Likelihood Parameterization of Bicycle Crash Injury Severities

doi:10.4236/jtts.2012.23023

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Journal of Transportation Technologies, 2012, 2, 213-219

doi:10.4236/jtts.2012.23023 Published Online July 2012 (http://www.SciRP.org/journal/jtts)

Likelihood Parameterization of Bicycle Crash Injury

Severities

Deo Chimba*, Daniel Emaasit, Boniphace Kutela

Department of Civil Engineering, Tennessee State University, Nashville, USA

Email: *[email protected]

Received March 23, 2012; revised May 3, 2012; accepted May 25, 2012

ABSTRACT

This paper evaluates different factors and parameters contributing to likelihood of bicycle crash injury severity levels.

Multinomial Logit (MNL) model was used to analyze impact of different roadway features, traffic characteristics and

environmental conditions associated with bicycle crash injury severities. The multinomial model was used due to its

flexibility in quantifying the effect of the independent variables for each injury severity categories. Model results

showed that, severity of bicycle crashes increases with increase in vehicles per lane, number of lanes, bicyclist alcohol

or drug use, routes with 35 - 45 mph posted speed limits, riding along curved or sloped road sections, when bicyclists

approach or cross a signalized intersection, and at driveways. In addition, routes with a high percentage of trucks,

roadway sections with curb and gutter, cloudy or foggy weather and obstructed vision were found to have high pro-

bability of severe injury. Segments with wider lanes, wide median and wide shoulders were found to have low likeli-

hood of severe bicycle injury severities. Limited lig hting locatio ns was found to be associated with in capacitatin g injury

and fatal crashes, indicating that insufficient visibility can potentially lead to severe crashes. Other findings are also

presented in the paper.

Keywords: Bicycle Crash; Injury Severity; Multinomial Logit

1. Introduction

The av erage annu al number o f bicycle fatal crashes from

1998 to 2008 in United States was 721. In 2008, 716

pedalcyclists were killed and an additional 52,000 bicy-

clists were injured in traffic crashes. Pedalcyclist deaths

accounted for 2 percent of all traffic fatalities, and made

up 2 percent of all the people injured in traffic crashes in

2008 (NHTSA, 2008 [1]). The same report highlights

that pedalcyclist fatalities occurred more frequently in

urban areas (69%), at non-intersection locations (64%),

between 5 p.m. and 9 p.m. (28%), and during the months

of June (9%) and September (12%). This paper evaluates

factors influencing bicycle crash injury severities.

Bicycle crashes have been studied by several re-

searchers for the past decade. Cheryl et al. [2] developed

a bicycle route safety rating model based on injury seve-

rity. The model development was conducted using a lo-

gistic transformation of bicycle crash data from Jersey

City, New Jersey, for the period 1997 to 2000. The re-

sulting model met 90% confidence level by using various

operational and physical factors like traffic volume, lane

width, population density, highway classification, and

presence of vertical grades, one-way streets, and truck

routes to predict the severity of an injury that would re-

sult from a motor vehicle crash that occurred at a specific

location. In another study, Jeremy and Asad [3] exam-

ined the effect of roadway and environmental factors on

injury severity in bicycle-motor vehicle collisions. An

ordered probit model for injury severity was estimated

using the Highway Safety Information System (HSIS)

data set for two-lane roadways. The model parameters

and the marginal effects of significant variables were

used to examine the influ ence of roadw ay and crash ch a-

racteristics on injury severity of cyclists. In this study,

speed limit, straight and curved grades, fog and unlighted

darkness were found to increase injury severity, while

average annual daily traffic, an interaction of the shoulder-

width and speed-limit variables, and street lighting were

found to be associated with decreased injury severity.

Karl and Lei [4] found that bicyclists are more likely

to be attentive than motorists, and slightly less likely to

be associated with misjudgment or alcohol or drug use

than motorists. The same study found that bicyclists are

much more likely to disregard traffic controls or go the

wrong way on a street just before becoming involved in a

collision than motorists. Motorists are more likely to fail

to yield, to engage in improper overtaking, or to follow

too closely before becoming involved in a collision than

*Corresponding Aut ho r.

D. CHIMBA ET AL.

214

bicyclists. Shankar and Mannering [5] found that riding

without a helmet, and under the influence of alcohol in-

creased the likelihood of a disabling injury or fatality.

The same study found that the use of alcohol, over-

speeding, and older motorcyclists were associated with

higher likelihoo d of severe injury.

Quddus et al. [6] used ordered probit model to study

how various factors, including specific characteristics of

the roadway and th e riders, can lead to different levels of

injury and damage severity. The rationale for using the

ordered probit model was due to its capability to model

categorical dependent variables. The authors dismissed

the use of unordered multinomial, nested logit, or probit

models because they do not account for the ordinal na-

ture of the injury categories and the association of inde-

pendence of irrelevant alternatives (IIA) in the multino-

mial logit (MNL) models. The ordered probit models are

known to have weakness in classification of injury seve-

rity. However they are useful when the coefficient for

each variable in the model is required to classify injury

severities category. On the other hand, unordered multi-

nomial model is appropriate for evaluating the effect of

the variables to each injury severity category. Shankar

and Mannering (1996) [5] used the multinomial logit

model to examine factors affecting injury severities.

Their findings revealed that the multinomial logit formu-

lation was a potential approach to determine significant

factors affecting severity. The main disadvantage of us-

ing the multinomial logit model was that the error term

follows a generalized extreme value (GEV) distribution,

which leads to the issue of IIA.

A review of these previous studies however indicated

plenty of methodolog ies in evaluating bicycle crashes. In

view of the methodologies used in previous studies and

their recommendations for further research, this paper

examines the use of the multinomial logit (MNL) model

in analyzing bicycle crash severity. Ordered models are

not used herewith due to their limited independent vari-

ables effect outcome probabilities, Washington et al. [7].

Based on the bicycle related statistics presented above,

it is therefore warranted to examine the factors contri-

buting to these types of crashes. Th is study complements

the desire of many all any tran sportation related agencies

and jurisdiction in ensuring the safe use of bicycle as the

mode of transportation. Understanding the factors con-

tributing to the levels of injury severity is an important

step towards making bicycle one of the safe and more

attractive modes. Furthermore, differentiating the con-

tributing factors may help establish safer bicycle mode of

transportation.

2. Methods

The MNL have been used widely on injury severity stu-

dies. As an extension from the Logit model, MNL is used

for dependent variable with more than 2 categories or

indicators, Quddus et al. [5] and Mouskos, et al. [8]. The

MNL model is built based on the assumption that the

choice between any pair of alternatives of the response

variable is independent of the availability of other alter-

natives. It implies that the random part of utility function

is independent among the alternatives. The multivariate

response variable can be distinguished depending whe-

ther the variable has an ordered or unordered category.

When categories in the response variable are not ordered,

MNL regression becomes appropriate compared to other

type of regressio ns, Shankar and Mann ering [4]. Su ppose

there are J categories of the injury severity as the re-

sponse variable, then there will be J – 1 equations for

MNL as a binary logistic regression comparing a group

with the reference (base) category or comparison group.

Using the maximum likelihood, MNL simultaneously

estimates the J – 1 logit functions. The probabilities of

other members in other categories are compared to the

probability of membership in the reference category.

Suppose the utility functio n is denoted as, Washington et

al. [7]:

kik iki







 (1)

where k

is the independent variable, i



is the coef-

ficient associated with each independent variable, and



is the error term. Suppose the response variable k,

is subjected to different categories of severity, 0, ···, i,

then

, if for

kkjki

qj UUji



.

In this study, i = 0, 1, 2 and 3 where 0k represent

non-injury crash, 1k represent possible injury or non-

incapacitating crash, 2k

U represent incapacitating in-

jury and Uk3 representing fatal crash. From the four in-

jury categories, three equations are formed, one for each

category in relation to the reference or base category, in

this case is Uk0. The general logistic equation is given as,

Washington, et al. [6], Shankar and Mannering [4];



kJX

Pq j







 (2)

The odds ratio





kj ki

PP will depend log-linearly on

, i.e.,



log kj nj i











 (3)

The interpretation of the effects of explanatory vari-

ables to the responses is based on comparing the coeffi-

cient of variable in the category modeled to the reference

(base) category. Possible or non-incapacitating injury,

incapacitating injury and fatal crash model results are

interpreted in relation to base category which is non-

D. CHIMBA ET AL. 215

injury crash. The marginal effect of an independent vari-

able k

on the choice probability for alternativ e j can be

expressed as:







jk k

Pqjx P





 (4)

Equation (4) depends not only on the parameter



but also on the mean of all other alternatives













(5)

Direct interpretation of the parameter estimates can be

done usi ng the log of odds ratio:



log ji





 (6)

This is reduced to,



log ji





 for compari-

sons with the reference category iif the coefficients

associated with the base category are set to zeros. A

positive coefficient to the variable will mean the relative

probability of injury severity J increases relative to the

probability of the same variable in the base categ ory. The

estimation can be performed by using the maximum like-

lihood (ML) method in which th e log likelihood function

is given as



log log

kj kj

LqP



 (7)

with kj = 1 if the crash record k falls into severity

category j and = 0 if otherwise.

3. Study Data

The study utilized crashes involving bicycles which oc-

curred on Florida State maintained highway s from 2004 t o

2008. A total of 10,708 bicycle related crashes were

screened, among them, 11% none injury, 28% possible

injury, 42% non-incapacitating injury, 16% incapacitating

injury, and 3% fatal crashes. The study combined the

severity into three main groups. The first group coded as

“0” (none-injury), representing bicycle crashes that re-

sulted in no injury. The second group is possible injury

and non-incapacitating injury combined together and

coded as “1” (moderate injury) representing bicycle

crashes that resulted in minor injuries. The third group is

incapacitating injury and fatal coded as “2” (severe in-

jury) representing all bicycle crashes resulted into body

disability or death occurring within 30 days after the

crash. The three categories were used in MNL model

where category 0 is pivoted as a base.

The analysis used both continuous and categorical

variables in the model. The summary of continuous va-

riables is included in Tab le 1. Categorical variables used

Table 1. Variables summary statistics.

Mean Std. Dev Min. Max.

Average Annual Daily Traffic

(AADT) 35,725 16,099 1000 161,000

Vehicle per Day per Lane 7206 2762 250 26,833

Number of Lanes 5 1 2 8

Lane Width 29 8 8 84

Shoulder Width 3 2 0 25

Medium Width 19 16 0 800

Percentage of Trucks 5 3 0 42

Age 35 21 15 100

Speed Limit 42 6 15 55

are listed in Table 2. Most of these categorical variables

were coded as binary (taking on values of 1 or 0).

Analysis showed that 25% of all crashes analyzed re-

sulted from the vehicle or bicycle making a right turn,

2% when changing lane, 9% when making left turn and

3% when slowing. For contributing causes failed to yield

right of way comprised of approximately 36% of all

crashes. With respect to land use, 24% of the bicycle

crashes occurred in residential areas while 76% occurred

in commercial or business areas. Signalized intersections

and intersection influenced crashes contributed to about

75% of the bicycle crashes. At intersection crashes are

those which are within 50 ft from the intersection or

ramp. The influenced areas are those within 250 ft from

an intersection or ramp. Alcohol and drug related bicycle

crashes comprised of about 10% of total crashes. For the

crashes that resulted from Driving under the Influence

(DUI) of alcohol, 15% resulted in fatality. General statis-

tics of some numerical variables analyzed are summa-

rized in Table 1.

4. Results

None-injury crash category (e.g. category 0) was kept as

a base in MNL model. The models developed compared

the coefficient magnitudes and signs of the independent

variables in relation to the base category. The MNL re-

sults are presented in Ta ble 3. The model result p arame-

ters are interpreted in relation to the base category as in-

dicated. It should be noted that some independent vari-

ables were significant in one injury category but insig-

nificant in other.

4.1. Curved Sections

The coefficient of the curved sections in the model is

positive in both categories. The magnitude of the coeffi-

cients increases steadily from category 1 to category 2,

indicating that crashes occurring in curved areas will

have strong probability of resulting into severe injury

D. CHIMBA ET AL.

216

Table 2. Coding of categorical variables.

Categorical variable Coding

Presence or absence of sloped roadway sections Coded as 1 and 0 respectively

Roadway section without or with shoulder Coded as 1 and 0 respectively

At intersection and influenced or not intersection Coded as 1 and 0 respectively

Driveways or non-driveway Coded as 1 and 0 respectively

Dusk, night, no light or dayli ght Coded as 1 and 0 respectively

Cloudy, rai n, fog or clear Coded as 1 and 0 re spectively

Curved roadway sections or straight Coded as 1 and 0 respectively

Special speed zone control or non-speed zone Coded as 1 and 0 respectively

Signal control or no control Coded as 1 and 0 respectively

Stop sign control or not Coded as 1 and 0 respectively

Vision obstructed or not Coded as 1 and 0 respectively

Urban areas or other areas Coded as 1 and 0 respectively

30 mph or less speed limi t or higher speed Coded as 1 and 0 respectively

35 - 45 mph spe e d Limit or lower sp e ed Coded as 1 and 0 respectivel y

Drug or alcohol use or none Coded as 1 and 0 respectively

Table 3. Injury severity modeling results.

Multinomial logistic regression Number of observations = 10,708

Likelihood ratio chi2 = 7363.23 Prob > chi2 = 0.0000

Log likelihood = –8082.3266 Pseudo R2 = 0.3130

Possible or non-incapacitating injury severity Coefficient Std. error Z-value

Vehicle per day per lane 9.0E–07 7.5E–08 12.03

Number of lanes 0.1530 0.061 2.49

Median width –0.0031 –0.002 1.82

Lane width –0.0287 –0.011 2.65

Shoulder width –0.0088 –0.005 1.74

Bicyclist age 0.0079 0.001 8.28

Percentage trucks 0.0089 0.006 1.42

Sloped roadway sections 0.0104 0.005 2.13

No shoulder 0.0468 0.004 10.83

At intersection of influ e n c ed 0.2249 0.064 3.49

Driveways 0.3101 0.071 4.37

Dusk, night, no lig ht 0.1010 0.048 2.1

Cloudy, rain, f og 0.1308 0.051 2.58

Curved roadway sections 0.2221 0.146 1.52

Special speed zone control 0.1607 0.071 2.26

Signal control 0.0685 0.031 2.22

Stop sign control 0.1083 0.057 1.9

Vision obstructed 0.1497 0.062 2.4

Urban areas 0 .2106 0.130 1.62

30 mph or less speed li mit –0.2057 0.103 –1.99

35 - 45 mph speed limit 0.1085 0.043 2.5

Drug or alcohol use 0.3130 0.077 4.05

D. CHIMBA ET AL. 217

Continued

Incapacitating injury or fatal

Vehicle per day per lane –2.3E–05 1.1E–05 –1.98

Number of lanes 0.4170 0.217 1.92

Median width –0.0020 0.001 –2.42

Lane width –0.0423 0.014 –3.11

Shoulder width –0.0842 0.033 –2.55

Bicyclist age 0.0248 0.003 8.56

Percentage trucks 0.0206 0.011 1.89

Sloped roadway sections 0.0499 0.022 2.22

No shoulder 0.3371 0.167 2.02

At intersection of influ e n c ed 1.1469 0.147 7.79

Driveways 1.9544 0.253 7.74

Dusk, night, no lig ht 0.8689 0.128 6.81

Cloudy, rain, f og 0.1854 0.080 2.31

Curved roadway sections 0.4855 0.196 2.48

Special speed zone control 0.4816 0.153 3.15

Signal control –0.0916 0.173 –0.53

Stop sign control 0.8683 0.248 3.5

Vision obstructed 0.1384 0.085 1.62

Urban areas 0 .8300 0.253 3.28

30 mph or less speed li mit –1.3688 0.319 –4.29

35 - 45 mph speed Limit 0.8890 0.160 5.55

Drug or alcohol use 1.7918 0.138 13.01

compared to light injury. The find ing coincides with pre-

vious study which found that higher crash rates can be

expected on curves than tangents, with rates ranging

from two to four times higher than tangents, Jeremy and

Asad [3].

4.2. Posted Speed Limit

Speed limit is a function of several roadway parameters,

sight distance and roadway co ndition. The study group ed

the speed limit into three, from 15 - 30 mph were coded

as “1” representing low speed, 35 - 45 mph coded as “2”

and 50 mph or above represen ting higher speed coded as

“0”. As it was found in curved sections, the coefficient of

high speed is positive in both models (Table 3). The

likelihood of severe injury is high at high speed com-

pared to low speed. The finding is consistent with the

previous researches which found speeding to be associ-

ated with severe injury, Jeremy and Asad [3].

4.3. Lighting

Lighting conditions is categorized in Florida crash form

into daylight, dusk, dawn, dark with street light and dark

without traffic light. These categories were grouped into

two, one coded “0” representing day light and the other

coded as “1” for limited lighting conditions, dusk, dawn

and dark which represent “limited lighting” resulted with

positive coefficient in both severe injury and fatal crash

models. Based on the results, severe injury or fatal bicy-

cle crashes will be expected at locations with limited

lighting conditions compared to locations with adequate

lighting.

4.4. Traffic Volume per Lane and Percentage of

Trucks

Percentage of trucks is the average proportions of trucks

to the total number of vehicles at that particular section.

The variable has positiv e coefficient in the model (Table

3). The safety problem between trucks and bicycles can

lie on the visibility of the truck drivers and smallness of

the bicycle itself. Traffic volume have strong positive

coefficient in less severe (possible or non-incapacitating)

but negative coefficient for incapacitating/fatal model

indicating crashes occurring in the congested areas will

have less severe injuries. The result related with AADT

might be different if crash frequency was the subject,

some previous studies has found increase in crash fre-

quency with increase in traffic volumes, Mouskos et al.

[8].

D. CHIMBA ET AL.

218

4.5. Location

Crash location refers to location on the roadway where

the crash occurred. The location can be at the intersection,

driveways, ramps, railroad, bridges, parking lots, toll

booth and public bus stops. In modeling, the factors were

grouped into 3 categories with code “0” representing

non-intersection related crashes, “1” representing at in-

tersection or intersection influenced crashes, “2” for

driveways and “3” representing other remaining location

categories. Result shows bicycle crashes occurring at

driveways and intersections are likely to result in either

non-incapacitating, incapacitating injury, or fatal (Table

3).

4.6. Age

Older bicyclists seem to be more vulnerable to fatal in-

jury than younger ones. The models show positive, sig-

nificant coefficient in the fatal injury category in both

models (Table 3). This finding is consistent with the

previous research which found increase in age to be as-

sociated with likelihood of severe injury crash (Shankar

and Mannering [5]).

4.7. Number of Lanes, Lane Width, Shoulder

Width and Median Width

As expected, number of lanes showed positive coeffi-

cients to injury severity, the finding which is consistent

with findings from previous studies that evaluated crashes

involving bicycle and all other vehicle types, Theodore et

al., Miao and Lump, Miao, Garber and Ehrhart [9-12]. In

multilane segments, as the number of vehicles per lane

increases, there become fewer gaps to allow lane chang-

ing, turning movements, or merging, which eventually

increases the likelihood of crashes. Median width is sig-

nificant with a n egative co efficient, indicating likeliho od

of bicycle crash injuries severity level decreases as me-

dian width increases. This is consistent with many pre-

vious studies, Milton and Mannering, Abdel-Aty and

Radwan and Lee and Mannering [13-15]. The results

show that wider lanes reduce the probability of severe

injury. Wider lanes can be used by a bicyclist as a room

for correcting errors in the situation of near crash occur-

rence. Wider shoulders have negative coefficient show-

ing its important role in reducing bicycle crash injury

severities. From a highway safety point of view, a

shoulder can be used by a bicyclist to stop in case of an

emergency or during an incident, and drivers can take

advantage of wider shoulders to avoid hitting roadside

objects. In addi tion, bicycli sts can veer to w ider shoulders

to avoid a crash.

5. Conclusion

The model results indicate that there are significant fac-

tors that influence bicycle injury severities on the high-

ways. Significance of these factors to the occurrence of

crashes varies depending on human judgment, contribut-

ing causes, environmental conditions, traffic characteris-

tics, geometrics and location on highways. The multino-

mial Logit (MNL) model was used for analysis as it al-

lows the use of one injury severity as a reference cate-

gory while analyzing others. The results showed that,

increase in number of lanes, alcohol and drug use, high

posted speed limit links, curved areas, turning move-

ments, intersection and driveways, and driving with no

adequate daylight have strong significance effects on

intensifying injury severity. In addition, the higher the

percentage of trucks and the older the bicyclist means the

more severe the injury. Regarding traffic volumes, the

study found that under congestion condition few severe

incidents occur though higher crash frequencies can be

expected. Limited lighting locations was found to be as-

sociated with incapacitating injury and fatal crashes, in-

dicating that insufficient visibility can potentially lead to

severe crashes.

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