JOURNAL OF NEUROTRAUMA
Volume 24, Number 2, 2007
© Mary Ann Liebert, Inc.
Multivariable Prognostic Analysis in Traumatic Brain Injury:
Results from the IMPACT Study
GORDON D. MURRAY,1ISABELLA BUTCHER,1GILLIAN S. MCHUGH,1
JUAN LU,2NINO A. MUSHKUDIANI,3ANDREW I.R. MAAS,4
ANTHONY MARMAROU,2and EWOUT W. STEYERBERG3
We studied the prognostic value of a wide range of conventional and novel prognostic factors on
admission after traumatic brain injury (TBI) using both univariate and multivariable analysis. The
outcome measure was Glasgow Outcome Scale at 6 months after injury. Individual patient data
were available on a cohort of 8686 patients drawn from eight randomized controlled trials and three
observational studies. The most powerful independent prognostic variables were age, Glasgow Coma
Scale (GCS) motor score, pupil response, and computerized tomography (CT) characteristics, in-
cluding the Marshall CT classification and traumatic subarachnoid hemorrhage. Prothrombin time
was also identified as a powerful independent prognostic factor, but it was only available for a lim-
ited number of patients coming from three of the relevant studies. Other important prognostic fac-
tors included hypotension, hypoxia, the eye and verbal components of the GCS, glucose, platelets,
and hemoglobin. These results on prognostic factors will underpin future work on the IMPACT
project, which is focused on the development of novel approaches to the design and analysis of clin-
ical trials in TBI. In addition, the results provide pointers to future research, including further
analysis of the prognostic value of prothrombin time, and the evaluation of the clinical impact of
intervening aggressively to correct abnormalities in hemoglobin, glucose, and coagulation.
Key words: GOS; multivariable analysis; multivariate analysis; prognosis; traumatic brain injury
IMPACT: International Mission on Prognosis and Analysis of Clinical Trials in TBI.
1Public Health Sciences, University of Edinburgh Medical School, Edinburgh, United Kingdom.
2Department of Neurosurgery, Virginia Commonwealth University Medical School, Richmond, Virginia.
3Center for Medical Decision Making, Department of Public Health, and 4Department of Neurosurgery, Erasmus Medical
Center, Rotterdam, The Netherlands.
PACT project (Maas et al., 2007a). A series of papers
based on the IMPACT database (Marmarou et al., 2007a)
ETAILED ANALYSIS of prognostic factors in traumatic
brain injury (TBI) forms an important part of the IM-
has reported details of the univariate associations be-
tween the Glasgow Outcome Scale (GOS) and demo-
graphic characteristics (Mushkudiani et al., 2007), cause
of injury (Butcher et al., 2007a), secondary insults
(McHugh et al., 2007a), Glasgow Coma Scale (GCS) and
pupil response (Marmarou et al., 2007b), blood pressure
MURRAY ET AL.
(Butcher et al., 2007b), computerized tomography (CT)
scan features (Maas et al., 2007b), and laboratory para-
meters (van Beek et al., 2007). These papers have con-
firmed the prognostic effects of many known predictors
(e.g., age, GCS, pupil response, and CT parameters), have
disclosed the predictive value of hitherto insufficiently
recognized parameters (e.g., race and laboratory param-
eters), and have identified potential candidates for ther-
apeutic intervention (e.g., blood pressure and laboratory
parameters). Notwithstanding the relevance of these uni-
variate analyses, the ultimate value of predictors can only
be established in multivariable analysis, adjusting for the
influence of other variables. In the univariate manu-
scripts, we reported exploratory analyses of associations
and performed a limited number of adjusted analyses.
This paper reports the results of a more systematic mul-
tivariable analysis, where each variable is adjusted in turn
for four sets of potentially confounding covariates. By
bringing together all of the covariates from the series of
earlier papers, this allows a direct comparison of the pre-
dictive power of each variable, as well as an assessment
of the “added value” of each predictor over and above
the predictive power of other groups of covariates. This
will help to identify those variables that are most impor-
tant in clinical trial design and prognosis.
Our analyses were based on individual patient data
from the three observational studies and eight random-
ized controlled trials (RCTs) in the IMPACT database
(Marmarou et al., 2007a). The endpoint for the prognos-
tic analyses was the 6-month GOS. In cases where the 6-
month assessment was not available, we imputed the
three month GOS. Thirty-five patients in the UK Four
Centres study had partial information on GOS and were
excluded to leave an analysis cohort of 8686 patients with
full information on GOS. The partial information on GOS
was sufficient to allow analysis of, for example, mortal-
ity, but not for the analysis over the full range of GOS,
as is reported in the paper. This explains the slight dif-
ferences between some of the sample sizes reported in
the earlier papers in this series and the numbers reported
in this paper. In addition, since the relatively small num-
ber of children in the database precluded accurate mod-
eling of the association between age and GOS in chil-
dren, the univariate analysis of age and all analyses
adjusted for age were restricted to patients aged ?14
years. This yielded a cohort of 8509 adults with full in-
formation on GOS. Multivariable logistic regression
analysis was performed on the association between the
prognostic factor of interest, with and without adjustment
for other prognostic factors (“covariates”) and outcome.
All analyses were stratified by study.
For each prognostic factor of interest, the cases with
that variable and GOS recorded were selected, and any
missing covariates were replaced by imputed values
(McHugh et al., 2007b). Such imputation is recom-
mended as being more efficient than dropping cases with
incomplete data (Little, 1992; Harrell, 2001). In addition,
the imputation of missing values for covariates means
that, for a given prognostic factor of interest, all adjusted
analyses are performed on the same cohort of patients.
Proportional odds models were fitted separately for
each study, and the resulting (adjusted) common odds ra-
tios were pooled over the studies using a random effects
model (McHugh et al., 2007b). The odds ratios were cal-
culated so that for the categorical variables a value greater
than one indicates an increased risk of a poor outcome
relative to the reference category. For the continuous
prognostic factors with a linear relation to outcome, the
odds ratios were scaled so that they correspond to chang-
ing from the 25thpercentile of that prognostic factor to
the 75thpercentile. For continuous prognostic factors
with a U-shaped relation to outcome, a categorical trans-
formation was performed and odds ratios calculated rel-
ative to the central category. This allows a direct com-
parison of the prognostic value of prognostic factors,
which are recorded in different units or on different
scales. An odds ratio of greater than one for a continu-
ous prognostic factor indicates that the risk of a poor out-
come increases as the variable increases.
Following the univariate analysis, a nested set of ad-
justed analyses was run. Model A used a core set of con-
ventional TBI prognostic factors: age, GCS motor score,
and pupil response to light. Model B added in the Mar-
shall CT classification (Marshall et al., 1991) to Model
A. Model C was taken from Hukkelhoven et al. (2005)
and added hypoxia, hypotension, and traumatic sub-
arachnoid hemorrhage (tSAH) to Model B. Finally,
Model D added two laboratory variables—glucose and
hemoglobin—to Model C. When presenting the odds ra-
tios, values that were statistically significantly different
from one at the 1% level (i.e., p ? 0.01) were flagged.
The 1% significance level was used in place of the more
conventional threshold of 5% to make an allowance for
the many tests that were being performed. It also allows
for the fact that, with such large sample sizes as are avail-
able for this analysis, an effect that is of little clinical rel-
evance can be statistically significant.
The predictive power of an individual prognostic fac-
tor was further assessed by using Nagelkerke’s R2
(Nagelkerke, 1991). Nagelkerke’s R2is used in logistic
regression and is an analogue of the conventional R2sta-
tistic, which is used in ordinary least squares (OLS) re-
MULTIVARIABLE PROGNOSTIC ANALYSIS IN TRAUMATIC BRAIN INJURY
gression. In the context of OLS, R2is precisely the per-
centage of the variability in the response variable which
is explained by the covariates. It is simple to calculate
under the assumption of a normally distributed continu-
ous outcome variable. In logistic regression the situation
is more complicated, but Nagelkerke’s R2can still be in-
terpreted as an approximation to the percentage of the
variability in the GOS which is explained by the differ-
ent prognostic factors. The calculation of Nagelkerke’s
R2uses the difference in the log-likelihood of a model
with and without the prognostic factor of interest.
Nagelkerke’s R2was used to measure the predictive
value of individual prognostic factors by comparing pro-
portional odds models with the prognostic factor of in-
terest and study in the model, to a model with only study
included. Nagelkerke’s R2was also used to measure the
predictive value of a prognostic factor after having ad-
justed for the effects of other covariates. This was done
by comparing proportional odds models with the prog-
nostic factor of interest, the covariates, and study in-
cluded to a model with only the covariates and study in-
cluded. Hence, all reported R2values are essentially
partial R2values, reflecting the “added predictive value”
of the prognostic factor of interest. Nagelkerke’s R2is
particularly useful in the context of these analyses in that
it gives a measure which can be compared directly from
variable to variable, irrespective of the sample size. This
is in contrast to the p-value, where for a given strength
of association, the p-value will become more extreme as
the sample size increases. Moreover, with such large sam-
ple sizes as are available for most of our analyses, a very
modest association, which would be of no clinical rele-
vance in terms of prognosis, could still be statistically
significant at even the 1% level.
Both p-values and R2are affected by the distribution
of categorical prognostic factors. If a prognostic factor
has a very skewed distribution, the p-value will be higher
and the R2lower, relative to a more balanced prognostic
factor with the same common odds ratio.
Table 1 gives the (adjusted) common odds ratios from
all of the models. Odds ratios which are significantly dif-
ferent from one at the 1% level (i.e., p ? 0.01) are high-
lighted in bold. Figure 1 shows the Nagelkerke partial R2
values for each prognostic factor under the five different
analyses. The open bars on the left of each cluster give
the partial R2values, which are the measures of the
strength of the univariate association of each variable
with GOS. These range from the order of 15% for pupils
to zero for gender. The hatched bars give the partial R2
values on adjustment for increasing numbers of covari-
ates. As more covariates are added the partial R2values
tend to fall. For example, the partial R2for pupils is 7%
on adjusting for Model A (in effect adjusting for age and
GCS motor score, since pupils is already included within
ModelˇA), falling to under 4% on adjusting for Model D.
Demographic Variables and Cause of Injury
As expected, age comes out as a powerful prognostic
factor. It is the single most powerful predictor in each of
the four models, having the largest partial R2values of
all the covariates considered. Cause of injury has the next
highest univariate R2value, but the partial R2values af-
ter adjustment are all negligible. Indeed, we found that
adjustment for age alone effectively abolishes any inde-
pendent predictive power of cause of injury (Butcher et
al., 2007a). Race and educational level both have mod-
est predictive value which persists after adjustment for
each of the models. The direction of these associations
(Table 1) is that black patients tend to have poor out-
comes relative to other racial groups and those with high
educational attainment tend to have better outcomes than
those with lower educational attainment. There is no sug-
gestion of any association between gender and GOS, with
or without adjustment for other covariates.
Secondary Insults/Blood Pressure
Hypotension and hypoxia have powerful univariate as-
sociations with GOS and modest but relevant associa-
tions remain after adjustment for the full Model D. Hy-
pothermia has a more modest association, and the effect
falls to a negligible level on adjustment for Model D.
Systolic blood pressure and to a lesser extent mean arte-
rial blood pressure have clear univariate associations with
GOS. A modest effect of systolic blood pressure remains
after adjustment for Models A or B, but the effect is re-
duced to a negligible level on adjustment for Model C
(which includes hypotension). Mean arterial blood pres-
sure has little effect after adjustment.
As expected, both the GCS motor score and pupil re-
sponse are powerful independent predictors of outcome,
with effects which persist strongly after adjustment for
all other covariates. The GCS eye and verbal scores are
powerful univariate predictors with modest but relevant
independent effects after adjustment for all of the other
Computed Tomography Scan Characteristics
The two most powerful CT characteristics are the Mar-
shall CT classification and evidence of traumatic sub-
TABLE 1. POOLED COMMON ODDS RATIOS DERIVED FROM PROPORTIONAL ODDS MODELS ADJUSTING FOR A RANGE OF COVARIATES
Over 12 years
Cause of Injury
Road traffic accident
No visible pathology
GCS eye score
GCS verbal score
GCS motor score
Common odds ratio from proportional odds model
120–150 mm Hg
?120 mm Hg
?150 mm Hg
Mean arterial BP
85–110 mm Hg
?85 mm Hg
?110 mm Hg
aThe adjusted analyses (Models A–D) are restricted to patients aged ?14 years.
Figures in bold correspond to p ? 0.01.
Model A: Adjusted for age, GCS motor score, and pupils. Model B: Model A plus CT class. Model C: Model B plus hypoxia, hypotension, and tSAH. Model D: Model C plus Hb and
The odds ratios for age through prothombin time are scaled to reflect the effect of an increase from the lower quartile of each variable to the upper quartile
CT, computerized tomography; tSAH, traumatic subarachnoid hemorrhage; EDH, epidural hematoma; SDH, subdural hematoma; GCS, Glasgow Coma Scale; BP, blood pressure.
TABLE 1. POOLED COMMON ODDS RATIOS DERIVED FROM PROPORTIONAL ODDS MODELS ADJUSTING FOR A RANGE OF COVARIATES (CONT’D)
Common odds ratio from proportional odds model
values for univariate association of each variable with the Glasgow Outcome Scale (GOS); the hatched bars give the partial R2
values on multivariable analysis adjusting for an increasing number of covariates.
Relative prognostic value of predictors expressed as Nagelkerke’s partial R2values. The open bars give the partial R2
MULTIVARIABLE PROGNOSTIC ANALYSIS IN TRAUMATIC BRAIN INJURY
arachnoid hemorrhage. Both have clear residual associa-
tions with GOS even after adjustment for all of the co-
variates in Model D. Presence of an epidural hematoma
is the next most powerful independent predictor, and is
associated with increased odds of a better outcome. Ab-
sent or compressed cisterns have a strong univariate as-
sociation with GOS and a modest but relevant effect per-
sists on adjusted analysis. Evidence of contusions has a
modest association with outcome on univariate analysis,
and this effect persists on multivariable adjustment. Both
evidence of midline shift and presence of a subdural
hematoma are strongly associated with adverse GOS on
univariate analysis, but these effects are greatly attenu-
ated on adjustment for the overall CT classification (i.e.,
going from Model A to Model B).
The results in Figure 1 show broadly that the findings
reported in van Beek et al. (2007) persist after adjustment
for all nine covariates in Model D. Prothrombin time has
a striking effect comparable in terms of partial R2to pupil
response or CT classification on adjusted analysis. Glu-
cose is a strong independent predictor of outcome, as to
a lesser extent are hemoglobin and platelets. The effects
of sodium and pH are modest on univariate analysis and
negligible on full adjustment (Model D).
There is a long history to the development of statisti-
cal models to predict outcome following head injury. This
dates back essentially to the seminal papers by Teasdale
and Jennett (1974), allowing quantification of impair-
ment of consciousness, and Jennett and Bond (1975),
standardizing the assessment of outcome following se-
vere brain damage. Key papers on prediction include Jen-
nett et al. (1976), Narayan et al. (1981), Titterington et
al. (1981), Choi et al. (1991), Signorini et al. (1999), and
Hukkelhoven et al. (2005). Many of the early papers on
prediction pre-date the widespread availability of high-
resolution CT scans, and others include data collected af-
ter admission. The IMPACT project focuses on the use
of predictive models in the context of clinical trials, and
so our analysis is restricted to data available at the time
that a patient would be recruited into such a trial.
Our results confirm much of the received wisdom in
the area of TBI prognosis: age is the single most power-
ful prognostic factor, followed by the GCS motor score,
and pupil response to light. The Marshall CT classifica-
tion, tSAH, and the secondary insults of hypotension and
hypoxia all add further relevant independent predictive
information. The GCS eye and verbal components then
add yet further independent information, but each corre-
sponds to a partial R2value of well below 1%. It is an-
ticipated however that the added predictive value of the
eye and verbal scores may well be greater in more mod-
erately injured patients.
The most striking novel finding is the added value of
several laboratory parameters over and above the conven-
tional prognostic factors in TBI. Data on prothrombin
time (PT) were only available in three of the 11 IMPACT
studies, and the total sample size for the analysis of PT
was only 840. Although modest in the context of
IMPACT, this is still a large sample size in terms of the
previously published literature on prognosis in TBI. Nev-
ertheless, further research on the prognostic value of PT
is required before one could recommend that PT be used
in prognostic models of TBI. Given the routine avail-
ability these parameters, prognostic models in TBI should
potentially include laboratory data, especially glucose,
and possibly also hemoglobin and platelets.
It appears that the CT scan contains more useful prog-
nostic information than is summarized in the Marshall
CT classification and by recording the presence or ab-
sence of tSAH. Maas et al. (2005) have previously
demonstrated that it may be preferable to combine indi-
vidual CT characteristics into a CT prognosis model. The
many interactions between CT characteristics however
make this a complex issue, which requires more detailed
Finally, we have identified modest but consistent in-
dependent effects of race and education. This possibly
reflects aspects of the delivery of care or access to care,
and merits further investigation.
The study has a number of limitations. First, the ap-
proach adopted for the regression modeling, even though
it was based on the proportional odds model, was rela-
tively unsophisticated. In particular, we assumed that all
effects were additive, and did not include interaction
terms in any of our models. We consider that this ap-
proach is appropriate for this paper which aims to give a
broad overview of the IMPACT database, but we shall
be reporting on more sophisticated approaches to the sta-
tistical analysis in future papers. Second, it may be ar-
gued that we included a large number of relatively old
studies in our analysis, which may not necessarily reflect
current practice in the management of TBI. We did not
however identify any clear differences in the prognostic
analysis between older and more recent datasets, but will
address this further by the addition of more recent TBI
trials and case series to the IMPACT database (Maas et
al., 2007a). Third, we chose to restrict the adjusted analy-
ses to adult patients (aged ? 14 years), as the low num-
ber of children in the database precluded confident re-
gression modeling in children (Mushkudiani et al., 2007).
As a consequence the number of patients in the univari-
ate analyses was in general slightly greater than for the
adjusted analyses. This increased the precision of the es-
timation of the univariate odds ratios, at the cost of po-
tentially introducing a very modest bias relative to the
adjusted odds ratios. However, on comparison of the par-
tial R2calculated for the age-selected cohort (N ? 8509)
versus the full unselected cohort (N ? 8686), we only ob-
served a marginal reduction of partial R2for the variable
age, but no difference either in univariate or multivariate
analyses for all other covariates.
In summary, we have quantified the prognostic strength
of many conventional and novel prognostic factors in
TBI. The most important prognostic factors identified in-
clude age, GCS motor score, pupil response, CT charac-
teristics, hypotension, hypoxia, and glucose. The com-
bination of the prognostic factors will provide a solid
foundation for the estimation of the probabilities of each
GOS category at 6 months for individual TBI patients.
These estimated probabilities will underpin the core
IMPACT activity of developing novel approaches to the
design and analysis of clinical trials in TBI.
Grant support was provided by NS-042691.
BEEK VAN, J., MUSHKUDIANI, N.A., STEYERBERG,
E.W., et al. (2007). The prognostic value of admission lab-
oratory parameters in traumatic brain injury. J. Neurotrauma
BUTCHER, I., MAAS, A.I.R., LU, J., et al. (2007b). The prog-
nostic value of blood pressure in TBI: results from the
IMPACT study. J. Neurotrauma 24, 294–302.
BUTCHER, I., MCHUGH, G.S., LU, J., et al. (2007a). The prog-
nostic value of cause of injury in traumatic brain injury: results
from the IMPACT study. J. Neurotrauma 24, 281–286.
CHOI, S.C., MUIZELAAR, J.P., BARNES, T.Y., et al (1991).
Prediction tree for severely head-injured patients. J. Neuro-
surg. 75, 251–255.
HARRELL, F.E. (2001). Regression Modeling Strategies with
Applications to Linear Models, Logistic Regression and Sur-
vival Analysis. Springer-Verlag: New York.
HUKKELHOVEN, C.W.P.M., STEYERBERG, E.W., HAB-
BEMA, J.D.F., et al. (2005). Predicting outcome after trau-
matic brain injury: development and validation of a prog-
nostic score based on admission characteristics. J.
Neurotrauma 22, 1025–1039.
JENNETT, B., and BOND, M. (1975). Assessment of outcome
after severe brain damage. A practical scale. Lancet 1,480–484.
JENNETT, B., TEASDALE, G., BRAAKMAN, R., MIN-
DERHOUD, J., and KNILL-JONES, R. (1976). Predicting
outcome in individual patients after severe head injury.
Lancet 1, 1031–1034.
LITTLE, R.J.A. (1992). Regression with missing X’s: a review.
J. Am. Stat. Assoc. 88, 125–134.
MAAS, A.I.R., HUKKELHOVEN, C.W.M.P., MARSHALL,
L.F., and STEYERBERG, E.W. (2005). Prediction of out-
come in traumatic brain injury with computed tomographic
characteristics: a comparison between the computed tomo-
graphic classification and combinations of computed tomo-
graphic predictors. Neurosurgery 57, 1173–1182.
MAAS, A.I.R., MARMAROU, A., MURRAY, G.D., TEAS-
DALE, G.M., and STEYERBERG, E.W. (2007a). Prognosis
and clinical trial design in traumatic brain injury: the
IMPACT study. J. Neurotrauma 24, 232–238.
MAAS, A.I.R., STEYERBERG, E.W., BUTCHER, I., et al.
(2007b). The prognostic value of computerized tomography
scan characteristcs in traumatic brain injury: results from the
IMPACT study. J. Neurotrauma 24, 303–314.
MARMAROU, A., LU, J., BUTCHER I., et al. (2007a). The
IMPACT database on traumatic brain injury: design and de-
scription. J. Neurotrauma 24, 239–250.
MARMAROU, A., LU, J., BUTCHER, I., et al. (2007b). The
prognostic value of the Glasgow Coma Scale and pupil reac-
tivity in traumatic brain injury assessed pre-hospital and on en-
rollment: an IMPACT analysis. J. Neurotrauma 24, 270–281.
MARSHALL, L.F., MARSHALL, S.B., KLAUBER, M.R., et
al. (1991). A new classification of head injury based on com-
puterized tomography. J. Neurosurg. 75, S14–S20.
MCHUGH, G.S., BUTCHER, I., STEYERBERG, E.W., et al.
(2007b). Statistical approaches to the univariate prognostic
analyses of the IMPACT database on traumatic brain injury.
J. Neurotrauma 24, 251–258.
MCHUGH,G.S., ENGEL, D.C., BUTCHER, I., et al. (2007a).
The prognostic value of secondary insults in TBI: results
from the IMPACT study. J. Neurotrauma 24, 287–293.
MUSHKUDIANI, N.A., ENGEL, D.C., STEYERBERG, E.W.,
et al. (2007). The prognostic value of demographic charac-
teristics in traumatic brain injury: results from the IMPACT
study. J. Neurotrauma 24, 259–269.
NAGELKERKE, N.J.D. (1991). A note on a general definition
of the coefficient of determination. Biometrika 78, 691–692.
NARAYAN, R.K., GREENBERG, R.P., MILLER, J.D., et al.
(1981). Improved confidence of outcome prediction in se-
vere head injury. A comparative analysis of the clinical ex-
amination, multimodality evoked potentials, CT scanning,
and intracranial pressure. J. Neurosurg. 54, 751–762.
SIGNORINI, D.F., ANDREWS, P.J., JONES, P.A., et al
(1999). Predicting survival using simple clinical variables: a
MURRAY ET AL.
MULTIVARIABLE PROGNOSTIC ANALYSIS IN TRAUMATIC BRAIN INJURY Download full-text
case study in traumatic brain injury. J. Neurol. Neurosurg.
Psychiatry 66, 20–25.
TEASDALE, G., and JENNETT, B. (1974). Assessment of come
and impaired consciousness. A practical scale. Lancet 2,81–84.
TITTERINGTON, D.M., MURRAY, G.D., MURRAY, L.S., et
al. (1981). Comparison of discrimination techniques applied
to a complex data set of head-injured patients. J. R. Statist.
Soc. Ser. A 144, 145–175.
Address reprint requests to:
Gordon D. Murray, Ph.D.
Public Health Sciences
University of Edinburgh Medical School
Edinburgh EH8 9AG, UK