1. Improving Trauma Triage Models for Motor Vehicle Crashes
Yaoyaun Vincent Tana
, Michael Elliotta,b
, Carol Flannaganc
aUniversity of Michigan Department of Biostatistics, bInstitute for Social Research cUniversity of Michigan Transportation Research Institute
Introduction
Delta-v, a measure of the near-instantaneous change in vehi-
cle velocity after the impact of a crash, is a strong predictor of
severe injury. However, most prediction models of severe in-
jury use delta-v estimated during after crash investigations. Be-
cause a realistic and comprehensive real-time prediction model
would help Emergency Medical Services (EMS) allocate re-
sources more efficiently and reduce morbidity and mortality in
crashes, we develop a real-time prediction model using the ve-
hicle’s acceleration profile during a crash, recorded by the vehi-
cle’s Event Data Recorder (EDR). We use functional data anal-
ysis (FDA) to estimate the mean trend of the acceleration and
then built our prediction model around summary measures of
the estimated mean trend (its absolute integral and absolute in-
tegral of its slope) as well as its residual variance. We applied
our method to the acceleration profiles recorded in 2002-2012
EDR reports from the National Transportation Safety Admin-
istration (NHTSA) website. We obtained our outcomes from
the National Highway and National Automotive Sampling Sys-
tem (NASS) Crashworthiness Data System (CDS) datasets of
the same years. Our results can be seen as an important step to-
wards the development of a comprehensive near real-time pre-
diction model for severe injury in a motor vehicle crash.
Dataset and variables
We have EDR data from 3,460 vehicles that were involved in
frontal impacts (direction of impact 0◦
to 40◦
and 320◦
to 350◦
)
from 2002-2012. We analyzed data from 249 usable crashes, of
which 27 had a severe injury outcome.
Outcome
• VAIS: Maximum AIS 3+ in vehicle (Yes/No)
Deceleration (crash pulse) Data
• Time (1 ms)
• Gs (9.8 m/sec2
)
Baseline Data
• Driver seat beat use (Yes/No/Not reported)
• Front-seat passenger belt use (Yes/No/No front-seat passen-
ger/Not reported)
• Curb weight (kgs)
• Body type (Car/Pickups & Vans/SUV)
• Multiple crash indication (Yes/No)
• Principal direction of force (o
)
• Sampling weight
Method
We used a two-stage approach with summary measures from a
1st
stage FDA model as inputs for the 2nd
stage model (Jiang et.
al., 2014). FDA requires converting observed values yi1, yi2, . . . , yimi
to a function yi(tij). For each crash, we considered four meth-
ods of estimating yi(tij).
3 millisecond (3mil) Method
ˆyi(tij) =
mi
l=1
bilφl(tij) (1)
where φl(tij) ≡ φl,d(tij) are basis splines matrices of degree d,
and φl,d(tij) was obtained by the recursion relation:
φl,d(tij) =
tij − κil
κi,l+d − κil
φl,d−1(tij) +
κi,l+1+d − tij
κi,l+1+d − κi,l+1
φl+1,d−1(tij).
(2)
κij were the internal knots set at 3 millisecond intervals.
Combinatorial (Combi) Method We considered all possible
combinations of choosing 5 internal knots out of the knots at
3 millisecond intervals. The optimum placement of knots was
determined by the placement that gave the smallest mi
j=1[yij −
ˆyi(tij)]]2
.
Penalized natural cubic splines (PNCS) Method
ˆyi(tij) =
mi
l=1
[yil − y(til)]2
+ λi
T
[L(til)]2
dti (3)
where L(t) = w0x + w1y (til) + . . . + wd−1yd−1
(til) + yd
(til)
and d is the degree of the polynomial. We estimated λi using
generalized cross-validation. (Ramsay et.al., 1997).
Mixed Model (MM) Method (Wang, 1998)
yi(tij) = β0i + β1itij +
mi−1
p=1
Zijpbp + ij ij
iid
∼ N(0, σ2
i ).
(4)
where ti ∈ [0, 1], (b1, b2, . . . , bn−1)T
∼ N(0, τ2
i I), ZiZT
i = Ωi,
and Ωi is an mi × mi matrix with the rows and columns defined
as Ωk,l = 1
0 (tk − µ)+(tl − µ)+dt = 1
2[min(tk, tl)]2
max(tk, tl) −
1
6[min(tk, tl)]3
. The tuning parameter ˆλi could be estimated by
ˆλi = ˆσ2
i
miˆτ2
i
. tij in equation (4) was a transformation from the
original time ˜tij given by tij =
˜tij−min
j
(˜tij)
max
j
(˜tij)−min
j
(˜tij)
so that ti1 = 0 <
ti2 < . . . < timi
= 1.
We obtained Zi by estimating the Cholesky decomposition of
Ωi using Smith’s (1995) method. We used standard linear mixed
model programs to estimate ˆyi(tij) as
ˆyi(tij) = ˆβ0i + ˆβ1itij +
mi−1
p=1
Zijp
ˆbp. (5)
Summary measure For each crash pulse estimated under the
four FDA methods, we computed four summary measures:
1. ˆG = ti
|ˆyi(tij)|dti - Absolute area under the deceleration pro-
file. This could be seen as an estimation of total delta-v.
2. ˆg = ti
|ˆyi(tij)|dti - Absolute integral of the slope of ˆyi(tij) for
the duration ti. This measure gave a sense of the amount of
fluctuation in ˆyi(tij).
3. ˆσ2
- The residual variance of ˆyi(tij).
4. tt025 - Time the crash pulse took to return to within ±0.25Gs.
Predicting severe injury risk. We merged the chosen sum-
mary measures together with VAIS and baseline data: driver
seat belt use, front-seat passenger belt use, curb weight, body
type, and multiple crash indicator. We applied the weighted
logistic regression and ran an all-subset analysis on the nine
covariates (summary measures in chosen form). We obtained
three models: 1. Model with the highest ROC (Model A),
2. Model with the highest ROC excluding any summary mea-
sure (Model B), and 3. Centered summary measures in model
A and their squared terms with baseline model A covariates
(Quadratic Model A). We compared the ROC between these 3
models by running 1,000 bootstrap samples. To complement
the weighted ROC results, we plotted the weighted precision-
recall (PR) curve (Davis and Goadrich, 2006) and constructed
a false discovery rate (FDR) table. Finally, we conducted a
leave-one-out cross-validation (CV) to investigate how well our
models would perform given new data.
Results
We selected the summary measures computed under the MM
method and log-transformation of the summary measures be-
cause its CV results were better compared to the model with the
highest ROC. Our all-subset analysis produced a Model A con-
sisting all covariates except log(ˆg). The coefficients of log( ˆG),
log(tt025), belted driver, and multiple crash were significant.
Model B consisted of all baseline covariates. The coefficients
of belted driver and multiple crashes were significant. Because
ROC of quadratic model A was smaller compared to model A,
we shall not focus on quadratic model A.
The weighted ROC of Model B was to the right of Model A
for false positive rates between 0 and 0.8. The loess PR curve
of model B was on the left of model A for all recall values
(Figure 1). FDR table (Table 1) reflected results similar to the
PR curve (Figure 1). The leave-one-out cross-validation results
were generally similar to non cross-validation results but with
the weighted ROCs shifted right, weighted PR curves shifted
left, capture rates decreased, and FDR increased for all three
prediction models (Results not shown here).
Figure 1: Weighted Reciever Operating Curves (ROC) and Precision-Recall
(PR) Curves for Models A and B.
0.0 0.2 0.4 0.6 0.8 1.0
0.00.20.40.60.81.0
False Positive Rate
TruePositiveRate
Receiver Operating Curves for Models A and B
Model A
Model B
0.0 0.2 0.4 0.6 0.8 1.0
0.10.20.30.40.5
Recall
Precision
q
q
q
q
q
q
q
q
q
q
qq
qq
q
q
q
q
qq
q
q
q
qq
qq
qqqq
qq
q
q
qq
qq
qqqqqqqqq
qq
qqqqq
qqqqqqqqqqqqqqqqqqqqqqqqq qqqqqqqqq
qqq qqq
qq
qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq
Model A
Model B
Precision Recall Curves for Models A and B
Table 1: Fraction of AIS 3+ Injury Crashes Captured and Associated Frac-
tion of Crash that are not AIS 3+ [False Discovery Rate (FDR)] at various
thresholds of injury risk cutpoints.
Model A Model B
Cutpoints (%) Captured (%) FDR (%) Captured (%) FDR (%)
1 93.60 94.95 87.90 97.22
2 81.04 88.50 54.41 95.63
3 77.45 85.54 44.88 94.46
4 76.07 81.09 40.47 90.72
5 71.13 82.10 24.92 87.28
6 71.13 82.09 17.17 86.32
7 70.32 81.30 17.17 82.85
8 70.32 79.44 17.17 80.71
9 46.36 78.87 17.17 80.71
10 46.36 78.81 17.17 80.71
15 44.17 68.74 17.17 68.46
20 40.74 63.27 17.17 47.76
25 40.74 60.36 17.17 47.76
30 40.16 37.73 2.45 83.15
Discussion
We successfully developed a new severe injury risk prediction
model able to estimate the probability of a severe injury in a
motor vehicle crash near real-time. Model A performed fairly
Table 2: Coefficient Estimates for model A and B with weighted ROC.
Model A Model B
Parameter/Statistic Estimate (Conf. Int) Estimate (Conf. Int)
log( ˆG) 3.34 (1.43, 5.25)∗∗
log(ˆσ2
) 0.19 (-0.41, 0.80)
log(tt025) -6.07 (−10.05, −2.07)∗∗
Driver belt use
Belted -2.95 (−4.55, −1.36)∗∗∗
-3.23 (−4.79, −1.68)∗∗∗
Not reported 2.77 (-0.58, 6.13) 0.25 (-1.78, 2.29)
Not belted
Front-seat passenger belt use†
Belted 1.79 (-1.99, 5.58) 1.01 (-1.66, 3.69)
No front passenger 2.52 (-0.23, 5.28) 1.58 (-0.34, 3.50)
Not belted
Curb weight 0.0003 (-0.001, 0.002) -0.0007 (-0.003, 0.001)
Body type
Car 0.85 (-1.43, 3.14) 0.96 (-1.15, 3.07)
Pickup or Van -0.58 (-2.88, 1.72) 0.31 (-1.49, 2.12)
SUV
Multiple crashes?
Yes 5.20 (1.09, 9.31)∗
2.04 (0.11, 3.96)∗
No
ROC 0.93 0.78
ROC A - ROC B 0.151 (0.040, 0.227)
† Crashes not reporting front-seat passenger belt status were the same with driver belt status.
* 0.01 ≤ p < 0.05; ** 0.001 ≤ p < 0.01; *** p < 0.001.
well in predicting the severe injury crashes from our data (ROC 0.93). We
used a novel variable – the crash pulse – as the main variable in our regres-
sion model. We were not aware of any such applications of FDA to crash
pulses to predict severe injury risk in trauma literature. The summary mea-
sures we defined were new in trauma research and helped us avoid problems
we faced when defining ˆyi(tij) for each crash with a different set of linear
combination of functions.
Limitations
A majority of our frontal crashes (92.4%) were unusable because vehicle
acceleration was not reported. A comparison (results not shown here) be-
tween the demographics (driver’s age, sex, belt use, and intrusion, front-seat
passenger belt use, maximum vehicle injury severity, and sampling weight)
of eligible and ineligible crashes showed no significant difference except
for driver intrusion. This implied that excluded crashes had greater rates of
driver intrusion, suggesting that our analytic dataset may under-report the
most severe crashes.
Future direction
• Develop a separate prediction model that uses information from the ad-
justed velocity change instead of acceleration.
• Develop a method to combine the crash pulse and adjusted velocity change
model.
• Add the lateral, vertical, and rollover of crash pulse and adjusted velocity
components into the model.
• Develop a joint model to compute the FDA estimates and logistic regres-
sion model in a single step. This will make estimated coefficients more
efficient i.e. smaller estimated variance.
References
• Davis, J., Goadrich, M. (2006). The Relationship Between Precision-Recall and ROC Curves. Proceed-
ings of the 23rd International Conference on Machine Learning, Pittsburgh, PA.
• Jiang, B., Wang, N., Sammel M.D., Elliott M.R. (2014). Modeling short- and long-term variability of
variation of follicle stimulating hormone as predictors of severe hot flashes in Penn Ovarian Aging Study.
Submitted for publication.
• Ramsay, J.O., Heckman, N., and Silverman, B.W. (1997). Spline smoothing with model-based penalties.
Behav. Res. Meth. Ins. C., 29(1):99-106.
• Smith, S. P. (1995). Differentiation of the Cholesky Algorithm. J. Comput. Graph. Stat., 4:134-147.
• Wang, Y. (1998). Mixed-Effects Smoothing Spline ANOVA. J. R. Stat. Soc. Ser. B Stat. Methodol.,
60:159-174.
Acknowledgments
We would like to acknowledge the help of Dr. Patrick Carter and Dr. Jonathan Rupp in providing an under-
standing of the background and goals of the analysis. This work was supported jointly by Dr. Michael Elliott
and an MCubed project awarded to Drs. Patrick Carter, Jonathan Rupp and Carol Flannagan.