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Appendix II. Multiple imputation of missing physiological data
A high proportion of patients had missing physiological data. Excluding patients with
missing data can lead to biased results, as physiological parameters are not missing
completely at random31. Imputation of missing data allowed us to include all data
observations in analyses. Multiple imputation is a method which has been shown to
provide unbiased results for data imputation58 and we have previously demonstrated the
accuracy of imputed Glasgow coma score, systolic blood pressure, and respiratory rate
using this method via a simulation study in QTR data12, 31. The validity of multiple
imputation does rely on the assumption that data are missing at random. This means that
the fact that data are missing can be explained by variables used in the imputation
process. While this can never be formally verified, previous simulation studies have
suggested that this assumption holds in study data31.
In the QTR, Glasgow coma score, systolic blood pressure, and respiratory rate were
missing for 52%, 10% and 34% of patients, respectively. Missing QTR physiological
data was imputed with multiple imputation as described previously12, 31. In the NTDB,
Glasgow coma score, systolic blood pressure, and respiratory rate were missing for
23.4%, 6.0%, and 13.3% of patients, respectively. A data imputation model was built
using the following variables: Age, injury mechanism, presence of head injury, AIS score
of the worst head injury, AIS score of the worst injury in any other body region,
destination from the emergency department (death, intensive care, surgery, ward), and
discharge destination (death, rehabilitation, long-term care, home). Multiple imputation
was performed with PROC MI using SAS (SAS Institute, Cary, version 9.1). The Markov
Chain Monte Carlo (MCMC) method was used with multiple chains and a noninformative prior59. Both time series plots and auto correlation functions of the worst
linear function were verified for convergence to a stationary distribution59. Five
imputations were sufficient given the fraction of missing information associated with the
GCS, SBP and RR 59; relative efficiency of estimates was between 92% and 99%. Prior
to multiple imputation, Glasgow coma score, systolic blood pressure, and respiratory rate
were clinically abnormal for 16.3%, 3.3% and 4.6% in the QTR sample and for 9.6%,
4.1% and 4.9% in the NTDB sample, respectively. Following multiple imputation
Glasgow coma score, systolic blood pressure, and respiratory rate were clinically
abnormal for 9.9%, 3.4% and 4.1% in the QTR sample and for 12.3%, 4.0% and 4.1% in
the NTDB sample, respectively.
Imputed variables were standardized for subsequent analyses. Multiple imputation lead to
the creation of five data sets which were analyzed separately. Results were then
combined according to the rules described by Rubin58.