Estimated by California model 274.3 (20.2) Observed 707 All Estimated by California model 692.9 (42.5) BEFORE-AFTER ANALYSIS OF CONVERTED INTERSECTIONS As mentioned earlier, the preferred approach for estimating the likely safety benefit of a contemplated signal installation requires a fundamental assumption that the safety of a newly converted intersection can be estimated from a model developed on the basis of intersections converted previously. A before-after study of converted intersections was essential to corroborate this assumption. This corroboration exercise was fundamental to this study. Basics of the Empirical Bayes Before-After Study The empirical Bayes methodology as documented by Hauer (3) and as recently applied by Persaud et al. (9) was used to estimate the safety effect of signalization at the conversion sites. This required the use of regression models for stop-controlled intersections presented earlier, and accident counts before signal installation, to estimate the expected number of accidents in the after period had the intersection remained stop-controlled. These estimates, along with the actual accident counts after signal installation, are then summed over all intersections in the conversion sample or some subset of interest. The change in safety is expressed as an index of effectiveness, θ, which is approximately equal to sum of accident frequencies after signal installation divided by the sum of accident frequencies expected without signal installation. This methodology accounts for possible regression-to-the-mean effects, changes in traffic volume and time trends in accident counts. The rudiments of empirical Bayes estimation are illustrated later in an application of this methodology to estimate the expected number of crashes without signalization at an intersection being considered for this measure. This application illustrates, in particular, how the methodology accounts for changes in traffic volume over time. Estimates of the Safety Effect of Conversions and Analysis of Results Estimates of the index of effectiveness,θ, are given in Table 6 for the 3 and 4-legged intersections that were previously two-way stop controlled. These results show that there is a

Persaud, McGee, Lyon & Lord 8 reduction in right angle injury accidents (e.g. for 4-legged, θ = 0.33 is equivalent to a percent reduction of 100(1-0.33) = 67%) and an increase in rear-end injury accidents, both effects in accord with conventional wisdom. The net of these disaggregate effects is a reduction for all impact types combined. TABLE 6 Estimates of Index of Effectiveness for Injury Accidents 3-legged (22 conversions) 4-legged (100 conversions) All Rightangle Rearend All Rightangle Rearend EB estimate of accidents expected after without conversion 142.37 (11.32) 22.13 (3.62) 35.02 (3.87) 756.73 (31.77) 314.72 (19.84) 113.22 (8.20) Injury accidents in the after period 123 15 53 585 105 157 Index of effectiveness θ 0.86 0.66 1.50 0.77 0.33 1.38 VAR{θ} 0.10 0.20 0.26 0.05 0.04 0.15 Viability of the proposed engineering study procedure Recall that the viability of the proposed procedure for conducting an engineering study depends on whether differences in safety predicted by models for stop and signal controlled intersections would be corroborated by the results of the before-after study. To this end, the number of crashes for the converted intersections was estimated using the stop-controlled and the signalized intersection models presented earlier. These estimates are presented in Table 7. TABLE 7 Injury Accident Predictions at Signalized Intersections that were Converted Number of Legs TOTAL RIGHT-ANGLE REAR-END Number Of Site- Years Stop Control Model Signal Control Model Stop Control Model Signal Control Model Stop Control Model Signal Control Model 3 75.33 149.7 106.7 26.6 7.1 29.8 54.4 4 311.35 549.2 586.2 205.0 116.0 81.2 219.9 It can be seen that the direction of the differences in these estimates (i.e., more rear-end crashes and fewer right-angle crashes at signalized compared to stop-controlled intersections) is the same as indicated by the results of the before-after study in Table 6. These results provide support for the use of the proposed approach in estimating the likely safety effect of installing signals at an intersection. In this, an empirical Bayes estimate of the expected number of crashes without signalization is compared to the number of accidents expected with signalization, the latter estimated from a regression model for signalized intersections. The next section documents the application of that approach. PROPOSED PROCEDURE FOR CONSIDERING SAFETY IN SIGNAL INSTALLATION DECISIONS Ideally the decision to install or not install a traffic signal would involve a detailed engineering study, with a benefit-cost analysis that considers the safety and other impacts. Indeed, the MUTCD (1) cautions that satisfying a warrant does not in itself justify the decision to install a signal and that a traffic control signal should not be installed unless an engineering study indicates that installing a traffic control signal will improve the overall safety and/or operation of the intersection.

Persaud, McGee, Lyon & Lord 9 What appears to be required, given the expressed intent of the MUTCD, is a procedure that would be used as part of an engineering study to estimate the likely impact on safety of a contemplated signal installation. This estimate could then be assessed in the light of estimates of the other impacts of signal installation -- delay, energy consumption, and so on using conventional engineering economic analysis. The proposed procedure for estimating the likely change in safety following the installation of signals at a stop controlled intersection under review is outlined below in a series of steps that need to be undertaken by an analyst in carrying out the engineering study. STEP 1: Assemble data and accident prediction models for stop-controlled and signalized intersections. For the past, say, 5 years, obtain the count of total, rear-end and right-angle injury accidents, - For the same period obtain or estimate the annual major and minor road AADTs, - Estimate the average annual major and minor road entering AADTs that would prevail for the period after the signal is installed, - Assemble required accident prediction models, with multipliers for each year of the analysis period. STEP 2: Use the empirical Bayes (EB) procedure with the data from Step 1 and the stop controlled intersection model to estimate the expected annual number of rear-end, right-angle and other injury accidents that would occur without conversion. (The EB estimate for other is the EB estimate for total minus the sum of the EB estimates for rear-end and right-angle.) STEP 3: Use the signalized intersection models in Table 4 and the volumes from Step 1 to estimate the expected number of rear-end, right-angle and other injury accidents that would occur if the intersection were converted. (The estimate for other is the estimate for total minus the sum of the estimates for rear-end and right-angle accidents.) STEP 4: Obtain for rear-end, right-angle and other accidents, the difference between the estimates from Steps 2 and 3. If there is a net decrease in total accidents, check that there is an expected decrease in right angle accidents and that this change is statistically significant for a signal to be warranted. If there is a net increase in total accidents, check that there is an expected increase in rear-end accidents and that this change is statistically significant. STEP 5: Applying suitable severity weights and dollar values for rear-end, right-angle and other accidents, obtain a net benefit of signal installation. STEP 6: Compare against the cost, considering other impacts if desired, and using conventional economic analysis tools. Illustration A 4-legged stop-controlled intersection, similar to an actual one in the database, with data from January 1996 to August 2000, is being considered for signal installation. Data and results of the analysis for all injury accidents combined are displayed in Table 8. Similar data and calculations were prepared for the analysis of rear-end and right angle crashes but only summary results of that analysis will be presented here. It should be emphasized that the calculations, though seemingly complex, can be greatly simplified with the use of a spreadsheet than can be developed with minimal resources. This would avoid the need to apply resource-saving

Persaud, McGee, Lyon & Lord 10 shortcuts, such as using average values to represent all years, and has the significant added advantage of setting up the calculations for a proper before-after safety evaluation if the signal actually gets installed. It should also be stressed that the data needs are not extensive. Table 8: Summary of Data and Example Calculations for ALL Injury Crashes 1) Year (y) 1996 1997 1998 1999 Jan- Aug 1999 (Signal) 2000 2) Crashes in year (X) 4 6 3 6 4 Sum = X b = 23 3) MAJAADT 41309 42169 43460 43891 44321 48441 4) MINAADT 3596 3671 3783 3821 3858 4295 5) Recalibrated α 10-4 4.26 4.40 4.01 4.20 4.36 4.30 6) Parameter K 2.30 2.30 2.30 2.30 2.30 3.1 7) Model Prediction E{κ y } 2.897 3.049 2.858 3.021 2.110 3.337 8) C i,y = E{κ y }/ E{κ 99 } 0.959 1.009 0.946 1 0.698 1.105 9) Comp. Ratio for period Sum = C b = 4.613 C a =1.105 10) Expected annual crashes without signalization (and variance) [based on last full year (1999)] κ(99) = C a (k+x b )/{[K/E{κ 99 }]+C b } = 1.105(2.30 + 23)/{(2.30/3.021) + 4.613) = 4.679 Var{κ(99)} = C a (K+X b )/[{K/E{κ 99 }+C b } 2 ] = 0.865 11) Expected annual crashes after signalization (and variance)[from model in Table 4 (based on 1999)] E{κ 99 } signal = exp(-5.751)(48441) 0.4911 (4295) 0.1975 = 3.318 Var{κ 99 } signal = E{κ 99 } 2 /K = 3.318 2 /3.1 = 3.551 STEP 1: Assemble data and accident prediction models Accident data The counts of all injury accidents in each year of the analysis period are shown in the second row of Table 8. AADT data Entering volumes for the major and minor roads are estimated for each year using suitable methods applied locally and are entered in the 3 rd and 4 th rows of Table 8. It is recognized that actual counts are typically not available for each year; however, in most jurisdictions trend factors are available that could be applied to estimate AADTs for each year. More formal and accurate methods for estimating missing AADTs (10) are available can be applied as was done for this project. A separate process can be used to provide the best estimate of the AADT after signalization, considering traffic that might be generated to the intersection in the future. In the absence of such an estimate, the AADT expected after signalization can be assumed to be same as that in the last year. Accident prediction models For this example, these are required for all, rear-end and right angle accidents (Note that the illustration presented only applies to the first type.) at 4-legged stop-controlled intersections for each of the years 1996 to 2000 and for signalized four-legged intersections for the last full year,

Persaud, McGee, Lyon & Lord 11 in this case 1999. Ideally each jurisdiction would have its own set of applicable models. Recognizing that this desideratum is not achievable in most cases, at least at present, default base models provided earlier can be used. For 4-legged stop controlled intersections, the default base models are shown in Table 2 while those for signalized intersections are shown in Table 4. For example the default base model for all injury accidents at 4-legged stop controlled intersections is: Accidents/year = α (Major Road AADT) b (Minor Road AADT) c where α, b, and c have calibrated values of 0.000426 (that is, e -7.76 ), 0.499 and 0.430 respectively. It is recommended that these models be recalibrated for each jurisdiction and for each year of the analysis period. The recalibration procedure is presented in (4) and has recently been tested by Persaud et al. (10). To apply this procedure requires yearly accident counts and AADTs for a sample of 4-legged stop controlled intersections in the jurisdiction that are typical of those that tend to be considered for signal installation. The default base model is first used to estimate accidents each year for each intersection in the sample. For each year, the sum of the observed counts divided by the sum of the model estimates gives a calibration factor that is applied as a multiplier to the model to obtain a recalibrated value of α. These recalibrated values of α are shown in row 5 of Table 8. A similar recalibration process was done to adjust the α parameters for rear end and right angle crashes and could be done for signalized intersections for the year 1999. In this example, it is assumed that this adjustment was not necessary for the signalized intersection model. The value of the calibrated parameter K that is used in the analysis is taken from Table 2 and shown in row 6 of Table 8. STEP 2 a) Estimate the expected number of accidents each year using the recalibrated prediction model. For example, for 1996, E{κ 1996 } all = 0.000426(41302) 0.499 (3596) 0.430 = 2.897 These estimates are shown in row 7 of Table 8. Note that for the last year, an estimate is also done for the anticipated volumes if the intersection were to be signalized (still using the stop controlled model). b) Calculate the comparison ratio (C i,y ) of the model estimate for a given year divided by the model estimate for 1999. These ratios are shown in row 8 of Table 8 and summed in row 9. c) Using the values in the previous rows and the formula shown in the Table 8 estimate the expected annual number of accidents without signalization (and its variance) for the last full year (1999). The values, shown in row 10 of Table 8, are κ(99) all = 4.679; Var{κ(99) all } = 0.865 Similar calculations (not shown) yielded κ(99) right angle = 1.885; Var{κ(99) right angle } = 0.248 κ(99) rear-end = 0.527; Var{κ(99) rear-end } = 0.053

Persaud, McGee, Lyon & Lord 12 STEP 3 Use the signalized intersection model from Table 4 to estimate the number of accidents in the base year if the intersection were signalized, using the expected annual AADTs after signalization (shown in the last column of Table 8). (Recall that, for this example, it was assumed that a recalibration of this default base model was not required.) This calculation yields E{κ 99 } signal/all = exp(-5.75)(48441) 0.491 (4295) 0.198 = 3.318 Var{κ 99 } signal/all = 3.551 Similar calculations produced E{κ 99 } signal/right-angle = exp(-3.77)(48441+4295) 0.329 [4295/(48441+4295)] 0.245 = 0.443 Var{κ 99 } signal/right-angle = 0.115 E{κ 99 } signal/rear-end = exp(-10.99)(48441+4295) 1.059 = 1.688 Var{κ 99 } signal/rear-end = 1.187 STEP 4 a) Estimate the change in accidents per year if signals were to be installed at the intersection. Total = 4.679 3.318 = 1.361 (decrease) Rear-end = 0.527 1.687 = -1.160 (increase) Right-angle = 1.885 0.443 = 1.442 (decrease) Other = 1.361 (-1.116 + 1.442)= 1.035 (decrease) b) Test for significance of the changes in major accident types. If there is a net decrease in total accidents, check that there is an expected decrease in right angle accidents and that this change is statistically significant. If there is a net increase in total accidents, check that there is an expected increase in rear-end accidents and that this change is statistically significant. If the expected changes do not materialize or are not statistically significant at the 10% level, then safety should not be used in evaluating the impacts of signalization In this case there is net decrease in total accidents and an expected decrease of 1.442 right angle accidents/year. The variance of this change can be taken as the sum of the variances of the numbers that yielded this value. = Var{κ(99) right angle } + Var{κ(99) signal/right angle } = 0.248+0.115 = 0.363 The standard deviation is 0.602, which means that the decrease of 1.442 is statistically significant since a value of zero lies outside of 1.64 standard deviations (for a 10% significance level). A more precise test can be conducted using a more sophisticated procedure that is outlined in (12). STEP 5 Consider the relative severities and costs of rear-end, right angle and other injury accidents. The best published information we have on severity weights at the moment for accidents types of interest is a 1998 paper (13) that reported the costs per collision for various accident types and locations. The costs given for multiple vehicle intersection accidents were used to estimate an average cost for right-angle, rear-end and other accidents, as defined for this project. This reestimation of accident costs and conversion to 2002 values produced costs per accident of $60,000, $25,000 and $40,000 for right-angle, rear-end, and other respectively. Using these numbers, the estimated net annual benefit of signal installation at this intersection is: 1.442(60,000) + 1.035(40,000) 1.160(25,000) = $ 98,920

Persaud, McGee, Lyon & Lord 13 STEP 6 Compare the cost of signal installation against the benefits, considering operational benefits as well. How this is done, and in fact whether it is done, is very jurisdiction-specific and conventional methods of economic analysis can be applied after obtaining estimates of the economic values of changes in delay, fuel consumption and other impacts. The results of the engineering study may indicate that signal installation is justified based on a consideration of safety benefits. This should not be taken to mean that a signal should be installed, since: a) Other measures may have higher priority in terms of cost effectiveness, considering the MUTCD's requirement of the "adequate trial of less restrictive remedies". b) The safety benefits may need to be assessed in the light of other signal installation impacts. c) Other locations may be more deserving of a signal installation. In other words, the results of the engineering study should be fed into the safety resource allocation process. FURTHER DEVELOPMENT The suggested procedure could be enhanced with the application of better accident prediction models as they become available. It was already mentioned that individual jurisdictions may estimate their own models, or at least, estimate an adjustment factor for the default models. Major research efforts are underway that would provide better models in the not too distant future. These include major FHWA research projects for IHSDM and for the development of a Comprehensive Highway Safety Improvement Model (CHSIM, now called SafetyAnalyst) and NCHRP research related to the development of a Highway Safety Manual such as a new project, NCHRP 17-26: Methodology to Predict the Safety Performance of Urban and Suburban Arterials. ACKNOWLEDGEMENT The authors wish to acknowledge the guidance and patience of the panel for NCHRP 17-16, in particular Ray Derr, the NCHRP staff liaison. Some of the fundamental research on which the paper is based was supported by an operating grant (to Persaud) from the Natural Sciences and Engineering Council of Canada (NSERC). This support is gratefully acknowledged as is the assistance of staff in the jurisdictions in which data were collected.

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