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Modeling Crash Risk of Highway Work Zones with Relatively Short Durations
Hong Yang, Ph.D.
(Corresponding author)
Post-doctoral Associate, Department of Civil and Urban Engineering;
Center for Urban Science and Progress (CUSP);
New York University (NYU)
One MetroTech Center, 19th Floor,
Brooklyn, NY 11201, USA
Phone: (646) 997-0548, Fax: (646) 997-0560
E-mail: [email protected]
Kaan Ozbay, Ph.D.
Professor, Department of Civil and Urban Engineering;
Center for Urban Science and Progress (CUSP);
New York University (NYU)
One MetroTech Center, 19th Floor,
Brooklyn, NY 11201, USA
Phone: (646) 997-0552, Fax: (646) 997-0560
E-mail: [email protected]
Kun Xie,
Ph.D. Candidate, Department of Civil and Urban Engineering;
Center for Urban Science and Progress (CUSP);
New York University (NYU)
One MetroTech Center, 19th Floor,
Brooklyn, NY 11201, USA
Phone: (646) 997-0547, Fax: (646) 997-0560
E-mail: [email protected]
Bekir Bartin, Ph.D.
Assistant Professor, Department of Civil Engineering
Istanbul Kemerburgaz University
Mahmutbey Dilmenler Caddesi No: 26
Bagcilar, 34217, Istanbul / Turkey
Phone: 00 1 (212) 604 01 00 Ext. 1411
E-mail: [email protected]
Word count: 5189 Texts + 3 Table + 3 Figures = 6689
Abstract: 231
Re-submission Date: November 15, 2014
Paper submitted for Publication in the
Transportation Research Record, Journal of Transportation Research Board after being presented
Transportation Research Board’s 94th Annual Meeting, Washington, D.C., 2015
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Abstract
Highway work zones greatly affect operational and safety performance of traffic. Existing studies
have primarily focused on exploring safety issues of long-term work zones whereas safety issues
associated with a large number of relatively shorter duration work zones are seldom examined. Thus,
this paper aims to present an investigation of traffic safety in these work zones with relatively short
duration. Considering low frequency of crashes due to this type of short duration work zones with
respect to its crash condition and non-crash condition, a “rare event” logistic regression model is
developed to explore the causal relationship between a set of contributing factors and the crash risk.
The proposed model accounts for the imbalance issues of events (crashes) vs. non-event (non-crash)
conditions in modeling low frequency crash occurrences. In addition, the model uses actual traffic
data to reduce the bias of using aggregated exposure data (i.e. averaged traffic volume over a day,
month, year, etc.). The modeling results based on a case study show that the work zone length, traffic
volume and lane closure are positively associated with the crash risk in those work zones with short
duration. The proposed model with specific model corrections and actual input data is found to
improve the depiction of the relationship between these factors and the crash risk based on the
comparison of the area under the ROC (Receiver Operating Characteristics) curves of different
models.
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INTRODUCTION
Transportation network is frequently affected by the disruptions of the increasing number of work
zones associated with construction, maintenance, and rehabilitation projects. Such issue is
particularly notable for critical freeways and arterials. For example, it was estimated that about 20
percent of the highways in the nation are undergoing some kind of construction work during the peak
period each year and the work zones accounted for over 20 percent of non-recurring delays and more
than 87 thousand of crashes including 576 fatalities during 2010 (1, 2). This number will be more
alarming when more work zones have to be deployed as a result of rapidly aging transportation
networks.
Many transportation agencies continuously make great efforts to reduce the operational and
safety impacts of work zones on road users as well as their own on-site workers by using various
work zone deployment strategies and advanced traffic control approaches. In order to make more
effective decisions, the underlying knowledge of work zone crash occurrence is essential. Therefore,
a number of research projects have been dedicated to explore the potential risk factors associated
with work zone crash occurrences and their consequence in recent decades (3). Despite the existence
of a large body of research literature developed in recent years, work zone safety issues still need
more investigation as many of the associated analysis have focused on long-term work zones. Other
than the long-term projects, there are thousands of work zones with relatively short durations (i.e.,
from several hours to several days) that have been less frequently explored. These work zones can
cause very different safety issues compared with those long-term work zones. For instance, drivers
are less likely to notice work zones with short duration whereas they become familiar with the
existence of long-term work zones after commuting along the same routes regularly.
Therefore, the main objective of this paper is to develop a novel statistical model for
exploring the causal relationship between crash risk and a set of explanatory variables in work zones
with relatively short durations. The most important contribution of this paper is that it treats the
crashes for short duration work zones as rare events compared to the long-term work zone crashes for
the same section of the same highway. Then a rare event regression model is adopted to specifically
model this unique problem.
Unlike existing studies only exploring work zones crashes based on aggregate data and crash
count models (i.e., Poisson and Negative Binomial), this study looks at the safety issue of work zones
from a more comprehensive perspective namely work zones with crash as well as work zones
without crash experiences. In addition, it emphasizes the importance of using data that reflect actual
work zone conditions to obtain reliable modeling results.
LITERATURE REVIEW
Numerous studies have been conducted in past decades to examine the influence of work zones on
roadway safety. A thorough review has been presented in (3). Despite the amount of increases varies
from study to study, these studies generally found that the presence of work zones on a roadway
increases the crash rate or the likelihood of crash occurrence (3). Potential contributing factors that
affect work zone crash occurrence and/or consequence have also been widely explored and discussed
(4-25).
Despite increasing concerns on work zone safety issues, only a limited number of research
specifically modeled the causal relationship between the occurrence of crashes and contributing
factors at work zones (24-34). TABLE 1 provides a summary of these studies. As seen in the table,
almost all studies were focused on long-term work zones on freeways (26-29, 31, 32). Other than
freeway work zones, some work zones on other types of roads were also analyzed in some studies
(24, 25, 30, 33, 34). However, no study specifically examined crash risk of work zones with a
relative shorter duration. Other than statistical techniques such as Poisson Regression and Linear
Regression, most studies examined the underlying causes of work zone crash occurrence based on
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Negative Binomial (NB) regression models. Factors such as length of a work zone, duration, and
traffic counts were commonly found to be positively correlated with crash occurrence at work zones.
TABLE 1. Summary of studies on modeling work zone crash occurrence.
Study
Pal and Sinha (26)
Khattaket al. (27)
Venugopal and Tarko (28)
Khattaket al. (29)
Qiet al. (30)
Roadway (Location)
freeway (IN)
freeway (CA)
rural freeway (IN)
freeway (CA)
multiple types of road (NY)
Lundevaller (31)
Srinivasanet al. (32)
Yanget al. (24)
Ozturket al. (33)
Ozturket al. (25)
Chen and Tarko (34)
freeway & non-freeway (IN)
freeway (CA, OH, NC, WA)
multiple types of road (NJ)
multiple types of road (NJ)
multiple types of road (NJ)
multiple types of road (IN)
WZ Duration
long-term
long-term
long-term
long-term
long/shortterm/moving
long-term
long-term
long-term
long-term
long-term
long-term
Sample Sites
34
36
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36
Unknown
Method
NB, PR, NLR
NB
NB
NB
TPR, TNB
Exposure
ADT
ADT
ADT
ADT
AADT
72
64
60
60
60
72
RENB
NB, EB
MENB
NB
NB
RE, RP
ADT
AADT
AADT
AADT
AADT
ADT
Note: NB= Negative Binomial Regression; PR=Poisson Regression; NLR=Normal Linear Regression;
TPR=Truncated Poisson Regression; TNB= Truncated NB; EB=Empirical Bayesian; RE=Random Effect; MENB=
NB with Measurement Error; RP=Random Parameters; ADT=Average Daily Traffic (vehicles per day);
AADT=Annual Average Daily Traffic.
The findings based on the above studies provide some useful information for work zone
safety improvement. However, the findings based on the developed crash occurrence models are still
questionable due to several major issues. First, these models were only built on work zones that had
many crashes. Many work zones, particular those with shorter duration, that have no crash
experience were not included (30). Second, data such as adjusted/estimated average daily traffic
(ADT) at non-work zone periods incorporated in the models did not reflect actual traffic conditions
when work zones present (27, 28, 35). The traffic condition might significantly change due to the
presence of the work sites. Consequently, the deficiencies of these work zone-specific data can lead
to uncertainty when quantifying work zone crash risk associated with different contributing factors
(35). Finally, almost all the existing studies used the aggregated data in their models (i.e., aggregated
crash counts and exposure data). These aggregated data cannot reflect the change of conditions over
time in the same work zones.
To sum up, most studies in literature only provided insight into crash risk of long-term work
zones. There is need to investigate crash risk of work zones/roadwork with a relative shorter duration
as they are unique but frequently present on our transportation networks. In addition, data issues have
to be addressed and studies based on more accurate work zone-related information are greatly
needed.
DATA DESCRIPTION
To investigate the mechanism of crash occurrence in work zones with a relatively short duration, the
work zones on a 25-mile section of the New Jersey Turnpike (NJTPK) between milepost 48 and
milepost 73 were used. This section of NJTPK has 3 lanes in both northbound and southbound
directions. As one of the busiest toll road corridors in the east coast, work zones present on the
NJTPK can possibly have an adverse impact on traffic operations and safety. In order to minimize
the impact of work zones, they are usually deployed for short durations during the off-peak periods.
In 2011, 562 work zones with relatively short durations were deployed along the studied section
(both directions). For instance, some of them were maintenance work zones, pavement rehabilitation,
etc. Despite deploying these work zones during off-peak periods, 56 crashes occurred due to these
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work zones. Therefore, it is of great interest to explore the crash risk posed by these and other similar
work zones.
The studied section also has 23 remote traffic microwave sensors (RTMS) placed
approximately at every one mile on the mainline, which provide real-time traffic data for these work
zones. The sensors continuously measure travel speed, volume, and occupancy. The raw data were
aggregated in 15-minute time intervals to capture the variation of traffic pattern. In addition, the time
interval was chose considering potential errors in reported crash time. For each work zone, the traffic
data from the nearest sensor was extracted for describing the actual traffic condition in the work
zone. Excluding those cases with missing data, 466 work zones with 44 crashes were used in the final
analysis. In total, these work zones consist of 16,285 periods (each period is 15 minutes based on the
aggregation of sensor data). In other words, 44 out of the 16,285 periods had a crash, which clearly
represent a very rare case of crash occurrence (0.27%). The characteristics of the data were
summarized in TABLE 2. Notably, the duration of these work zones on average is 11.5 hours and the
maximum one is 78.9 hours (less than 4 days).
TABLE 2. Descriptive statistics of variables.
Variable
Type
Description
Mean
SD
Min
Max
Crash
Categorical
Crash occurrence =1; otherwise = 0
0.0027
0.0519
0
1
WZLength
Numerical
Work zone length (mile)
2.33
1.52
0.2
21.1
Volume
Numerical
Traffic volume in each time interval (veh/15min) 284
191
1
1183
Laneclosed Numerical
Number of lanes closed in a work zone
1.34
0.49
0
2
Duration
Numerical
Hours a work zone presents
11.5
11.7
0.1
78.9
Season
Categorical
Winter=1; otherwise=0
0.43
0.49
0
1
Unlike long-term work zones that have many crashes, it should be noted that work zones with
relatively short durations usually have no crash or one crash during the entire active work period.
Therefore, traditional models such as those listed in TABLE 1 may be not appropriate as they mainly
rely on a higher frequency of crash counts. Therefore, a more reliable and appropriate approach to
describe the crash risk in these work zones is needed.
METHODOLOGY
In this study, instead of assessing crash frequency/rate, we are interested in whether or not the
presence of a short term work zone will cause a crash. Hereinafter crash risk is defined as the
probability of short-term work zone having a crash. Then work zone-related factors that are
hypothesized to affect the crash risk are investigated.
Logistic Regression
Denote y as the crash occurrence at a work zone. Crash occurrence at work zones can be described as
a binary outcome. Let y = 1 represent that a crash occurs in a work zone whereas y=0 indicates no
crash occurred in a work zone. A binary logistic regression model can be developed to examine the
influence of factors that may affect the crash risk of a short-term work zone.
Let us define  ( x) as the probability of a work zone having a crash during its presence and
1   ( x) as the probability of a work zone having no crash. The binary logistic regression model
identifies the relationship between the log odds of the dichotomous outcome and various risk factors.
It can be formulated as following equation (1):
  ( x) 
'
logit  ( x) = log 
  α  Xβ
1   ( x ) 
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Based on the above equation, the probability that a work zone having a crash can be
described by the logistic distribution shown in following equation (2):
P(y  1X)
|   ( x) 
exp(α  X'β)
1  exp(α  X'β)
(2)
where  ( x) is the conditional probability of the form P  y  1| X  ; X is the vector of explanatory
variables (contributing factors) that could be numerical or categorical;  is the corresponding vector
of the coefficients; and  is an intercept parameter.
The maximum-likelihood estimation (MLE) technique can be used to determine the
regression model’s parameters. The likelihood function is constructed as equation (3). By
maximizing the log likelihood expression shown in equation (4), the best estimate of parameters 
and  can be obtained accordingly.
n

l       ( xi ) yi 1   ( xi )
i 1
12
6
(1 yi )

(3)
n
LL     ln l      yi ln  ( xi )  1  yi  ln 1   ( xi )
(4)
i 1
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where yi denotes the observed outcome at the i th period of a work zone, with the value of either 0 or
1 only; i  1,2,..., n and n is total number of observed periods.
The overall goodness-of-fit of the logistic regression model is tested by likelihood ratio test.
The significance of individual contributing factors within the model is examined using the Wald z
statistic. Moreover, the influence of j th factor on work zone crash risk can be revealed by the odds
ratio (OR), which is defined as equation (5):
OR  exp   j 
(5)
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where  j is the coefficient of the j th factor. OR measures the ratio of the predicted odds for a one-unit
increase in a continuous variable x j or the presence of a dichotomous variable x j when other
variables in the model are held constant. The 95% confidence interval of OR is
exp   j  1.96s  ,exp   j  1.96s  , where s is the standard error of the coefficient  j . An OR greater


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than 1 suggests that the j factor increases the likelihood of crash occurrence in the work zone and
vice versa.
j
j
j
th
Rare Events Logistic Regression
Although the binary logistic regression models have been frequently used in traffic safety studies, the
models can yield biased estimates when sample data exhibits class imbalance (36). In this study, the
crash occurrence at work zones with short duration can be an example of class imbalance. As noted
in Section 3, there were many periods that the work zones have no crash  y  0 whereas only a small
number of them had crashes  y  1 .
In such cases, if the MLE of the binary logistic regression model is used, it can result in
biased estimates of coefficients for the factors related to work zone crash occurrence (37, 38).
In order to avoid these estimation issues, (King and Zeng (37)) have developed the rare
events logistic regression for the cases that include three types of corrections for the ordinary logistic
regression. First, a case-control sampling design based on endogenous stratified sampling is
recommended. It consists of taking all periods with a crash  y  1 and a random selection of periods
with no work zone crash  y  0 . Empirically, the proportion of periods with a crash to the periods
with no crash can be set around 1:10 (39, 40). A sensitivity analysis can be performed by using
different sampling proportions.
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The second correction is called prior correction. The purpose of prior correction is to avoid
selecting dependent variables that may introduce sampling bias on the logistic coefficients (King and
Zeng, 2001). The intercept  is corrected using the following equation.
1
  ˆ  ln 
 

y 

1 y 
(6)
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where  is corrected intercept, ̂ is the uncorrected intercept,  is the actual true faction of 1s
(events) in the population, and y is the observed fraction of 1s (events) in the sample.
The last correction is to adjust the MLEs of the logistic regression parameters and the
predictions of the estimated model. When we substitute the corrected intercept  in equation (6),
there is an underestimation of predicated probability because of the uncertainty in the estimation of
ˆ . Therefore, ˆ has to be adjusted. King and Zeng (2001) described the procedure to obtain the
"approximately unbiased" coefficients,  . Based on the adjusted intersect and coefficients, the
predicted crash occurrence probability for a given work zone is obtained as ˆi based on a correction
factor Ci incorporated into the original estimated probability  i . When events are rare, the predicted
probability of an event using logistic regression is adjusted. In our case, it denotes the predicted work
zone crash risk.
ˆi   i  Ci
(7)
The correction factor Ci is obtained using the following equation:
Ci   0.5  pi  pi 1  pi  XV ( ) X '
(8)
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where pi is the event probability estimated using the bias-corrected coefficient  ; X is a 1  n  1
vector of values for each explanatory variable; and V ( ) is the variance-covariance matrix.
To implement the rare event logistic regression model, we have processed all the traffic and
work zone data, and estimated models using the open source statistical software package R. The rare
event logistic regression model built in the “relogit” function of the R package "Zelig" was used to
estimate the work zone crash risk (41).
RESULTS AND DISCUSSION
As mentioned in the literature review section, existing studies usually use the aggregated traffic
volume (AADT) to describe the traffic condition in work zones. Since the traffic condition may
greatly change during the presence of a work zone, the use of actual observed traffic data during this
time period are preferred. Unlike existing studies, the present study, therefore, uses real-time sensor
data as the input to the risk prediction models to accurately describe the traffic condition when a
crash occurs in a work zone. FIGURE 1 illustrates the actual traffic conditions of four work zones.
FIGURE 1 (a) and FIGURE 1 (b) show work zones without a crash whereas FIGURE 1 (c) and
FIGURE 1 (d) show work zones that experienced crashes. It can be seen that the traffic volumes
greatly change during the duration of the work zone. For example, the average traffic volume is 173
vehicles per 15 minutes for FIGURE 1 (c), but when a crash occurs then volume is observed to be
234 vehicles per 15 minutes. Larger differences are observed in FIGURE 1 (d). Therefore, the use of
averaged/aggregated exposure data (i.e., ADT & AADT) obviously may yield biased results for this
type of analysis. Instead of using the aggregate data, this study describes the crash risk in each 15minute interval and uses the corresponding sensor data to capture the variation in traffic. Despite the
fact that higher resolution sensor data (i.e., 30-second interval, 1-minute interval, 5-minute interval,
etc.) were available, the 15-minute interval was chosen based on two major considerations: (a) the
desire to have a reasonable size interval that can capture the traffic variation, and (b) the need to
define a time interval that can better capture/approximate actual crashes.
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FIGURE 1. Examples of traffic volumes in the presence of work zones
Based on the traffic conditions during the time period where the crash actually occurs and
work zone information, the rare event logistic regression model is estimated. The estimation results
are presented in TABLE 3. The final rare event logistic regression model only includes variables that
are statistically significant at the significance level of 0.1. The results suggest that all the three
variables are positively associated with the crash risk in work zones with relatively short durations.
More specifically, if the log-transformed work zone length increases one unit, the likelihood of
having work zone crash increased, with an odds ratio of 2.415. Similarly, when the log-transformed
volume increases one unit, the corresponding crash risk will be increased, with an odds ratio of
1.679. When one more lane is closed, the odds ratio is 1.662. For these work zones with relatively
short duration, the seasonal impact on the crash risk was not significant. The underlying reason for
this observation should be attributed to the fact that most of these work zones were only deployed
during the off-peak periods under good weather condition. Since the work zone durations are short,
they can be easily rescheduled to avoid severe weather impact.
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TABLE 3. Results of rare events logistic regression model (Event: Non-Event =1:30).
Variable
Estimate
Std. Error
z value
Pr(>|z|)
Odds Ratio
Intercept
-10.063
1.435
-7.012
0.000
----
log(WZLength)
0.882
0.317
2.780
0.005
2.415
log(Volume)
0.518
0.219
2.364
0.018
1.679
Lanes closed
0.508
0.304
1.672
0.095
1.662
The results presented in TABLE 3 are based on a sampling ratio of 1:30 (crash conditions vs.
non-crash conditions). To test the sensitivity of the modeling results, different sampling ratios are
also analyzed. FIGURE 2 shows the estimated coefficients under different sampling ratios. It can be
seen that as long as the ratio of non-event conditions vs. event conditions increases (i.e. sampling
ratio ≥ 30), the estimates are relatively stable. This suggests that without losing modeling accuracy,
the work of data preparation can be reduced in terms of processing the real-time sensor data to reflect
actual work zone conditions required by our model.
FIGURE 2. Effect of different sampling ratios on estimates of coefficients
A regular logistic regression model is also estimated for the same case study with all the
observed crash periods and non-crash periods of work zones. To compare the performance of the rare
events logistic regression model with the regular logistic regression model, the areas under the
Receiver Operating Characteristics (ROC) curves, or simply the area under the curve (AUC) of two
models are examined. This is a frequently used measure for the comparison of learning algorithms
(42). According to this reference, a ROC curve is said “to dominate another one if it is always above
and to the left of the other one”. If most of the curves overlap each other, the AUC is used as the
measure for comparison (42). FIGURE 3 shows the ROC curves of logistic regression model vs. the
rare events logistic regression model with different sample ratios. The AUCs of the rare events model
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are larger than the logistic regression model in both examples (The AUCs for rare events models are
0.6807 in FIGURE 3 (a) and 0.6804 in FIGURE 3 (b). Both are larger than the AUC of 0.6748 for
the logistic regression model), which indicate that the rare events model should be preferred.
FIGURE 3. ROC of rare event model vs. logistic regression model for different sampling ratios
CONCLUSIONS AND FUTURE WORK
This study examined the statistical relationships between a set of explanatory variables and the crash
risk in work zones with relatively short durations. Instead of using traditional logistic regression
model, i.e., Harbet al. (19), a rare event logistic regression model was estimated to capture the
characteristics of crashes occurring during the of short duration work zones on highways. The
proposed rare event regression model contributes to the literature in several aspects: First, it
incorporates all work zones with and without crash experience in the model. Existing studies have
only focused on those work zones with crash records. Second, it accounts for the imbalance between
periods with crash occurrence(s) and other large amount of periods with no crashes. In addition,
instead of using aggregated crash and traffic data, this study modeled the crash risk at each time
interval with the actual sensor data. The bias introduced by using aggregated data can be reduced.
For instance, existing studies generally adopt Poisson and/or Negative Binomial Models to estimate
work zone crash frequency. However, these models hardly differentiate the periods with crashes from
others without any crash. Instead, they usually use the "duration" as a variable to aggregate these
periods together based on the assumption that the crash risk of each period is the same. In contrast,
by using discrete data, the work zone crash risk in each short-time interval can be reliably captured
under its prevailing traffic conditions. Based on the analysis of the developed rare event logistic
regression model, it is found that the work zone length, actual traffic volume, and the number of
lanes closed are positively associated with the crash risk in those work zones with short duration. The
sensitivity analysis shows that the modeling results are stable even when only a part of the non-event
periods are sampled. The use of the rare events model also improved the prediction performance of
crash occurrence compared with the traditional logistic regression model. Future work will include
extending the rare event regression model to multiple sites with different characteristics.
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ACKNOWLEDGEMENTS
The contents of this paper reflect views of the authors who are responsible for the facts and accuracy
of the data presented herein. The contents of the paper do not necessarily reflect the official views or
policies of any agency mentioned in the paper. The authors thank for the insightful comments and
suggestions from all the anonymous reviewers that helped improve the paper.
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