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Jahanjooetal.
BMC Medical Research Methodology (2023) 23:221
https://doi.org/10.1186/s12874-023-02041-0
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BMC Medical Research
Methodology
A hybrid ofregularization method
andgeneralized path analysis: modeling
single-vehicle run-o-road crashes
inacross-sectional study
Fatemeh Jahanjoo1, Mohammad Asghari‑Jafarabadi1,2,3,4*† and Homayoun Sadeghi‑Bazargani1*†
Abstract
Background Determining risk factors of single‑vehicle run‑off‑road (SV‑ROR) crashes, as a significant number of all
the single‑vehicle crashes and all the fatalities, may provide infrastructure for quicker and more effective safety
measures to explore the influencing and moderating variables in SV‑ROR. Therefore, this paper emphasizes utilizing
a hybrid of regularization method and generalized path analysis for studying SV‑ROR crashes to identify variables
influencing their happening and severity.
Methods This cross‑sectional study investigated 724 highway SV‑ROR crashes from 2015 to 2016. To drive the key
variables influencing SV‑ROR crashes Ridge, Least Absolute Shrinkage and Selection Operator (Lasso), and Elastic net
regularization methods were implemented. The goodness of fit of utilized methods in a testing sample was assessed
using the deviance and deviance ratio. A hybrid of Lasso regression (LR) and generalized path analysis (gPath)
was used to detect the cause and mediators of SV‑ROR crashes.
Results Findings indicated that the final modified model fitted the data accurately with
X2
3
= 16.09, P < .001,
X2
/
degrees of freedom = 5.36 > 5, CFI = .94 > .9, TLI = .71 < .9, RMSEA = 1.00 > .08 (90% CI = (.06 to .15)). Also, the presence
of passenger (odds ratio (OR) = 2.31, 95% CI = (1.73 to 3.06)), collision type (OR = 1.21, 95% CI = (1.07 to 1.37)), driver
misconduct (OR = 1.54, 95% CI = (1.32 to 1.79)) and vehicle age (OR = 2.08, 95% CI = (1.77 to 2.46)) were significant
cause of fatality outcome. The proposed causal model identified collision type and driver misconduct as mediators.
Conclusions The proposed HLR‑gPath model can be considered a useful theoretical structure to describe
how the presence of passenger, collision type, driver misconduct, and vehicle age can both predict and mediate
fatality among SV‑ROR crashes. While notable progress has been made in implementing road safety measures, it
is essential to emphasize that operative preventative measures still remain the most effective approach for reducing
the burden of crashes, considering the critical components identified in this study.
†Mohammad Asghari‑Jafarabadi and Homayoun Sadeghi‑Bazargani
contributed equally to this work.
*Correspondence:
Mohammad Asghari‑Jafarabadi
m.asghari862@gmail.com
Homayoun Sadeghi‑Bazargani
homayoun.sadeghi@gmail.com
Full list of author information is available at the end of the article
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Page 2 of 14
Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
Keywords Accident, Traffic accidents, Causal effect, Ridge regression, Lasso regression, Elastic net regression,
Generalized path analysis
Introduction
Single-vehicle run-off-road (SV-ROR) crashes could
include a vehicle that runs off the road and strikes a fixed
object on the roadside (e.g., traffic sign, utility pole, tree,
ditch, embankment, barrier, or culvert) or rolls over [1].
SVROR crashes account for a significant percentage of all
fatal traffic accidents worldwide. For example, according
to the statistical data released by the FHWA’s Roadway
Departure Safety Program, SV-ROR crashes accounted
for 51 percent of all traffic fatalities from 2016 to 2018 in
the United States [2]. In Sistan & Baluchestan, a province
in South-East Iran, single-vehicle and rollover crashes
accounted for 32.6% and 33.8% of all crash types between
2009 and 2010. ere were also 4.80% fixed-object colli-
sions [3]. ROR crashes are often more severe than other
crash types When a vehicle crosses the center line and
is involved in a head-on collision or leaves the roadway
and collides with immovable roadside items. As stressed
in the FHWA’s Roadway Departure Safety Program,
crossing a center line, Overturns, and hitting trees or
shrubs on the roadside is the reason for more than 70%
of ROR crashes [4]. In a study by Liu and Subramanian,
ROR crashes accounted for 80.6% and 56.2% of crashes
on highways and urban routes, respectively [5]. Conse-
quently, it is important to develop an efficient method for
investigating the unique characteristics and contributing
factors of single-vehicle run-off-road (SV-ROR) crashes
to reduce traffic injuries on highways. is would result
from the fact that driving on highways is fundamen-
tally different from driving in urban areas. Highways are
more likely to have higher speeds and more instances of
fatigue.
Several past studies have explored causal factors
contributing to the occurrence and the consequent
injury severity of ROR crashes. For example, Roque
etal. evaluated the variables influencing the severity of
ROR traffic crashes on freeways of Portuguese. eir
empirical results highlight the problems with the pre-
sent Portuguese road design, particularly regarding the
requirements for providing forgiving slopes and justi-
fications for installing safety barriers [6]. According to
Liu and Subramanian, significant factors associated with
a high risk of fatal single-vehicle ROR crashes include
drunk-driving, curved road design, over-speeding, rural
roads, high-speed limit roads, passenger cars, and unfa-
vorable weather conditions [5].
In the analysis of crash severity, common statisti-
cal approaches such as regression models have been
implemented in the long term because these models
provide good indicators of the probability of an acci-
dent, and the results are interpretable. ese stand-
ard approaches to statistical modeling require several
assumptions about the underlying probability distribu-
tion of the data and pre-assumed relationships between
the independent and dependent variables. If the
assumptions are violated, biased estimates and incor-
rect inferences can be reached. Supplementary to this,
although large population-based studies are frequently
used to estimate predictors’ effects in a real-world set-
ting, they are susceptible to confounding bias for the
lack of randomization. For this concern about rand-
omization, methods from the causal inference frame-
work have been explored as an approach for advancing
robust and relevant science.
On the other hand, the number of variables to be
entered in the causal modeling’s conceptual dia-
gram is always a problem, especially in traffic studies
with many risk factors. First, it is difficult to identify
true confounders concerning substantive knowledge
alone. Also, ignoring a real confounder may lead to
biased results, while including non-confounders can
increase the variance. To address these challenges,
Machine learning algorithms have been developed.
Machine learning techniques have been proposed to
solve problems in conventional statistical modeling.
ese techniques are now successful due to advances in
computing power. ese methods do not involve pre-
defined relationships between study variables, and pre-
dictions are available without the need to understand
the necessary mechanisms. Applied statistical methods
and machine learning techniques overlap significantly
because they deal with data analysis.
In this paper, we propose a hybrid method using
machine learning techniques and path analysis to main-
tain sufficient number and efficient variables in the
causal model of SV-ROR crashes. Beyond the meth-
odological novelty, this study utilizes Haddon’s matrix
[7] to comprehensively analyze the phenomenon under
investigation. Focusing variables on post-crash phases
and human, vehicle, and environmental factors ensures
a systematic and holistic approach to variable selection,
capturing a wide range of factors that contribute to the
occurrence and severity of the phenomenon. e study
also focuses on establishing causal relationships to
provide practical and applicable findings. By bridging
the gap between interventional studies and real-world
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Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
applicability, the research enhances understanding
of how the studied variables influence the outcome,
resulting in more accurate and meaningful findings.
Additionally, the study addresses the traditional engi-
neering perspective in traffic research and redirects the
focus toward the health dimension of traffic. Moreover,
considering the statistics of accidents and the severity
of ROR crashes of a car, as well as the lack of sufficient
information in this field in Iran (as far as we know),
there is a need for clear and specific lines of accounta-
bility and improving the quality and quantity of techni-
cal resources available to all stakeholders to implement
a safe system to reduce ROR crashes which can be
addressed using the results of this study.
Methods
Study design andvariables
is cross-sectional study includes information about
724 highway SV-ROR Crashes documented in Integrated
Road Traffic Injury Registry System (IRTIRS) [8] from
March 2015 to March 2016. All in all, there were 30 vari-
ables representing details of each crash in three main cat-
egories: i) crash scene-related, ii) Vehicle-related, and iii)
driver-related information. e study’s outcome, fatality,
included two categories; non-fatal crash (Y = 0) and fatal-
ity as fatal crash (Y = 1).
Ethics approval andconsent toparticipate
is study used the information of people who entered
the study voluntarily. Before participating in the study, all
participants were given an informed consent form. Par-
ticipants were assured that all their identifying informa-
tion would remain confidential. is study was approved
by the Research Committee under Protocol No. #1396.465
and the Ethics Committee under ethic No. #IR.TBZMED.
REC.1398.1244of the Tabriz University of Medical Sciences.
Statistical analysis
STATA (Release 17: 2021, StataCorp LCC, College Sta-
tion, Texas 77845–4512 USA) and MPlus (Release 7.4:
2015, Computer Software. Los Angeles, CA: Muthén &
Muthén) software were used to conduct statistical analy-
sis. In the initial step, the dataset maintained a ratio of
80% and 20% for training and testing sets, respectively.
e proposed hybrid model used three machine learn-
ing regularization algorithms, namely: Ridge Regression
(RR), Least Absolute Shrinkage and Selection Operator
Regression (LR), and Elastic Net Regression (EnetR) for
variable selection. e primary knowledge behind these
models is the regularization of least squares through a
regularization parameter λ [9].
For studying the regression model’s regularization, it
is necessary to solve optimization problems in norms
terms. Accordingly, the
Lq
-norm for a real vector x ϵ
Rn
and q
≥
1 is defined as the following:
For q = 1 on obtains the L1-norm, and for q = 2 the
L2-norm (called Euclidean norm as well). The L2-norm
will be revisited while discussing RR and the L1-norm
for LR.
Ridge Regression (RR)
RR is a regularization method that benefits from regu-
lar least-squares approaches to minimize a loss fiction
involving a sum of squared residuals. But in contrast to
least squares methods, there is also a term called λ as a
penalty parameter in the loss function, which is meas-
ured by the sum of squared regression weights. As indi-
cated, this penalty parameter reduces the over-fitting
and variability of the estimate by shrinking the weight of
non-significant regression coefficients towards zero. RR
minimizes the following function equation to estimate
regression coefficients (β^) [10]:
Here the residual sum of squares (RSS) is called loss
of the model, λ is the tuning, regularization, or penalty
parameter which controls coefficients’ shrinkage and
λ
β
2
2
is the tuning, regularization, or penalty term.
e L2-norm β
2
is sometimes known as Tikhonov
regularization.
Lasso Regression (LR)
LR bears several parallels to RR since it also regularizes
the loss function employing λ regularization param-
eter. Nevertheless, LR can choose the most significant
independent variables and ignore those with negligible
impact on the dependent variable. LR minimizes the fol-
lowing function equation to estimate regression coeffi-
cients (β^) [10]:
||
x||q=
n
i=1
|xi|q
1
q
β
∧RR =arg min
1
2n
n
i=1yi−
j
βjxij2+�β�2
2
=
arg min
1
2n
RSS(β)+||β||2
2
=
arg min
1
2n
||y−βX||2
2+||β||2
2
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Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
Here λ is the tuning, regularization, or penalty param-
eter that must be estimated. It should be mentioned that
there are some limitations to the LR estimator:
1. For p > n, the LR selects the most variables, which can
be a limiting factor if the true model contains more
than n variables.
2. For n > p and high correlation between predictors,
the LR prediction performance is inferior to the RR.
3. e LR does not provide grouping property. In bet-
ter words, it prefers to select just one variable from a
group of highly correlated ones.
Elastic net regression
EnetR is a combination of RR and LR. It is a highly
effective algorithm since it uses two regularization
parameters to combine the strengths and advantages
of both RR and LR. EnetR minimizes the following
function equation to estimate regression coefficients
(β^) [10]:
Here
P∝(β)
is the elastic net penalty term. For the par-
ticular case
α
= 1, it leads to the RR penalty, and for
α
= 0, the LR penalty. is penalty term is tuned out to be
highly advantageous if p > n or when the predictors are
highly correlated.
e regularization models can deal with multicolline-
arity and be used for variable selection. e hyperparam-
eters, namely λ and α in the models’ elastic net, have been
tuned through several procedures: tenfold cross-valida-
tion (CV), minimum Bayesian information criteria (min
BIC), and adaptive lasso, wherever possible. Deviance
β
∧LR =arg min
1
2n
n
�
i=1
(yi−
�
j
βjxij)2+||β||1
=
arg min
1
2n
||y−βX||2
2+||β||1
β
∧EnetR =argmin
1
2n n
i=1yi−
j
βjxij2+P∝(β)
=
argmin
1
2n
�y−βX�2
2+P∝(β)
WhereP∝
(β)=
a
�β�
2
2
+(
1
−α)�β�
1
=p
j=1
αβ2
j+(1−a)
βj
and deviance ratios were used to assess the goodness of
fit in a testing sample [10]. In the final step, to maximize
the benefits of the algorithm in this hybrid approach, the
output data from the advantageous method detected in
the previous step with the selected variables were then
presented to generalized path analysis (gPath). e gPath
was performed to describe the direct and indirect rela-
tionships among a set of selected variables and enhance
the prediction accuracy and interpretability of the results.
ere aresix following steps in each path modeling [11].
Figure1 illustrates an overview of the proposed HLR–
gPath model.
1. Model specification
Model specification is necessary to detect relationships
among a set of research variables. In this step, a graphical
language, a practical and convenient approach to depict-
ing complicated relationships, is used to design a concep-
tual model. e associations found in various studies are
considered key clues and supporting information in con-
structing the conceptual model.
2. Model Identification
Model identification involves formulating the relation-
ships mentioned in the model specification phase. Indeed
it is related to the model to be fit to find the solution. It
contains two conditions:
I. Rank condition: e rank condition is defined by
the rank of the matrix, which should have a dimen-
sion (M-1), where M is the number of endogenous
variables in the model. is matrix is formed from
the coefficients of the variables (both endogenous
and exogenous).
II. Order condition: is condition is defined by
counting included and excluded variables in each
equation. Although the rank condition tells us
whether the equation under consideration is iden-
tified or not, the order condition tells us if it is pre-
cisely identified or over-identified.
3. Model estimation
e set of equations is simultaneously solved in the
model estimation step to estimate the model fitting
parameters. ere are plenty of estimation methods
namely: maximum likelihood parameter estimates with
conventional standard errors and chi-square test statis-
tic (ML), maximum likelihood parameter estimates with
standard errors and a mean-adjusted chi-square test
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Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
statistic (MLM), maximum likelihood parameter esti-
mates with standard errors and a mean- and variance-
adjusted chi-square test statistic (MLMV), maximum
likelihood parameter estimates with standard errors
and a chi-square test statistic (MLR), maximum likeli-
hood parameter estimates with standard errors approxi-
mated by first-order derivatives and a conventional
chi-square test statistic (MLF), Muthén’s limited infor-
mation parameter estimates with standard errors and
chi-square test statistic (MUML), weighted least square
parameter estimates with conventional standard errors
and chi-square test statistic (WLS), weighted least square
parameter estimates using a diagonal weight matrix
with standard errors and mean-adjusted chi-square test
statistic (WLSM), weighted least square parameter esti-
mates using a diagonal weight matrix with standard
errors and mean- and variance-adjusted chi-square test
statistic (WLSMV), unweighted least squares param-
eter estimates (ULS), unweighted least squares param-
eter estimates with standard errors and a mean- and
variance-adjusted chi-square test (ULSMV), general-
ized least square parameter estimates with conventional
standard errors and chi-square test statistic (GLS), and
Bayesian posterior parameter estimates with credibil-
ity intervals and posterior predictive checking (BAYES).
Parameter estimates of the MLM and MLMV methods
are robust to non-normality. e estimates of the MLR
are robust not only to non-normality but also to non-
independence of observations. e WLSM, WLSMV,
and ULSMV methods use a full-weight matrix, and the
GLS method uses a normal-theory-based weight matrix
[12]. In this study, the WLSMV was used. is robust
estimator does not assume a normal variable distribution
and provides the best option for modeling categorical or
ordered data [13].
4. Model testing
Path analysis supplies straightforward significance
tests to determine the probable relationships between
Fig. 1 The overview of the proposed HLR–gPath model. Abbreviations Lasso: Least Absolute Shrinkage and Selection operator; CV: cross‑validation;
min BIC: minimum Bayesian information criteria; gPath analysis; generalized path analysis
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Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
study variables, group differences, or the magnitude of
explained variance. ere is not a Straightforward test
for deciding about model fit in path analysis. e best
method for determining model fit is to examine several
test outcomes. e collection of these numerous tests is
known as model goodness of fit indices, which includes
chi-square test/degree of freedom values (
X2
df
) below five,
root mean square error of approximation (RMSEA) val-
ues below 0.08, Tucker-Lewis index (TLI), and compara-
tive fit index (CFI) values over 0.90. e chi-square test
was used to conclude the significance of relationships,
and P-values were calculated based on the statistics of
this test.
5. Model modification
If the model’s fit is unacceptable, it can be edited using
significant modifications. Model modification entails
changinganestimated and identifiedmodelby fixing free
or freeing parametersthat were fixed using modification
indices provided by the model.
6. Model validation
e bootstrap and jackknife methods, which fall under
non-parametric and resampling techniques, are used
for model validation. Confidence intervals are gener-
ated using these two techniques for direct and indirect
effects. In this study, bootstrap was used, and changes in
percent between the width of the original model’s confi-
dence intervals and the ones resulted from the Bootstrap
resampling method were calculated using the following
formula:
We decided to set 15% as a predetermined amount so
that models with a < 15% difference% according to this
statistics would be considered model overlap, leading to
suitable external validity.
Results
Main variables andmeasures
Among all the 724 SV-ROR Crashes, 101 (13.61%) were
fatal. Overall, the information related to 28 explanatory
variables was recorded. ese explanatory variables are
shown in Table1 in more detail.
Results ofmodel selection methods foridentifying risk
factors ofSV‑ROR crashes
As evident in Fig. 2, the LR and EnetR with min BIC
method for selecting λ presented minor deviance.
P
change =
CI width
original model −
CI width
Bootstrap method
CI width
Bootstrap method
×
100
However, comparing deviance ratios revealed that LR
outperforms EnetR with the largest Deviance-ratio.
Based on the results from LR with min BIC λ select-
ing method, the presence of a passenger, collision type,
vehicle age, and driver misconduct were identified as
the main factors attributing to the severity of SV-ROR
crashes. In the next step, these four variables were used
to design the conceptual model and causal inference in
the gPath model.
Conceptual model
Figure3 represents the hypothetical direct and indirect
effects utilized for path analysis within the conceptual
model. e relationships found in the numerous studies
[15–21] were considered the key clues and supporting
evidence to make this framework. In this model, fatality
has been defined as the final endogenous variable (i.e.,
dependent). e presence of passenger and vehicle age
have been defined as the exogenous variables (i.e., inde-
pendent) and driver misconduct and collision type as the
mediating variables. In Fig.1, the arrows have been used
to represent hypothetical direct effects, and the lines that
comprise variables that simultaneously play exogenous
and endogenous roles represent the mediating effects
(e.g., collision type is an endogenous variable to pas-
senger presence but an exogenous variable to fatality).
With regard to present evidences the subsequent general
objective is assumed:
A Hybrid of the Regularization method and generalized
path analysis is a parsimonious model showing direct and
indirect effects in modeling SV-ROR Crashes.
Results ofthehybrid LR‑gPath model
Five variables were in the hybrid LR-gPath (HLR-
gPath) model; one variable was final endogenous, two
were exogenous, and the other two were meditating.
Initially, the model started with a conceptual model
hypothesis that resulted in the following indices: with
X2
3
= 16.09, P < 0.001,
X2
/df = 5.36 > 5, C FI = 0.94 > 0.9,
TLI = 0.71 < 0.9, RMSEA = 1.00 > 0.08 (90% C I = (0.06
to 0.15)). Based on modification indices and add-
ing a path from driver misconduct towards collision
type, the final full model fitted the data accurately with
X2
2
= 6.09, P < 0.001,
X2
/df = 3.05 < 5, CFI = 0.99 > 0.9,
TLI = 0.96 > 0.9, RMSEA = 0.04 < 0.08 (90% CI = (0.01 to
0.08)). All conclusions hereinafter were drawn using the
perfect fitted model (Fig.4).
Direct eects
All coefficients on the perfect fitted model were statis-
tically significant except at the 0.05 significance level.
Findings showed significant direct relationship between
fatality and following variables: passenger presence
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Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
Table 1 Explanatory variables description in Single‑vehicle Run‑off‑road Crashes (n = 724)
Variable Variable level Total crashes Fatal crashes
n (%) n (%)
Passenger presence no 321 (43.26%) 29 (28.71%)
yes 421 (56.74%) 72 (71.29%)
Crash day weekday 501 (67.52%) 65 (64.36%)
weekend 241 (32.48%) 36 (35.64%)
Lighting day 498 (67.12%) 72 (71.29%)
night 218 (29.38%) 27 (26.73%)
twilight/dawn 26 (3.5%) 2 (1.98%)
Clear/cloudy weather no 41 (5.53%) 2 (1.98%)
yes 701 (94.74%) 99 (98.02%)
Dry road surface no 45 (6.06%) 2 (1.98%)
yes 697 (93.94%) 99 (98.02%)
Curved geometric design no 628 (84.64%) 82 (81.19%)
yes 114 (15.36%) 19 (18.81%)
Vehicle factor no 731 (98.52%) 99 (98.02%)
yes 11 (1.48%) 2 (1.98%)
Human factor no 196 (26.42%) 24 (23.76%)
yes 546 (73.58%) 77 (76.24%)
Collision type head‑on collision 176 (23.72%) 38 (37.63%)
rear‑end collision 311 (41.91%) 41 (40.59%)
T‑bone collision 220 (29.65%) 11 (10.89%)
side‑swipe collision 35 (4.72%) 11 (10.89%)
Road shoulder unpaved 35 (4.72%) 1 (0.99%)
paved with soil 349 (47.04%) 47 (46.53%)
paved with asphalt 358 (48.25%) 53 (52.48%)
Road design one‑way road 709 (95.55%) 100 (99.01%)
two‑way road 33 (4.45%) 1 (0.99%)
Road defect no 702 (94.61%) 91 (90.1%)
yes 40 (5.39%) 10 (9.9%)
Permitted speed 60–80 77 (10.38%) 1 (0.99%)
80–95 38 (5.12%) 5 (4.95%)
95–110 545 (73.45%) 83 (82.18%)
110–120 82 (11.05%) 12 (11.88%)
Vehicle type low 578 (77.9%) 83 (82.18%)
high 153 (20.62%) 14 (13.86%)
tricycle/ bicycle/motorcycle 11 (1.48%) 4 (3.96%)
High‑risk vehicle colorano 560 (75.47%) 72 (71.29%)
yes 182 (24.53%) 29 (28.71%)
Vehicle safety equipment low risk 456 (61.46%) 60 (59.41%)
high risk 286 (38.54%) 41 (40.59%)
Vehicle age less than 5yrs 261 (35.18%) 44 (43.56%)
5 to 9 yrs 279 (37.6%) 34 (33.66%)
10 to 14 yrs 154 (20.75%) 14 (13.86%)
15 and more than 15yrs 48 (6.47%) 9 (8.91%)
Vehicle plaque description personal regional 647 (87.2%) 90 (89.11%)
other 95 (12.8%) 11 (10.89%)
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Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
(odds ratio (OR) = 2.31, 95% CI = (1.73 to 3.06)), colli-
sion type (OR = 1.21, 95% CI = (1.07 to 1.37)), vehicle age
(OR = 1.54, 95% CI = (1.32 to 1.79)), and driver miscon-
duct (OR = 2.08, 95% CI = (1.77 to 2.46)).
Indirect eects
e mediated path model indicated that passenger pres-
ence (β = 0.003; 95% CI = (-0.007 to 0.013)) and driver
misconduct (β = 0.108; 95% CI = (0.030 to 0.186)) had an
indirect positive effect on fatality through their impacts
on collision type. Furthermore, collision type (β = 0.181;
95% CI = (0.175 to 0.187)) was significantly and directly
related to fatality through driver misconduct (Fig.3).
Model validation utilizing theBootstrap method
e changes in percent statistics between the width
of the original model’s confidence intervals and those
resulting from the Bootstrap resampling method were in
the range of 0.43 to 10.01. Considering the high overlap
of the confidence intervals of the original model and the
Bootstrap method, we assumed that the model has suf-
ficient external validity.
Table 1 (continued)
Variable Variable level Total crashes Fatal crashes
n (%) n (%)
Vehicle maneuver forward 723 (97.44%) 100 (99.01%)
turn 14 (1.89%) 0 (0%)
other 4 (54%) 1 (0.99%)
backward 1 (0.13%) 0 (0%)
Driver fault status at fault 733 (98.79%) 98 (97.03%)
not at fault 9 (1.21%) 3 (2.97%)
Driver gender male 667 (89.89%) 94 (93.07%)
female 75 (10.11%) 7 (6.93%)
Driver educationbilliterate 13 (1.75%) 3 (2.97%)
primary 69 (9.3%) 7 (6.93%)
nonacademic 595 (80.19%) 76 (75.25%)
academic 65 (8.76%) 15 (14.85%)
Driver job jobs with high economic status 642 (86.52%) 85 (84.16%)
jobs with middle economic status 60 (8.09%) 14 (13.86%)
jobs with low economic status 40 (5.39%) 2 (1.98%)
Driver age (years)cChild (< 18) 1 (0.13%) 0 (0%)
Adult (18 ‑65) 694 (93.53%) 92 (91.09%)
Elderly (> = 65) 47 (6.33%) 9 (8.91%)
Type of driving license class A 83 (11.19%) 7 (6.93%)
class B 250 (33.69%) 33 (32.67%)
class C 393 (52.96%) 58 (57.43%)
motorcycle 6 (0.81%) 0 (0%)
no license 10 (1.35%) 3 (2.97%)
Driver seatbelt usage status used 525 (70.75%) 58 (57.43%)
not used 217 (29.25%) 43 (42.57%)
Driver Judiciary cause carelessness 725 (97.71%) 94 (93.07%)
other 17 (2.29%) 7 (6.93%)
Driver misconduct spiral movement 356 (47.98%) 6 (5.94%)
over speeding 326 (43.94%) 66 (65.35%)
other 60 (8.09%) 29 (28.71%)
a Low-risk colors: white, yellow, cream, pink, orange, brown; High-risk colors: silver, graphite gray, black, blue, green, dark blue, gray, purple, red [14]
b Primary: literacy and elementary education; non-academic: cycle, middle school, and diploma; academic: Bachelor’s (B.Sc.), Associate’s (A.Sc.), Master’s (M.Sc.), and
Doctorate (Ph.D.) degrees
c Age categories based on the driving regulations in the country
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Page 9 of 14
Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
Discussion
is study is the first to discover that the cutting-edge
HLR-gPath model’s applicability may identify relation-
ships and predict fatality in SV-ROR crashes. e pro-
posed innovative HLR-gPath detects the most important
risk factors in SV-ROR crashes and demonstrates the
direct and indirect relationships between the selected
variables. Traditionally, the gPath analysis has its own
advantages when examining complicated relations
among the many variables than having several inde-
pendent variables with one dependent and comparing
different assumed models against another to find which
one best fits the used data. And LR can execute variable
selection, leading to human effort and time-saving. In
the proposed model in this study, the valuable variables
were firstly extracted using LR, followed by the adaption
of the gPath analysis to reveal stronger direct and indi-
rect relationships to model SV-ROR crashes. ough
Fig. 2 Results of model selection methods for identifying risk factors of SV‑ROR crashes
Fig. 3 Hypothesized conceptual model
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Page 10 of 14
Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
our proposed hybrid model achieves promising results,
it takes more processing time than standalone machine
learning algorithms. In machine learning research, we
aim to provide even better results with faster execution
and greater effectiveness.
e findings from our study indicate a significant rela-
tionship between fatality and various factors, including
the presence of passengers, collision type, driver miscon-
duct, and vehicle age. We also observed that the presence
of passengers influenced fatality through the mediation
of driver misconduct and collision type. Furthermore,
collision type was a mediator in assessing the relationship
between fatality and driver misconduct.
In a similar local crash context, Yousefifard etal. (2021)
[22] conducted a systematic review and meta-analysis
to identify key risk factors contributing to road acci-
dent-related mortality in Iran. eir study included 20
studies involving 2,682,434 traffic accident victims and
23,272 deaths. e findings revealed that men had a 1.66
times higher risk of death than women, and each year
increase in age raised the risk by 1%. Urban streets, road-
way defects, not driving on flat and straight roads, and
exceeding the speed limit were significant road-related
mortality risk factors. Independent risk factors among
road users included not maintaining focus on the road,
not fastening seatbelts, and reckless overtaking. Pedes-
trians had a 2.07 times higher mortality risk than drivers
and passengers. Accidents during daylight hours had a
lower risk of death, while no significant relationship was
found between mortality and vehicle types.
e authors of Yousefifard etal.’s study concluded that
the limited number of studies on vehicle-related factors
has resulted in a lack of comprehensive analysis of these
important aspects. ey also emphasized the absence
of adjustment for key potential confounders in all the
included studies, making it challenging to obtain a com-
prehensive and reliable understanding of the most crucial
risk factors for road accident fatalities in Iran.
Our study focused specifically on single-vehicle run-
off road crashes, which are known to be associated with
higher risks and severity [23]. We observed a higher mor-
tality rate than Yousefifard et al.’s study, which can be
attributed to this specific focus. However, our study find-
ings align with Yousefifard etal.’s study, demonstrating a
consistent pattern of increased risk of death associated
with several factors, including being male, advancing age,
road defects, exceeding the speed limit, not maintaining
focus on the road, failure to fasten seatbelts, and reckless
overtaking.
It’s important to note that our study did not include
pedestrian data, a significant group in assessing over-
all mortality rates in road accidents. erefore, cau-
tion should be exercised in interpreting the findings of
our study. In contrast to Yousefifard etal.’s findings, our
Fig. 4 Perfect fitted model with standardized path coefficients *: P < 0.05
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Page 11 of 14
Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
study revealed that accidents occurring during daylight
hours were associated with a higher risk of death. is
discrepancy in results may be attributed to factors such
as increased traffic volume and higher speeds during the
daytime, potential driver complacency or distraction due
to better visibility, or variations in road user behaviors
and characteristics specific to the studied population.
Further research is necessary to explore and understand
the underlying reasons behind this contrasting observa-
tion and its implications for road safety measures and
interventions.
Our study addresses the knowledge gap highlighted
by Yousefifard etal. in the context of local crash stud-
ies. We specifically focused on vehicle-related factors
and aimed to account for crucial potential confounders
lacking in previous studies. Our research contributes to
a more comprehensive and reliable understanding of the
most critical risk factors for road accident fatalities in
Iran, considering the adjusted predictors. It’s worth not-
ing that Yousefifard etal.’s study, being a meta-analysis,
covers the cumulative evidence up until 2021.
Here, we will expand the discussion on essential varia-
bles to provide a deeper and more comprehensive under-
standing of how they impact SV-ROR crash fatalities.
The presence ofapassenger impact ondriver misconduct
e presence of passengers can exert both positive and
negative effects on a driver’s behavior and crash risk, con-
tingent upon various factors [24]. Notably, previous stud-
ies have revealed that the presence of passengers can lead
to reduced attention to driving and psychological pres-
sure to drive less safely, particularly among young driv-
ers [25–27]. Moreover, teenage passengers, particularly
males, have been associated with an increased crash risk
[27]. Passengers can distract drivers or encourage them
to engage in risky behaviors, including speeding and
other dangerous driving practices [28]. Similarly, it can
be posited that having a passenger may induce elevated
stress levels, thereby resulting in diminished driving pro-
ficiency [29].
Research has substantiated that conversing with pas-
sengers can distract drivers and serve as a predictor of
driving misconduct [19]. A study conducted by Heck
and Carlos sheds light on the various distractions driv-
ers face when accompanied by passengers. Findings
from this study indicated that, particularly for teenag-
ers, engaging in conversation with friends in the vehicle
can be distracting, and peers may even intentionally cre-
ate hazardous situations due to the excitement or humor
they derive from it. In addition to unwanted distractions
from conversations or verbal exchanges, passengers can
create further distractions for drivers by altering the
radio, using drugs, physically interfering with or tickling
the driver, or attempting to manipulate vehicle controls
[30]. Moreover, another study identified the male gender,
lower education levels, and an increased number of years
of driving experience as factors predicting the occurrence
of distinct distractions [31].
Nevertheless, it is crucial to acknowledge that the
impact of passengers on driver behavior is not uniform
across all drivers and passenger types [24]. In certain
instances, passengers can offer a protective effect to
drivers, thereby reducing their crash risk. For instance,
drivers sometimes exhibit safer driving behavior when
accompanied by passengers, and the presence of more
passengers can diminish a driver’s crash potential [32].
However, this protective effect is less pronounced among
young drivers, during nighttime conditions, insituations
involving slow traffic, and at crossroads [25].
Based on the outcomes of this study, it is plausible to
consider the development of tailored driver education
programs specifically addressing passenger distractions
with the aim of reducing their frequency. In this con-
text, cognitive psychology suggests that high-risk traveler
behavior may represent a developmental norm that edu-
cation can address.
The presence ofapassenger impact oncollision type
e presence of passengers has a discernible impact on
the type of collisions that may occur. Specifically, it has
been observed that young drivers transporting only
younger passengers are more prone to being involved in
single-vehicle crashes transpiring under high-speed and
low-volume conditions [32]. Such collisions, predomi-
nantly single-vehicle nature, render young drivers carry-
ing passengers particularly vulnerable. However, for adult
drivers, this collision type was found to be more injuri-
ous when the driver was unaccompanied in the vehicle
[26]. A study conducted by Goel and Sachdeva sought to
identify the causative factors, types, timing, and vehicle
categories associated with crashes. Consequently, they
ascertained that driver error predominantly contributes
to head-on or rear-end collisions [33].
All in all, the presence of passengers has the potential
to impact both driver misconduct and the specific type
of collision that transpires. e influence exerted by pas-
sengers on driver behavior and crash risk is contingent
upon various factors, including the age of the driver and
passengers, as well as prevailing driving conditions. It is
imperative for drivers to be conscious of these factors
and take appropriate precautions to ensure the safety of
themselves and their passengers on the road.
Vehicle age
It is evident that older vehicles are generally less safe than
their modern counterparts due to the lack of advanced
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Page 12 of 14
Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
safety features and improvements in crashworthiness. A
study conducted by Ryb etal. [34] aimed to explore the
relationship between the model year of vehicles and the
risk of crash-related mortality for occupants. e analy-
sis drew upon data from the National Automotive Sam-
pling System Crashworthiness Data System (NASS-CDS)
between 2000 and 2008. e study specifically focused
on adult occupants seated in the front of vehicles. e
findings unveiled that mortality rates decreased among
later model year groups, indicating that newer vehi-
cles were associated with lower crash-related mortality.
After adjusting for potential confounding factors, it was
observed that vehicles with model years ranging from
1994 to 2008 exhibited decreased odds of death com-
pared to those with model years predating 1994. As a
result, the researchers concluded that introducing newer
vehicles into the automobile fleet likely contributed to
the overall decline in mortality rates witnessed over the
past two decades.
In a research article [35], the authors sought to inves-
tigate the impact of both aging drivers and vehicles on
the severity of injuries sustained by vehicle occupants
involved in road traffic crashes in Spain. e study find-
ings revealed a linear escalation in crash severity with
increasing vehicle age up to 18 years, after which the
severity remained consistently at the highest level in bod-
ily injury. Notably, no significant interaction was detected
between driver and vehicle age regarding their impact
on injury severity. ese research outcomes hold par-
ticular significance for countries like Spain, where the
driver population is experiencing extended longevity and
the average age of vehicles on the road is progressively
advancing.
Several reasons account for the heightened risk asso-
ciated with older vehicles, including diminished crash-
worthiness (i.e., the ability of a vehicle to safeguard
occupants during crashes), outdated safety devices that
are more susceptible to failures due to aging, and the
absence of contemporary safety features such as airbags,
crumple zones, and electronic stability control. e cor-
relation between newer vehicles and decreased crash-
related fatalities is evidently established. Integrating
these vehicles into the overall automotive fleet has played
a substantial role in declining mortality rates. Conse-
quently, the retirement of older cars from the fleet rep-
resents a pivotal step that undoubtedly contributes to a
considerable reduction in crash-related deaths. is pro-
active measure underscores the importance of embracing
advanced technology to enhance road safety.
Strengths andweaknesses
e first limitation of the current study, there is not a
precise and thorough registry system in the country to
incorporate these data with hospital data and take them
into account. e fact that accidents are likely not ade-
quately reported to the authorities is another issue with
this study. e study’s strength can be seen in the fact
that it took into account data from six of the country’s
most densely inhabited provinces, which allows for the
generalizability of the findings. Another study’s strength
is introducing a hybrid model for modeling data from
traffic crashes.
To further enhance the methodology for future
research, it is crucial to acknowledge and address the
limitations of this study. Firstly, we defined "traffic fatal-
ity" as deaths at the crash scene. However, it is essential
to note that this definition was limited to deaths imme-
diately at the crash scene. is limitation arose due to
the lack of access to in-hospital data, which would have
allowed us to include fatalities within 30 days of the time
of the crash. Future research in this field must address
this limitation and incorporate a more comprehensive
assessment of traffic fatalities. Secondly, given the lim-
ited scope of this study, which only considered data from
2015 to 2016, it is crucial for future research to incor-
porate more up-to-date information. By extending the
analysis period and including recent data, researchers
will gain a deeper understanding of the evolving trends
more accurately. is comprehensive approach will pro-
vide valuable insights into how we can further improve
road safety measures moving forward.
is study is also limited to underreporting in road
traffic crash studies, leading to incomplete and inaccurate
data. It can result from official reporting mechanisms
that fail to capture minor crashes or incidents without
severe injuries or significant property damage. Addition-
ally, individuals may choose to resolve minor crashes
privately, bypassing official reporting channels. Social
and cultural factors, including stigma and mistrust, fur-
ther discourage reporting. To address underreporting,
researchers and policymakers are suggested to utilize
multiple data sources, such as police records, hospital
records, and insurance claims, to ensure comprehensive
data collection. Protecting confidentiality and anonymity
encourages more accurate reporting, while public aware-
ness campaigns can help overcome barriers and stigma
associated with reporting incidents. By implementing
these strategies and continuously monitoring and evalu-
ating reporting systems, efforts can be made to minimize
underreporting bias and improve the accuracy and com-
prehensiveness of road traffic crash studies.
Conclusions
e introduced novel HLR-gPath model was practi-
cal in identifying rational crash pathways in SV-ROR
crashes. ey could predict fatality by Considering both
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Page 13 of 14
Jahanjooetal. BMC Medical Research Methodology (2023) 23:221
exogenous and mediator variables simultaneously in a
model. is study identified collision type and driver
misconduct as mediator variables of SV-ROR crashes.
It is suggested that when developing prevention strat-
egies for SV-ROR crashes, health policymakers and
healthcare professionals should consider the predomi-
nance of the mediators examined in this study.
Abbreviations
SV‑ROR Single Vehicle Run‑Off‑Road
IRTIRS Integrated Road Traffic Injury Registry System
RR Ridge Regression
LR Least Absolute Shrinkage and Selection operator Regression
EnetR Elastic Net Regression
gPath Generalized Path Analysis
CV Cross‑Validation
min BIC minimum Bayesian Information Criteria
x2
df
Chi‑square test/Degree of Freedom
RMSEA Root Mean Square Error of Approximation
TLI Tucker‑Lewis Index
CFI Comparative Fit Index
HLR‑gPath Hybrid Least Absolute Shrinkage and Selection Operator Regres‑
sion Generalized Path Analysis
ML Maximum likelihood parameter estimates with conventional
standard errors and chi‑square test statistic
MLM Maximum likelihood parameter estimates with standard errors
and a mean‑adjusted chi‑square test statistic
MLMV Maximum likelihood parameter estimates with standard errors
and a mean‑ and variance‑adjusted chi‑square test statistic
MLR Maximum likelihood parameter estimates with standard errors
and a chi‑square test statistic
MLF Maximum likelihood parameter estimates with standard errors
approximated by first‑order derivatives and a conventional chi‑
square test statistic
MUML Muthén’s limited information parameter estimates with stand‑
ard errors and chi‑square test statistic
WLS Weighted least square parameter estimates with conventional
standard errors and chi‑square test statistic
WLSM Weighted least square parameter estimates using a diagonal
weight matrix with standard errors and mean‑adjusted chi‑
square test statistic
WLSMV Weighted least square parameter estimates using a diagonal
weight matrix with standard errors and mean‑ and variance‑
adjusted chi‑square test statistic
ULS Unweighted least squares parameter estimates
ULSMV Unweighted least squares parameter estimates with standard
errors and a mean‑ and variance‑adjusted chi‑square test
GLS Generalized least square parameter estimates with conventional
standard errors and chi‑square test statistic
BAYES Bayesian posterior parameter estimates with credibility intervals
and posterior predictive checking
Acknowledgments
We are thankful to all of the people who helped us to conduct this study. The
authors would like to acknowledge the staff of the Road Traffic Injury Research
Center of Tabriz University of Medical Sciences for supporting this study. This is
a database report from a Ph.D. thesis registered in Tabriz University of Medical
Sciences with Number 64041 by Fatemeh Jahanjoo.
Authors’ contributions
FJ, MA‑J and HS‑B designed the research; MA‑J, HS‑B and FJ discussed inves‑
tigation methodology and contributed to result interpretation; FJ performed
data analysis; MA‑J and HS‑B supervised the study conduction; MA‑J, FJ wrote
the original draft; MA‑J, revised contents; all authors revised the paper and
agreed with the final version of the manuscript.
Funding
This study was based on data from Fatemeh Jahanjoo’s Ph.D. thesis, which
was financially supported by the Research Deputy of the Tabriz University of
Medical Sciences (TUOMS) under Grant No. 64041 and approved by the Insti‑
tutional Review Board of TUOMS with ethics code: IR.TBZMED.REC.1398.1244.
Availability of data and materials
The dataset created and supported the current study’s findings is not acces‑
sible by the general public since not requesting consent during the study
protocol submission and from participants. However, they are available from
the corresponding author upon reasonable request.
Declarations
Ethics approval and consent to participate
Participation in the study was voluntary for everyone, and participants’ privacy
was respected. All participants provided their informed consent on research
participation before entering the survey. The participants are assured that
their personal information will remain confidential and not be disclosed.
All methods were carried out in accordance with relevant guidelines and
regulations. This study was approved by the Research Committee under Proto‑
col No. #1396.465 and the Ethics Committee under Ethic No. #IR.TBZMED.
REC.1398.1244of the Tabriz University of Medical Sciences (TUOMS).
Consent for publication
Not applicable.
Competing interests
The authors declare no competing interests.
Author details
1 Road Traffic Injury Research Center, Tabriz University of Medical Sciences,
Tabriz 5167846311, East Azerbaijan, Islamic Republic of Iran. 2 Cabrini Research,
Cabrini Health, Malvern, VIC 3144, Australia. 3 Biostatistics Unit, School of Public
Health and Preventative Medicine, Faculty of Medicine, Nursing and Health
Sciences, Monash University, Melbourne, VIC 3004, Australia. 4 Department
of Psychiatry, School of Clinical Sciences, Faculty of Medicine, Nursing
and Health Sciences, Monash University, Clayton, VIC 3168, Australia.
Received: 10 October 2022 Accepted: 25 September 2023
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