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Publication Number: FHWA-HRT-05-048
Date: April 2005

Safety Evaluation of Red-Light Cameras

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VIII. Study Methodology for Economic Analysis

As noted, two experimental plans were developed for this study. The first, described in detail in the preceding sections, was aimed primarily at examining changes in crash frequency resulting from the installation of RLC systems. The second experimental plan involved development of a database and methodology to examine the costs and benefits of RLCs in economic terms, thus allowing changes in crash severity and frequency to be analyzed simultaneously and identification of factors associated with the greatest RLC benefits.

The use of economic analysis in the study of RLCs is important because of the nature of the expected effect of the treatment. Based on past research, RLCs probably will lead to decreases in right-angle crashes, for which injuries are often severe, and increases in rear end crashes, for which injuries tend to be less severe. It is also possible that within each of these crash types, the average level of injury severity is different with and without RLCs; therefore, it is probable that an evaluation of the economic benefits could result in a different conclusion about the effect of RLCs than might result from an analysis of changes in crash frequency by crash severity (e.g., the examination of changes in the frequency of injury crashes). Gaining a handle on the economic benefits is also important from the perspective of being able to assess cost-effectiveness of RLCs and to compare this against the cost-effectiveness of other safety treatments aimed at reducing crashes at signalized intersections.

To combine changes in both crash frequency and injury severity, each crash can be characterized by one measure-a dollar value based on the average level of injury severity for that type of crash. After that conversion is done, the results of the analysis can be reported in terms of changes in total economic cost of crashes expected without RLCs and those that actually occurred in the period after RLC installation. The unit crash costs can then be applied to the crash frequencies recorded after RLC implementation and those expected without RLC as estimated by the empirical Bayes method being used for evaluation.

The key is the successful conversion of police-reported crash injury levels to a set of acceptable dollar-cost measures. As described in the following sections, the team explored different alternatives for this economic conversion and then worked with FHWA to define a final study design.

Initial Economic Analysis Study Design

In Charlotte, NC, there were accessible files of hospital and emergency room data that could be linked to traffic crashes, the initial discussion of an economic analysis study design centered on using these linked data. After further thought and exploration, it was clear that the possible use of these data raised a number of critical issues:

  • The available database covers only one of the two major hospitals in the catchment area, meaning that information for the remaining patients in the other hospitals would need to be estimated. That is, it must be assumed that there are no shifts from one hospital to the other between the before-and after-period, and that the medical cost changes seen in one hospital would be similar in the other hospital.)
  • The database would not include information on nonhospitalized fatalities or on nonhospitalized occupants experiencing either lesser injuries or no injuries. Because the proportion of car crash occupants who are hospitalized is a small proportion of the total crash-involved population, costs for the nonhospitalized groups would need to be developed from other sources.
  • Most important, the economic data available in the database to be linked with crashes would contain only medical/hospital costs, which is only one component of either human capital cost or comprehensive cost.

FHWA agreed that the issues were significant, and it required that a feasibility study be conducted to determine if these issues could be overcome.

The following section describes the results of this exploration.

Examination of Alternative Economic Analysis Methods

The research team identified the following major issues that require resolution to successfully conduct an economic study:

  • RLC systems potentially could affect the full injury distribution from fatally injured to no injury; thus, the economic cost chosen must cover this complete distribution.
  • Hospital-related data (even that including costs for emergency room visits in addition to hospital admissions) include perhaps 15 percent of the total crash population. The data do not include information on those who die before reaching the hospital nor those whose injuries do not require hospital or emergency room treatment.
  • Medical costs most likely to be captured by hospitals are only one element of the total cost of crashes. Other elements such as lost work productivity, rehabilitation costs, insurance cost, quality of life losses, and others are not captured in medical cost data.
  • As requested by FHWA, data on both "comprehensive costs" (including "willingness to pay" costs related to pain and suffering) and "human capital costs"[4] (including many other economic elements, but not "pain and suffering") should be considered in this analysis.
  • Research conducted by and for the U.S. Department of Transportation (DOT) National Highway Traffic Safety Administration (NHTSA) has provided a detailed analysis of human capital costs for motor-vehicle crash victims in terms of Year 2000 dollars. Unfortunately, these costs are keyed to injury severity levels defined by the Abbreviated Injury Scale (AIS) rather than by the KABCO[5] scale found in police reports, which will be the basic data being provided by the participating localities for this evaluation.
  • There has been no conversion from AIS-based cost to KABCO cost for FHWA since 1994. There is agreement that the updating of the 1994 data to current year costs using changes in the Consumer Price Index would not be sufficient because these costs would not be consistent with the current NHTSA research nor current economic cost for fatalities being used by other federal agencies, and the 1994 costs did not include costs for each of the levels of the KABCO scale, only for "injury."(25) Because RLCs may cause tradeoffs in injury severities within the injury category (e.g., a decrease in serious injuries and an increase in minor injuries), these 1994 costs are not considered sufficient for this study.

Given these issues, the team explored two alternative approaches that led to exploring two databases containing information on the economic costs of motor vehicle crashes.

Analysis of the Economic Benefits of RLCs Using Maryland CODES Data:

First, an attempt was made to find hospital and emergency room cost data similar to that originally proposed from Charlotte. Information on NHTSA's Crash Outcome Data Evaluation Systems (CODES) project was examined on the current CODES Web site. There are no CODES projects in either California or North Carolina, but the State of Maryland has one, where three of the test cities are located. E-mail and telephone discussions were held with the database engineer for the National Study Center for Trauma and EMS, University of Maryland-Baltimore, the current Maryland CODES coordination agency. This group has data on all motor vehicle crashes reported to the State of Maryland beginning in the early 1990s, including nonhospitalized injury and property-damage-only (PDO) crashes. For a typical CODES analysis, the crash data are linked to hospital discharge data or emergency room data, or both, based on a probabilistic match of variables linking the crash to hospital admission or emergency room visit records. Medical cost data can then be extracted for each driver of each vehicle and linked with the crash data. The project team requested data files from the CODES administrator for all linked and unlinked crashes occurring in Howard and Montgomery Counties and Baltimore City for the period of 1994-2001. After discussions with the administrator, the CODES Advisory Committee overseeing the Maryland data granted approval for the request and data were prepared and sent to the project team.

If these Maryland CODES data were used in the economic analysis, they would provide more complete, but similar data to that of the Charlotte source. While slightly more difficult to work with than the Charlotte-linked data, these data include all hospital admissions and emergency room visits (at least, all that can be linked) rather than just those for one hospital, as was the case in Charlotte.

However, the same problems with the Charlotte study were present in the Maryland data. The only cost data available are medical costs. After again considering how other cost items could be added to the data set, such as how to add costs for lost productivity, perhaps from NHTSA data based on the AIS level of injury, the authors concluded that this study approach was not sufficient.

Economic Benefits Analysis of RLCs Using Pacific Institute for Research and Evaluation Comprehensive Cost Data:

As noted earlier, the key to this economic analysis effort is to assign a human capital or comprehensive crash cost to each relevant crash in a test city. If accomplished, the economic analysis could be conducted in each of the seven cities rather than in just one, as originally envisioned. Because the city data are based on police-reported KABCO injury scales, this could be done only if AIS-based comprehensive cost could be mapped to the KABCO scale with suitable precision. That mapping became the goal of the efforts.

Dr. Ted Miller of the Pacific Institute for Research and Evaluation (PIRE), a leading U.S. expert on economic costs for motor vehicle crashes, developed the earlier KABCO-mapped comprehensive costs for FHWA. Because of this, the project team initiated a detailed review of his more recent publications related to this topic. Subsequent discussion with Miller indicated that it was feasible to update the mapping. In addition to providing comprehensive costs for this RLC study, the proposed approach would result in KABCO-mapped costs that could be used by FHWA in future evaluations and problem analysis efforts.

In a 1997 article, Miller et al., used National Automotive Sampling System (NASS) Crashworthiness Data System (CDS) files, Fatal Analysis Reporting System (FARS) data, and General Estimates System (GES) data to develop an estimate for the total direct cost (not human capital or comprehensive costs) and years of functioning life lost for occupants involved in 30 different crash geometries (e.g., cross-path crashes at signalized intersections).(27) While comprehensive costs were not calculated directly, it is noted that "years of functioning life lost" is a measure that can be converted to comprehensive costs, combining human capital direct and indirect costs with pain and suffering costs, as discussed in appendix A of the earlier cited report.(25) Miller's goal was to better identify the highest cost geometries, and thus the ones to best target for treatment efforts. Because direct (and comprehensive) costs can be developed for AIS levels, his approach involved developing such occupant-based costs for each AIS level in each of the 30 different crash geometries. The NASS-CDS files contained the AIS level for each occupant; however, because the FARS and GES data to be used in the national estimates do not include the AIS level, Miller had to map his AIS costs to KABCO levels. Because a KABCO rating from the original investigating police officer was also included for each occupant in the NASS CDS file, the occupant-injury cost of each level on the KABCO scale within each geometry could also be calculated. Because current CDS files do not contain crashes involving nontowaway vehicles or pedestrians, the old NASS files were used to fill in these missing data. Then, using national crash-occupant frequencies within each KABCO level for each of the 30 crash geometries based on GES and FARS data, Miller et al., produced an estimate of the total national direct cost for each geometry.(27)

While this current project's goal was not to produce such national estimates of cost by crash geometry, there was the critical need for human capital and comprehensive cost for each KABCO level within certain intersection-related crash geometries (e.g., right-angle crashes at signalized and stop-controlled intersections). Thus, it appeared logical that Miller could use his data to produce such estimates.

Possible Study limitations in Miller's Dataset:

Three critical study limitations based on files available to Miller were identified by the project team before the development of the final data request: (a) sample size limitations in the NASS and CDS crash files to be used, (b) whether available variables in the Miller files would allow further classification of crash geometry by urban and rural crash location, and (c) whether Miller's earlier occupant-based cost findings could be converted to costs per crash within each geometry of interest.

The possible sample size limitations in NASS files containing both AIS and KABCO injury scaling arose from the need to estimate cost for each KABCO level within each of the more than 30 crash geometries, further categories by urban versus rural crash location. Such detailed estimates had never been attempted before, and low sample sizes could result in both unstable and illogical findings. As indicated later, such problems did arise.

Second, Miller's earlier analysis did not separate crash geometries by urban and rural location or by speed limit. Because KABCO levels are much broader than AIS levels, the cost of injury within any KABCO level for a given crash geometry might differ depending on speed limit or urban and rural location. For example, the severity and thus the cost of A-injury angle crashes at rural higher-speed intersections may be greater than A-injury right-angle crashes at urban intersections. Given this fact, it was desirable to further categorize Miller's 30 geometries by either speed limit or urban and rural location.

Unfortunately, examination of documentation for the databases to be used by Miller indicated no urban and rural indicator in one of the critical files; however, speed limit variables were present. The team then used FARS, NASS, GES, and Highway Safety Information System (HSIS) data from two states to compare crash-related speed limits to various urban versus rural designations. There was significant overlap of limits within urban and rural designations in all three files. Based on the distributions and the need to have sufficient samples sizes in all the subcategories, a decision was made to attempt to categorize cost estimates by locations with speed limits of 72.42 km/h (45 mi/h) and slower versus 80.47 km/h (50 mi/h) and faster.

Third, the primary need in this study (and in future FHWA studies) is cost estimates per crash rather than per occupant. Fortunately, Miller's preliminary investigations indicated that cost per crash could be developed from the existing databases.

Possible Economic Study Limitations from Small Jurisdictional Samples of Crash Data:

This discussion is based solely on information available in Miller's databases; however, the choice of what economic analyses to conduct, and thus what specific cost categories to request from Miller, also depended on the nature of the database to be used in this RLC analysis-the sample size of crashes within different KABCO severity levels in the seven jurisdictions. Two significant issues deserve further attention.

First, in the initial analysis planning, the project team developed estimates of sample sizes necessary for analysis. The team then examined the total right-angle and rear end crash estimates and the injury right-angle and rear end crash estimates from each of the seven jurisdictions to determine if individual site-by-site analysis would be feasible. As shown in table 8, while each of the seven jurisdictions should provide adequate data for a "total crash" analysis, an "injury-crash" analysis may yield only statistically significant effects in two of the seven jurisdictions. This finding was based on combining all injury levels (K,A,B,C) in the latter analysis. Even there, five of the seven individual analyses may not yield significant effects.

In this economic analysis, the best methodology would be to assign a human capital or comprehensive cost to each occupant injury in each of the involved vehicles, and sum these to produce a total crash cost as the outcome variable. This requires assigning a cost to each level of injury, then subdividing the "combined injury" category in more detail. While the costs will be multipliers for each injury, and thus the magnitude of cost as the outcome variable will be much larger than the magnitude of individual injury crash counts, there remains the logical question of whether these small samples of individual injury-level crashes will support such an analysis. While the cost numbers will be large enough, the question is whether the sample is large enough to produce a stable measure of cost in the before-and-after periods for an individual site.

The second issue raised by the sample sizes within the RLC database is whether a cost should be assigned to each severity level, including fatalities, or should some levels be combined. The primary issue here is that even in right-angle crashes, fatalities will represent a small proportion of the total injury distribution (perhaps less than 2 percent). The comprehensive and human capital cost assigned to a fatality will always be multiples of cost for even an A-injury. The final analysis showed that the fatal crash costs were 10 to 30 times the A-injury crash costs within the same crash type; thus, one or two fatalities in either the before-or after-period for a given location could greatly affect the cost-related analysis. While this could be legitimate if one could expect repeated similar samples to have the same number of fatalities, this is not likely, particularly in samples this small. (It is also noted that Hall, in crash-cost research done for the State of New Mexico, argues that not only are such fatalities somewhat random in any crash sample, the main factors determining whether an injury is a fatality rather than a severe injury probably are not affected by roadway-related treatments. They are more likely to be related to factors such as occupant age, restraint use, and type and size of vehicles involved. He argues that such small numbers of fatalities should not be allowed to affect decisions on roadway-based treatments such as RLCs).(28)

The issue becomes whether to assign separate cost to a fatality and an A-injury or combine these two into one category (perhaps representing approximately 10 percent of the injury distribution in these crashes) and assign some type of "average K/A cost."

This same argument can be carried further, combining other categories of injury. Ultimately, this could result in an "average crash cost" (in a similar proportion-weighted manner) for each crash geometry. The cost would be assigned to a crash based on crash type rather than crash injury; however, this would assume that only the crash type frequencies (or ratios) change between before-and after- periods in the RLC evaluation, and that there is no internal shift in injury distribution within a given crash type. Right-angle crashes could be reduced, but it would be assumed that the severity distribution of the right-angle crash in the before-period is the same distribution as in the after-period. While this might be a good assumption based on a hypothesis that RLCs should not change the impact speed in right-angle crashes (because impact speed is a major predictor of crash severity), whether or not this is a good assumption is unknown. It can also be argued that red-light-running right-angle crashes targeted by RLCs tend to be at higher speeds than other right-angle crashes.

A final problem is that the reporting thresholds appear to differ across the seven jurisdictions. For example, PDO crashes are less likely to be reported in California sites and Howard County and Montgomery County, MD, than in Baltimore, MD, or Charlotte, NC. Given that PDOs are assigned a cost in this cost analysis, this differing threshold will lead to different economic outcomes across sites. The same will be true for the frequency analysis of total crashes. This factor will be taken into consideration when the results from different jurisdictions are compared, and when combination of the results is attempted.

Final Methodology for Economic Analysis

Types and Levels of Economic Cost Estimates

A number of issues are present in an attempt to measure the economic effect of RLC systems. Some occur because of a lack of current data on the human capital or comprehensive cost of a crash referenced to individual levels of the police-reported KABCO scale. Others occur because of the nature of the seven-jurisdiction database that will be used in this overall evaluation of RLCs, with available sample sizes of observations in each severity level for pertinent crash types (right-angle and rear end) being the most critical one. Given all these issues and uncertainties, and the fact that the same issues will arise in future FHWA studies, a decision was made to have Miller and the PIRE staff develop multiple levels of both comprehensive and human capital costs. The following levels were requested:

  • Level 1-For each of the 22 crash geometries (categorized by two speed limit categories as a surrogate for urban/rural), estimates of cost for crash severity levels K, A, B+C, and O. (Sample size issues in the cost databases made it impossible to develop reasonable estimates of B versus C separately.) This analysis was first done for each of the two speed limit categories, and then with all speed limits combined.
  • Level 2-For each crash geometry, estimates of cost when K and A are combined into one cost level and B and C are combined into one cost level - thus K+A, B+C, O. (Again, estimates were calculated with and without categorization by the two speed limit categories.)
  • Level 3-Allows for comparison of "injury" versus "noninjury" crashes. Some crash forms (and some reporting officers) define a "C- injury" as a "minor injury" while others define it as a "possible injury." Thus, two definitions of Level 3 costs were used:
    • - Level 3A-For each crash geometry (with and without speed limit categorization), estimates of cost when all injuries are combined into one cost level separated from the PDO cost level, thus K+A+B+C versus O.
  • Level 3B-For each crash geometry (with and without speed limit categorization), estimates of cost when K, A, and B injuries are combined into one cost level separated from the C and PDO cost levels, thus K+A+B versus C+O.
  • Level 4-For each crash geometry (with and without speed limit categorization), estimates of crash cost without regard to crash severity, in other words, no division by levels of severity.
  • Level 5-For each level of crash severity (with and without speed limit categorization), estimates of cost without regard to crash geometry.
  • Level 6-Level 5 cost estimates, but with the following categories: K+A, K+A+B, K+A+B+C, B+C, C+O.

Choice of Cost Levels

Because it was not feasible or necessarily desirable to conduct economic analyses at all these levels for each of the seven jurisdictions, a pilot economic analysis study using one jurisdiction was chosen. Charlotte, NC, data were chosen because Charlotte has a medium sample size that provides some knowledge of whether smaller and larger samples can be analyzed, and Charlotte data contain all KABCO crash levels, allowing a multilevel analysis. Here, four economic analyses were conducted, one for each of levels 1-4:

  • All KABCO levels within each geometry.
  • Costs for K+A, B+C, 0 within each geometry.
  • Costs for injury versus no-injury within each geometry (based on both definitions of "no injury").
  • "Urban costs" (those with lower speed limits) based on crash geometry only.

The outcomes of these four analyses were used to determine which level is most appropriate given the available sample sizes in the remaining six jurisdictions.

Economic Analysis Statistical Method

The general analysis methodology used to define the economic effects of the RLC program for a given jurisdiction closely parallels the methodology used for total crashes and injury-crash frequencies. Here, instead of the difference between the crashes "expected without treatment" versus "observed with treatment" in the after-period, the measure of effectiveness would be the difference between the net economic costs "expected without treatment" and "observed with treatment" in the after-period.

For simplicity, the theory is presented for estimating the change in crash costs over all treatment sites in a jurisdiction, for a specific crash type, aggregated over all KABCO subgroups (e.g., two subgroups K+A+B+C, O). The crash types of interest are right-angle, rear end, and other (i.e. other than rear end and right-angle). The following notation is used:

CostBi equals the cost of crashes in KABCO subgroup i actually occurring at the treatment sites in the before-period.

ΛcostA equals the cost of crashes actually occurring at the treatment sites in the jurisdiction in the after-period.

VAR{CostB} equals the variance of the cost of crashes in the before-period.

VAR{ΛcostA} equals the variance of the cost of crashes in the after-period.

ΠcostA equals the expected cost of crashes in the after-period over all treatment sites had there been no RLC (after correcting for regression to the mean and traffic volume and other differences between before-and after-periods).

VAR{ΠcostA} equals the variance of the expected cost of crashes over all treatment sites in the after period without RLC.

Bi equals the observed number of crashes in KABCO subgroup i over all treatment sites in the before-period.

Πi equals the expected number of crashes in KABCO subgroup i over all treatment sites in the after-period without RLC (after correcting for regression to the mean and traffic volume and other differences between before-and after-periods). These were derived for the crash frequency analysis presented by Persaud et. al using the empirical Bayes methodology.(2)

The estimated change in crash costs is

The equation reads capital letter phi subscript cost equals capital letter pi subscript cost A minus capital letter lambda subscript cost A.
(7)

The variance of change in crash costs is

The equation reads Var times open curly bracket capital letter phi subscript cost, close curly bracket equals Var times open curly bracket, capital letter pi subscript cost A, close curly bracket plus Var open curly bracket, capital letter lambda subscript cost A, close curly bracket.
(8)

The cost modification factor is

The equation reads theta subscript cost equals open parentheses capital letter lambda subscript cost A divided by capital letter pi subscript cost A, close parentheses divided by open parentheses VAR times open curly bracket, capital letter pi subscript cost A close curly bracket, divided by capital letter pi subscript cost A, superscript two, close parentheses, close bracket.
(9)

The variance of cost modification factor is given by

The equation reads VAR times open curly bracket theta subscript cost, close curly bracket equals theta subscript cost, superscript two times open curly bracket, open bracket VAR times open parentheses, capital letter lambda subscript cost A, close parentheses divided by capital letter lambda subscript cost A, superscript two, close bracket plus VAR times open parentheses, capital letter pi subscript cost A, close parentheses divided by capital letter pi subscript cost A, superscript two close bracket, close curly bracket divided by open bracket 1 plus open parentheses VAR times open curly bracket, capital letter pi subscript cost A, close curly bracket divided by capital letter pi subscript cost A, superscript two close parentheses, close bracket, superscript two.
(10)

Of interest at this point is how estimates were obtained for the four terms, ΛcostA, VAR{ΛcostA}, ΠCostA , and VAR{ΠcostA}. Following are the approximate methods used.

The value of ΛcostA (i.e., actual after crash cost) was estimated by summing the individual PIRE costs for each crash in the after-period over all treated intersections in the jurisdiction. The value of VAR[ΛcostA] was estimated by summing the variance for each individual cost of the crashes of interest in the after-period.

ΠcostA, (i.e., the expected after cost without treatment) was estimated for a KABCO subgroup by first estimating an expected cost for each site as the product of Πi (i.e., the expected number of crashes in the KABCO subgroup) and the PIRE unit economic cost for the crash type, KABCO subgroup, and speed limit category. These were then summed over all treatment sites and KABCO subgroups to get ΠcostA..

VAR{ΠcostA} for each site and subgroup was taken as product of Πi and the PIRE unit variance for the crash type, KABCO subgroup, and speed limit category. These variances were then summed over all sites and KABCO subgroups. This is an approximation that likely underestimates the variance, considering there is variance in the EB estimates of the expected number of crashes without treatment; however, the PIRE unit cost variances are also approximations because they do not include all components (e.g., variance in medical costs by diagnosis). Fortunately, the point estimates of the economic effects, which are of primary interest in this analysis, are quite insensitive to VAR{ΠcostA}.

As noted, the theory so far applies for a given crash type of the three comprising all crashes. To obtain estimates of economic effect for all crash types combined, ΛcostA, VAR{ΛcostA}, ΠCostA, and VAR{ΠcostA} are first determined for each crash type as outlined and then summed over the three crash types before applying equations 7 to 10.

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