Safety Evaluation of Corner Clearance at Signalized Intersections

CHAPTER 3. STUDY DESIGN

While the current state-of-the-art method for developing high-quality crash modification factors (CMFs) is to employ an Empirical Bayes before–after study design, several factors can preclude its use. One of these factors is the availability of treatment information, including the installation date and location for the treatment of interest. For strategies such as closing or opening an access point (driveway) and changing the corner clearance, there is often insufficient information to determine the exact timing of the treatment. Obtaining records of traffic and crashes before and after the change is likely infeasible. Using FHWA’s A Guide to Developing Quality Crash Modification Factors, the research team determined that a rigorous cross-sectional study design would serve as a suitable alternative.⁽⁴⁾ The following study design considerations include steps to account for potential biases and sample size considerations in cross-sectional analysis.

ACCOUNTING FOR POTENTIAL ISSUES AND SOURCES OF BIAS

An observational cross-sectional study design is a type of study used to analyze a representative sample at a specific point in time. The researcher estimates the safety effect by taking the ratio of the average crash frequency for two groups, one with the feature of interest and the other without the feature of interest. The feature of interest could also be a continuous variable, and the safety effect is estimated based on the predicted crash frequency at different values of the variable representing the feature of interest. In this case, the feature of interest is the corner clearance. For this method to work, the study sites should be similar in all regards except for the feature of interest. In practice, this is difficult to accomplish, and researchers typically use multivariable regression models to estimate the safety effects of the feature of interest while controlling for other characteristics that vary among sites.

Multivariable regression models use explanatory variables, such as geometric and operational characteristics, to predict a response variable, such as frequency of crashes. While cross-sectional models provide a means to estimate the safety effects of treatments, these models are susceptible to a number of biases that researchers should account for during sampling and modeling. The research team identified the following issues and biases from the Recommended Protocols for Developing Crash Modification Factors that are potentially applicable to this study.⁽⁵⁾ A list of general issues with safety evaluations is provided in the next section, followed by a list of potential biases specific to cross-sectional studies. The research team made an effort to address all applicable biases.

General Issues

• Measure of effectiveness. Direct measures of safety effectiveness, including crash frequency and severity, are preferable over surrogate measures. This study employed a crash-based analysis to evaluate the safety impacts of corner clearance at signalized intersections.
  
  
• Exposure. Neither crash frequency nor severity alone provides adequate information to determine the safety effectiveness of a particular design feature. Exposure is an important factor in assessing crash risks. This study used traffic volumes on the major and minor roads (i.e., total entering volume) of each intersection as explanatory variables.
  
  
• Sample size. Crashes are rare and random events. It is necessary to include a sufficient number of sites and/or years in the study sample with enough crashes to develop a valid relationship between the treatment and safety effect. The following section, Sample Size Considerations, presents a lengthier discussion of sample size for this study.
  
  
• Site selection bias. In highway safety, transportation departments often select sites for treatment based on need. In other words, sites with the highest crash frequency, severity, or potential for improvement are addressed first. When countermeasure evaluations use these sites exclusively, the results of the evaluation are only applicable to sites with similar safety issues. The research team selected sites for this study based on the intersection type of interest (i.e., four-leg, signalized intersections) with various corner clearance and geometric characteristics, rather than crash experience. The research team used propensity score matching, discussed later in this chapter, to select suitable reference sites and to help to mitigate potential site selection bias.
  
  
• Crash data quality. There is no national standard for crash data reporting. Although many States adopt some or all of the Model Minimum Uniform Crash Criteria data elements, there is a lack of uniformity in crash data across jurisdictions, and most crash data are susceptible to issues with data quality and timeliness. It is necessary to account for these types of issues in the study design and analysis. For example, if the reporting threshold varies among States in the study, and crash data from those States are aggregated in modeling, then the analyst should account for the difference in thresholds. The data used in this research are from the Highway Safety Information System (HSIS) database, which ensures a higher level of quality control and documentation in each participating State than data obtained directly from State agencies.

Issues Specific to Cross-Sectional Models

• Control of confounding factors. Confounding factors are significant predictors of the response variable and are associated with the treatment in question. Driveways near the corners of signalized intersections are often present at higher traffic volumes, but they are not a consequence of higher volumes (e.g., gas stations, businesses in high-traffic areas). Traffic volume is also a significant predictor of crashes and is, therefore, a potential confounding factor. Consequently, the model accounts for it as an independent variable. While difficult to control for all potential confounding factors, the research team considered and addressed these factors to the extent possible in the study design and evaluation. The research team used propensity score matching, discussed later in this chapter, to select suitable reference sites and to help to mitigate potential confounding effects.
  
  
• Omitted variable bias. It is difficult to account for the potential effects of omitted variable bias in an observational cross-sectional study such as this. The research team addressed omitted variable bias to the extent possible by carefully considering the roadway and traffic characteristics that the models should include. With the rich data in HSIS, the research team tested a wide range of variables in the models and selected suitable variables for the final models. There was some potential for omitted variable bias due to other factors the models do not include directly, such as weather, driver population, and vehicle fleet. The results of this research indicate that factors relating to corridor operations may have improved the models.
  
  
• Selection of appropriate functional form. The research team applied generalized linear modeling techniques to calibrate crash prediction models. The research team specified a log-linear relationship using a negative binomial error structure, following the state of the art in modeling crash data. The negative binomial error structure is recognized as more appropriate for crash counts than the normal distribution used in conventional regression modeling. The negative binomial error structure also has advantages over the Poisson distribution, allowing for overdispersion that is often present in crash data.
  
  
• Correlation among independent variables. Correlation refers to the degree of association among variables. A high degree of correlation among the predictor variables makes it difficult to determine a reliable estimate of the effects of specific predictor variables. The research team examined the correlation matrix to determine the extent of correlation among independent variables and used it to prioritize variables for inclusion.
  
  
• Overfitting of prediction models. Overfitting is related to the concept of diminishing returns. At some point in the analysis, adding additional independent variables to the model is unnecessary because they do not significantly improve the model fit. Overfitting also increases the opportunity to introduce intercorrelation between independent variables. The research team considered several combinations of predictor variables and employed relative goodness-of-fit measures to penalize models with greater estimated parameters.
  
  
• Low sample mean and sample size. The research team dismissed low sample mean as a potential issue as many sites had experienced one or more crashes during the study period. The research team addressed sample size through preliminary sample size estimates (see Sample Size Considerations) and during the early stages of the study and analysis.
  
  
• Temporal and spatial correlation. Temporal correlation may arise if a study uses multiple observations for the same site. In this study, the research team aggregated 3 years of data into a single observation at each site. The research team dismissed temporal correlation as a potential issue as a result. Spatial correlation was a potential issue. To help account for spatial correlation, the research team selected the sample corridors from various regions of California to achieve diversity of sites with respect to weather, topography, and driver population.
  
  
• Endogenous independent variables. Endogeneity occurs when one or more of the independent variables depend on the dependent variable. For example, States may install left-turn lanes due to the frequency of left-turn crashes at an intersection, and thus their presence depends on crash frequency. The potential concern in an observational cross-sectional study is incorrectly associating treatments with higher crashes when compared with sites where the treatments are absent and may be prone to lower crash frequency. The research team used propensity score matching, discussed later in this chapter, to select suitable reference sites and to help to mitigate potential endogeneity issues.

SAMPLE SIZE CONSIDERATIONS

For crash-based studies, the total number of crashes is the primary measure of sample size, rather than sites or years. However, including a sufficient number of sites and years in the study is necessary to attain an adequate sample of crashes. Further, selecting sites based on features of interest, and not crash history, is important to minimize the potential for site selection bias and increase the applicability of the results.

The number of locations required for multivariable regression models depends on a number of factors, including the following:

• Average crash frequency.
• The number of variables desired in a model.
• The level of statistical significance desired in a model.
• The amount of variation in each variable of interest across sample sites.

The determination of whether or not the sample size is adequate can only be made once preliminary modeling is complete. If the variables of interest are not statistically significant, then more data are required to detect statistically significant differences, or it is necessary to accept a lower level of confidence. Estimation of the required sample size for cross-sectional studies is difficult, and it requires an iterative process, although through experience and familiarity with specific databases it is possible to develop an educated guess.

Table 2 presents the average crashes per site-year for the sample sites by number of approach and receiving corners with clearance less than 50 ft. The 275 sites represent nearly 1,225 total crashes per year and are reasonably representative of the range of site characteristics at four-leg, signalized intersections. While there was no formal stratification of the data by site characteristics during site selection, the research team included sites with a range of traffic volumes and other characteristics among sites to increase the practical applicability of the results. This sample data are likely sufficient to develop reliable cross-sectional models. The information in table 2 should not be used to make simple comparisons of crashes per year between different groups, since it does not account for factors, other than the strategy, that may cause a change in safety between groups. Such comparisons are properly done with the regression-based analysis, as presented later.

Table 2. Crashes per site-year from data collection sites.

PROPENSITY SCORE MATCHING

In experimental studies, researchers select a sample from the reference population and apply the treatment randomly to one group while leaving another group untreated for control purposes. Using this approach, the treatment and control groups are similar, and the only difference is the presence of treatment. This helps to ensure the treatment effect does not include effects due to other differences between the two groups.

In observational studies, it is desirable to replicate the random assignment of treatment while accounting for the fact that States often select sites for treatment based on safety and operational performance measures. Matching treatment and reference sites that have similar characteristics helps to reduce the potential for site selection bias and confounding factors. Selecting reference sites that are geometrically and operationally similar to treatment sites provides a more reliable comparison in cross-sectional studies, and propensity score matching is a rigorous approach to match treatment and reference sites.

This study employed propensity score matching to select reference sites that closely match the treatment sites in terms of general site characteristics. Propensity score matching was based on regression modeling. The research team developed a regression model to estimate scores (i.e., the probability of treatment or nontreatment) for all treatment and non-treatment sites based on site characteristics. The research team then used propensity scores to select reference sites most comparable with treatment sites for forming the study sample. Detailed discussions of propensity score matching and its application in traffic safety research are available in papers by Rosenbaum and Rubin, and Sasidharan and Donnell.^(6,7)

It is important to note that in this study there were no “treated” or “untreated” sites. The “treatment” of interest in this study was corner clearance at signalized intersections, and its value varies. Therefore, the terms “treatment,” “treated,” and “untreated” are all nominal, and the discussions related to these terms need to be considered in that context. A group of intersections with similar values for corner clearance was considered “treated” and the rest “untreated.” Specifically, intersections with at least one corner with a clearance less than 50 ft on the mainline belonged to the treatment group (treated), while those with no corners with a clearance less than 50 ft on the mainline were considered the reference group (untreated).

The research team implemented this process in an effort to group intersections with similar corner clearances in the same category. This process also allowed the research team to use the propensity score matching technique to account for differences among sites with corner clearances less than 50 ft and sites with corner clearances greater than 50 ft. Moreover, the process allowed the research team to explore additional corner clearance distances as potential cutoff points for separating the dataset into two categories and applying the propensity score matching. Therefore, the research team tested the following corner clearance distances: 50, 75, 100, 150, 250, and 500 ft.