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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.