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                        Synthesis of Methods for Estimating Pedestrian and Bicyclist Exposure to Risk at Areawide Levels and on Specific Transportation Facilities


            
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                Chapter 2. Definitions and Concepts
This chapter summarizes basic definitions and concepts for risk and exposure, and then discusses these terms in the context of pedestrian and bicyclist safety analysis. It is important to define these terms and related concepts in the early stages, such that subsequent development work in this project has a clear and unambiguous foundation.

The following discussion draws from key research articles and papers written about risk and exposure in the past 40 years. The published literature on risk and exposure is vast and extensive, as Hauer indicates in his discussion to a published article (Molino 2009):

“The number of papers and books written about the concept of exposure can fill a large bookcase. It is an elusive and controversial concept.”

Defining Risk

In the literature, risk and exposure are fundamentally related but have specific individual meanings. Also, several authors provide theoretical definitions of risk or exposure that are challenging to put into practice. In some cases, these or other authors have provided an operational or working definition to complement the theoretical definition. The following discussion will differentiate between theoretical and operational definitions.

Most authors agree on the theoretical definition of risk as a measure of the probability of a crash to occur given exposure to potential crash events. Specifically, risk has been defined as:

“...conditional probability that an accident occurs given the opportunity for one.” (Chapman 1973)
	“...a measure of the probability of a potential accident event resulting in an accident.” (Cameron 1979)
	“... the probability (chance) of accident occurrences in a trial”, where a trial corresponds to a unit of exposure, such as a defined time spent walking or a defined number of street crossings. (Hauer 1982)
	“...probability of an accident happening in a particular road environment.” (Bly et al. 1999)
	“...the probability that a pedestrian-vehicle collision will occur, based on the rate of exposure.” (Raford and Ragland 2004)
	“Probability of collision/injury/fatality per unit of exposure.” (Greene-Roesel et al. 2007)Relationship of Risk to Exposure

The relationship between risk and exposure is implied in some definitions, but more explicit in others; exposure is a normalization factor (i.e., denominator) to equalize for differences in the quantity of potential crash events in different road environments. There is general agreement in the literature on this relationship between risk and exposure.Â  For example, consider the following (most of which are operational definitions of risk):

Formula. Risk is defined as the number of pedestrian accidents divided by pedestrian accident exposure. (Cameron 1982)
	Formula. Risk is defined as the expected number of accidents by severity divided by exposure. (Hauer 1982)
	Formula. Risk is defined as the number of casualties divided by exposure. (Keall 1995)
	Formula. Risk is defined as the number of crashes divided by exposure. (Molino et al. 2009)Defining Exposure

In the literature, most theoretical definitions of exposure are similar, in that exposure is a measure of the number of potential opportunities for a crash to occur. Specifically, exposure has been defined as:

“...number of opportunities for accidents of a certain type in a given time in a given area...” (Chapman 1973)
	“...number of potential accident events, i.e., an event involving a pedestrian and a vehicle which is a pre-condition of a collision between them, but does not necessarily result in such.” (Cameron 1982)
	“...a [probabilistic] trial... the results of such a trial is the occurrence or non-occurrence of an accident (by type, severity, etc.).” (Hauer 1982)
	“...being in a situation which has some risk of involvement in a road traffic accident, a risk which theoretically can be measured for both active and passive elements of the traffic system.” (Wolfe 1982)
	“...a condition which must be present in order to have an accident.” (Tobey et al. 1983)
	“...measure of the opportunity for accidents to occur...” (Bly 1999)
	“...rate of contact with potentially harmful vehicular traffic.” (Raford and Ragland 2004)
	“Contact or amount of contact with potentially harmful situation.” (Greene-Roesel et al. 2007)Despite the consensus on a theoretical exposure definition, there is wide divergence on operational definitions of exposure, and an even wider range of exposure measures being used in practice. For example, exposure measures in the literature have been quantified in terms of:

Pedestrian or bicyclist volume.
	Sum of entering flows (motorized and nonmotorized) at intersection.
	Product of pedestrian or bicyclist volume (P or B) and motor vehicle volume (V), (P or B) × V.
	Square root of the above product, Formula. The square root of the product of pedestrian or bicyclist volumes and motor vehicle volumes..
	Estimated number of streets or travel lanes crossed.
	Estimated total travel distance, in person-miles of travel.
	Estimated total travel time, in person-hours of travel.
	Total number of pedestrian or bicyclist trips made (from travel survey).
	Overall census population.
	Proportion of census population who report regular walking or bicycling (from travel survey).Chapters 3 and 4 provide more detail on the use of these various exposure measures. All of these exposure measures were intended to represent the same theoretical construct of pedestrian or bicyclist contact with potentially harmful traffic situations (i.e., exposure). However, several key factors are likely to explain the wide divergence in exposure measures used:

**Exposure scale:** For example, is an exposure measure sought for individual intersection crossings and/or road segments? Or for aggregate zones or user groups in an entire city?
	**Data availability and accuracy at application scale:** For example, what data could be feasibly gathered at that application scale for a jurisdiction, and how accurate are those data?
	**Varying application judgment:** For example, there are differing opinions on the best approach to operationalize the theoretical definition of exposure for different applications.Public Health and Epidemiological Approaches to Estimate Exposure

Within the broad field of public health, quantifying the risk of injury or other health condition or disease is a focus of the discipline of epidemiology.Â  The goal is to compare the risk in exposed groups to unexposed groups in order to identify risk factors or factors that cause a health condition such as injury.Â  Ideally, the identified risk factors are then targeted for intervention in order to prevent injury or lessen its negative impact on health and well-being.Â  Epidemiologists define risk as the “probability of an event during a specified period of time” (Rothman, Greenland, and Lash 2008). This is similar to the theoretical definitions provided by Hauer (1982) and others earlier in this chapter.

For how risk is computed, the basic equation is similar when comparing applications in transportation safety versus epidemiology.Â  However, the terminology differs in how the denominator is described and how the term exposure is used.Â  In addition, epidemiologists place an emphasis on defining the population and the time period for estimates of risk. Ideally, the estimates of risk can be generalized to a population larger than the sample upon which the estimate is based. Two common measures of risk in epidemiology are frequently referred to as cumulative incidence and incidence density.Â  These are computed as follows:

Formula. Cumulative incidence is defined as the number of events (e.g., injured people) divided by the number of people at-risk. (Gordis 2014)
	Formula. Incidence density is defined as the number of events (e.g., injured people) divided by the amount of time at-risk. (Gordis 2014)The key difference between these two measures is the denominator.Â  In the first, the denominator is number of people at-risk of developing the injury or other health outcome.Â  In the second, the denominator is the amount of time at-risk which is often expressed in terms of person-years, person-hours, or person-days, as examples. Epidemiological studies that focus on transportation populations often use vehicle miles of travel (VMT) as the denominator for person-time at-risk of sustaining an injury or being involved in a crash. Since these measures of risk focus on the frequency of events such as injury during a specified time period, they are often referred to as rates.Â  This is especially true when the denominator is based on the amount of person-time at-risk (i.e., incidence density) rather than simply the number of people at-risk (i.e., cumulative incidence).

Although different terminology may be used, these equations and the conceptual underpinning behind them are very similar to those presented earlier in this chapter for pedestrian and bicyclist safety. The main difference is how the denominators are described and how the term exposure is used. In pedestrian and bicyclist safety, exposure tends to refer to the denominator, which is quantified in many ways including person-hours of travel or person-miles of travel. In epidemiology, the term exposure tends to be used within the context of identifying specific factors that cause or contribute to injury or some other health outcome. Examples include lack of restraint use or helmet use and its role in the occurrence of fatal injury. As described above, the denominator refers to the people at-risk or amount of time at-risk.

The basic method for determining whether or not an exposure is associated with injury is to compare the risk of injury in the exposed versus the unexposed group.Â  As an example, a study of the efficacy of bicycle helmets could involve comparing the risk of death due to brain injury among bicyclists not wearing a helmet to the risk of death due to brain injury among bicyclists wearing a helmet. This comparison is accomplished by computing a measure known as relative risk.Â  Relative risk that is computed based on cumulative incidence is called a risk ratio whereas relative risk computed based on incidence density is called a rate ratio.Â  The basic equations are below:

Formula. Risk ratio is defined as the risk in the exposed category divided by the risk in the unexposed category. (Gordis 2014)
	Formula. Rate ratio is defined as the rate in the exposed category divided by the rate in the unexposed category. (Gordis 2014)Their interpretation is similar.Â  A relative risk value equal to 1.0 is indicative that the exposure did not contribute to injury or other outcome.Â  A relative risk value greater than 1.0 is interpreted as the exposure increasing the risk of sustaining an injury. A relative risk value less than 1.0 is indicative that the exposure decreases the risk of sustaining an injury. Although this is the more typical use of the term exposure in epidemiology, the term also is used when referring to person-time at-risk of sustaining an injury.Â  This could be expanded to include person-distance traveled or other similar metrics. In this context, it could be used as the amount of time exposed to a potential hazard such as the roadway.Â  This use is in line with the definitions provided earlier in this chapter. While the computations provided here illustrate the basic concepts of risk and exposure in epidemiology, a wide array of statistical methods are used in epidemiology. These range from simplistic computations such as those illustrated above to complex modeling.

In the published literature, there is much overlap between risk and exposure studies in the fields of traffic safety and epidemiology. Greene-Roesel et al. (2007) provide definitions and descriptions for pedestrian exposure that are nearly identical to textbooks in epidemiology.Â  This includes the elements of risk discussed above along with in-depth discussions of target populations and methods for sampling larger populations. This is beneficial so that inferences can be drawn from a sample to a larger population, which is often more cost-effective and efficient.Â  There are many other examples of individual epidemiological studies of pedestrian and bicycle safety where risk and relative risk are estimated based on quantified exposure. Recent examples include a study from North Carolina wherein pedestrian and bicycle crash-related injury rates were computed (Kerr et al. 2013).Â  For risk or rate estimates, the numerator was nonfatal and fatal injury while the denominator was the number of trips at-risk. In this study exposure or time at-risk was estimated using methods from traffic safety (Durham Comprehensive Bicycle Transportation Plan 2006).Â  DiMaggio et al. (2015), in their evaluation of the Safe Routes to School program in Texas, estimated the risk of pedestrian and bicyclist injury in school-age children.Â  They used population for the denominator in their estimates of risk over time. Both of these studies used more complex statistical modelling to compute relative risk measures or assess program impact. In addition, others have used more complex methods for estimating crash and injury risk such as decomposition methods (Dellinger et al. 2001).Â  These were implemented in a recent Spanish study of pedestrian traffic-related fatalities (Onieva-Garcia et al. 2016).

Some reports may use the same terminology, but use markedly different equations to calculate measures such as relative risk.Â  For example, Raford and Ragland (2004) present an equation for relative risk that, in an epidemiological context, fits better with the definition of a risk or rate.Â  A similar discrepancy can be found in the report by Bly et al. (1999) in their comparison of child pedestrian safety in three European countries. To contrast, the United States Road Assessment Program (Harwood et al. 2010) employs equations for relative risk that are more in line with traditional epidemiological computations.

In summary, there is much similarity in how risk is conceptualized and estimated between the fields of public health and transportation safety. There are many examples in the literature of epidemiological studies that use similar methods for estimating time at-risk or some other metric needed to compute risk or rates. Differences between the two fields exist in terminology such as relative risk, and these differences need to be considered when interpreting and comparing findings across the two fields.

Importance of Geographic Scale in Exposure Analysis

Many articles in the literature emphasize the importance of scale in estimating exposure. Similarly, scale has already been mentioned several times in this chapter when discussing how the theoretical definition of exposure can be operationalized in a practical way. In this report, exposure scale is defined as the most granular geographic level for which an exposure measure is desired. For example, is an exposure measure sought for a selected number of individual street crossings? Is an exposure measure sought for certain roadway segments? Or is an exposure measure sought for a defined areawide geography, such as traffic analysis zones (TAZs), Census tracts, or Census block groups?

There is a need to differentiate between scale and coverage when discussing exposure estimation:

**Scale** is the **geographic level** of the desired exposure estimation.
	**Coverage** denotes the **total geographic area** that is included in an exposure analysis.For example, consider an exposure estimation approach that uses a travel demand forecasting model to estimate segment-based pedestrian and bicyclist volumes and exposure for the entire region. In this example, the scale is at a segment level, since that is the most granular geographic level for travel demand models. The coverage of the travel demand model is for the entire region.

The original statement of work for this project referenced four different scale levels:

Facility.
	Corridor.
	Network/system.
	Regional.The literature review indicated that most exposure analyses were more closely aligned to these four scales:

Street crossing (intersection or mid-block).
	Road segment (typically between major intersections or nodes).
	Network for various area definitions (such as a TAZ, Census tract, or Census block group).
	Regional (such as city, county, metropolitan statistical area, or state).Chapters 3 and 4 provide additional details on the scale and coverage of exposure analyses that were documented in this literature review.

Future methodological development in this project could benefit from the use of clear, unambiguous terms for various scales. In particular, the 2010 Highway Capacity Manual (HCM) is widely used for street and highway analysis and provides clearly-defined terms for various roadway system elements, such as points, segments, facilities, corridors, areas, and systems.Â  Figure 1 shows HCM roadway system elements to provide context and their relative scales to one another.Â  These HCM roadway elements were chosen as scale classifications in Chapter 4 since they are widely accepted and are easily understandable to practitioners attempting to conduct an exposure assessment.

For the network/system and regional scales, standardized terms and definitions do exist for areawide geography. The U.S. Census Bureau has defined several different area geographies, including Census tracts, block groups, and blocks (Figure 2). Â These area geographies are regularly used in collecting and reporting travel survey data (e.g., the number of pedestrian and bicyclist trips) have been used in many areawide exposure analyses (see Chapter 3).

TAZs are another common areawide geography that are defined by metropolitan planning organizations (MPOs) for use in their travel demand forecasting models (see polygons with blue outlines in Figure 3). TAZs are typically composed of multiple Census blocks, since the demographic information in travel demand models is typically populated by aggregating Census data. However, there are cases where a TAZ definition may deviate from Census geography units to accommodate local conditions.

To provide a visual comparison example of TAZs to Census geography, Figure 3 also shows Census block groups (see polygons with red outline). In Figure 3, the following can be seen from this comparison example: 1) although individual zone sizes vary, TAZs are somewhat comparable in size to Census block groups; and 2) TAZ boundaries can deviate from Census geography boundaries when necessary to better account for traffic conditions.

Figure 1. This figure illustrates standard definitions of roadway system elements as contained in the Highway Capacity Manual. The uppermost portion of the figure shows a schematic and highlights the differences between points, segments, facilities, and corridors. The lowermost portion of the figure shows a more aggregate schematic and highlights the differences between corridors, areas, and systems.

(Source: 2010 HCM Volume I, Exhibit 2-1)
Figure 1. HCM Standard Definitions of Roadway System Elements (Scale)

Figure 2. This figure illustrates the granularity relationships of Unites States Census geography definitions. In particular, the figure shows the relationship between these units (starting with most aggregate and proceeding to most granular): Nation, State, County, Tract, Block Group, Block, Block Centroid.

(Source: Created by TTI using 2010 U.S. Census Data)
Figure 2. U.S. Census Bureau Standard Definitions of Areawide Geography

Figure 3. This figure shows a map view comparing the granularity of traffic analysis zones and Census block groups in Austin, Texas. The figures shows that in some cases, these two geography definitions coincide, but that in other cases, they also deviate slightly.

Figure 3. Visual Comparison of TAZs and Census Block Groups in Austin, Texas

When and Where Does Exposure Occur for Pedestrians and Bicyclists?

Most theoretical definitions of pedestrian and bicyclist exposure include references to contact with harmful vehicular traffic or opportunities for a pedestrian or bicyclist crash. For pedestrians, this occurs most explicitly during a street crossing. But several authors in the literature (Goodwin and Hutchinson 1977; Cameron 1982; Hauer 1982, Molino 2009; Elvik 2015) have posed a series of questions about when and where pedestrians or bicyclists can be considered “exposed”. For example, are pedestrians “exposed” while walking along a sidewalk that is separated from motor vehicle traffic? Are pedestrians “exposed” if they cross the street but no motor vehicles are present at the time of their crossing? Are bicyclists “exposed” when they travel in a bike lane immediately adjacent to a motor vehicle travel lane, but then “not exposed” if they are riding in a separated bikeway? However, aren’t bicyclists “exposed” in a separated bikeway when they cross intersecting streets and driveways?

In most cases, the feasibility and practicality of data collection has been used to operationalize this theoretical definition of exposure. Data cannot be collected on all pedestrian, bicyclist, and motor vehicle movements at all locations at all times. Therefore, most operational definitions of exposure have been based on pedestrian and bicyclist activity data that are already available (e.g., from travel surveys) or can be feasibly measured or estimated (e.g., from direct counts or models). Chapters 3 and 4 provide more detail on how various exposure analyses have constructed operational definitions of exposure based on the feasibility and practicality of data collection.
      
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      ‹ Chapter 1. Introduction
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                    Chapter 3. Exposure Analysis at Areawide Levels ›
                
                Book:Synthesis of Methods for Estimating Pedestrian and Bicyclist Exposure to Risk at Areawide Levels and on Specific Transportation Facilities
              Acknowledgments
                Glossary
                Executive Summary
                Chapter 1. Introduction
                Chapter 2. Definitions and Concepts
                Chapter 3. Exposure Analysis at Areawide Levels
                Chapter 4. Exposure Analysis on Specific Transportation Facilities
                Chapter 5. Risk Factors Other than Exposure
                Chapter 6. Conclusions
                Bibliography U.S. DEPARTMENT OF TRANSPORTATION

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