Download Logistic regression models were developed to examine the

Appendix One
Supplementary methodological information
LOGISTIC REGRESSION MODELS
Logistic regression models were developed to examine the independent effect of EMS interval on
mortality. The aim of the modelling strategy was to gain a valid estimate of the exposure-outcome
relationship rather than achieving good predictive metrics. A 3 stage approach was undertaken with:
variable specification, interaction assessment, and confounding assessment followed by
considerations of precision.
A fully specified model was initially built with mortality as the dependent variable, EMS interval as
the exposure variable (categorical), and confounders as additional explanatory variables. These
additional covariates comprised Injury Severity Score, extra-cranial injury, age, and prehospital GCS,
systolic blood pressure and oxygen saturations. The relationship of each continuous variable with
the logit of the dependent variable was examined graphically, with fractional polynomial
transformations used to correct any lack of linearity. Coding of each variable is described in table 1.
Clinically plausible Interactions between EMS interval category and extra-cranial injury, ISS, PH SBP
and PH hypoxia were pre-specified and examined together using a Wald ‘chunk’ test,[13] with a null
hypothesis that the ratio of odds ratios was 1. Non-significant interactions terms were omitted prior
to assessment of confounding, with planned manual backward elimination of variables whose
omission did not materially affect exposure odds ratios and resulted in increased precision.
Goodness of fit was assessed using the Hosmer-Lemeshow statistic and model checking performed
by using: pregabilons delta b’s for influential outlying observations; variance inflation factors for
collinearity; and events-per-variable for adequate sample size.
Variable
Coding
Rationale
Age
Fractional polynomial
Assumption of linear relationship with logit of
outcome not valid.
Pre-hospital systolic
Fractional polynomial
blood pressure
Assumption of linear relationship with logit of
outcome not valid.
Pre-hospital
6 groups: GCS=3, GCS=4-5,
Categorisation produce clinically relevant
Glasgow Coma Score
GCS=6-8, GCS=9-12, GCS=
groups and allows inclusion of intubated
13-15, intubated (reference
patients with unknown GCS
category GCS 13-15)
Pre-hospital oxygen
Categorised into 2 groups:
Categorisation produces clinically relevant
saturations
<93%, ≥93%.
groups. Sats of 92% are a recognised
threshold for hypoxia.
Injury Severity Score
Linear
Approximately linear relationship with logit of
outcome
Extra-cranial injury
Yes / No
Dichotomous variable
EMS interval
7 categories :<20, 20-40, 40-
Categorisation allowed calculation of odds
60,60-80,80-100, 100-120,
ratios for meaningful time periods. Reference
>120 minutes (reference
category had highest number of cases.
category 40-60).
Table 1. Coding of modelled variables
MULTIPLE IMPUTATION
Multiple imputation was performed under a missing at random assumption using chained equations.
An inclusive modelling strategy was adopted including: the outcome variable; all independent
variables and interaction terms in the analysis model; and auxiliary variables (e.g. trapped in vehicle)
from the TARN dataset that might predict missingness in outcomes, EMS interval, or other
covariates. Normality of all variables was checked, with appropriate transformations used as
appropriate for imputations. Interval limits were used to prevent clinically implausible outlying
imputations.
The procedure was checked by comparing distributions of complete and imputed data. The missing
data method was utilised using the ice procedure in STATA, with 5 sets of imputed data generated.
The mim command was subsequently used to combine results from imputed data sets according to
Rubin’s rules.
PROPENSITY SCORE MATCHING
In non-experimental epidemiological studies patient treatments and outcomes are observed in
everyday real-life settings. Treatment selection is therefore likely to be influenced by subject
characteristics, resulting in ‘confounding by indication’ where systematic differences between study
groups leads to biased effect estimates. Traditionally multivariate regression models have been used
to control for confounding, but empirical research suggests that use of propensity score matching
may be a superior method to produce less biased results.
The propensity score is the probability of treatment or exposure status conditional on observed
patient characteristics. Treated and untreated cases with identical propensity scores will have a
similar distribution of measured covariates. Thus matching of patients on propensity scores will
produce balanced and comparable study groups, mimicking a randomised controlled trial, if an
assumption of ‘strongly ignorable treatment assignment’ can be made based. This assumption
requires two conditions: firstly that there is no unmeasured confounding with ‘treatment
assignment independent of the potential outcomes conditional on the observed baseline covariates’;
and secondly that every subject has a nonzero probability to receive either treatment.
Consensus guidelines and expert opinion were followed to implement propensity score matching
with the greatest validity and precision. Logistic regression modelling was used to generate the
probability of EMS interval within 60 minutes. A non-parsimonious modelling strategy was utilised
including all variables available within the TARN data set potentially related to outcome or EMS
interval. Adequacy of specification of the propensity score model was assessed by comparing the
comparability of exposed and unexposed subjects for important confounders using standardised
differences. In the presence of clinically significant differences the propensity score was modified
with addition of interaction terms, transformation of non-linear variables and revision of included
covariates. This iterative process was continued until systematic differences between the two groups
were reduced to a minimal level. Rubin’s balancing score across 5 strata of propensity score was also
examined.
Propensity score matching was then performed within the area of common support using one-toone, nearest neighbour, greedy matching without replacement, within a propensity score calliper
width of 0.01. This process was implemented using the user-written psmatch2 command in Stata
version 12.1 (StataCorp, College Station, USA). Treatment effect in the propensity score matched
sample was then estimated by calculating the average effect of treatment on the treated with
absolute risk reductions and marginal odds ratios subsequently calculated. To account for the paired
nature of the data McNemar’s test was used to test the statistical significance of differences in
proportions of mortality. Finally the variance of the treatment effect was estimated using
bootstrapping with 1,000 replications to calculate 95% confidence intervals.
SUBGROUP ANALYSIS
An a priori subgroup analysis was planned to investigate the influence of EMS interval on mortality in
patients likely to require urgent resuscitation. Patients identified as unstable on ED arrival were
examined, with ED Instability was defined as: GCS <9; SBP <90mmHg; abnormal respiratory rate of
<6 or >29; pulse rate of <50 or >120, hypoxia (sats<93%). These parameters were chosen based on
Revised Trauma Score categorizations;[14] established values for defining clinical states e.g. shock,
arrhythmias, cardiac arrest, or hypoxia;[13] thresholds at which management would change e.g.
intubation;[13] and are consistent with the American College of Surgeons Committee on Trauma’s
Field Triage Decision Scheme.[15] Crude and adjusted odds ratios for the association between EMS
interval categories and mortality were calculated as above; both in complete case and multiple
imputation analyses.
EXTREME OUTCOMES SENSITIVITY ANALYSIS
The effect of loss to follow up was examined in a scenario analysis providing the most optimistic
assumptions on missing outcome data consistent with a positive relationship between short EMS
intervals and increased survival. Patients with missing outcomes with EMS intervals <60minutes
were all assumed to have survived, while those over 60 minutes were assumed to have died. An
adjusted multiple imputation multivariate analysis was then repeated.
SENSITIVITY ANALYSES EXAMINING ALTERNATIVE SPECIFICATIONS OF MULTIVARIATE LOGISTIC
REGRESSION MODELS
To further explore the possibility of confounding by head injury severity we examined the
association between mortality and EMS interval in post hoc sensitivity analyses specifying Marshall
Score and Head region AIS as explanatory variables. To avoid colinearity, but still account for
potential confounding from non-head injury severity we replaced ISS with a binary extra-cranial
injury variable in these models (corresponding to any extra-cranial AIS scores of >=3). Age, prehospital systolic blood pressure, pre-hospital hypoxia, and pre-hospital GCS were also controlled for
as in previous analyses. Additionally we also examined EMS interval as a continuous variable in our
base case logistic regression model. All models were developed and checked using the principles
described above; and were evaluated in both complete case and multiple imputation datasets.