Data management and statistical analyses
Data were extracted onto a secure encrypted server controlled by NHS England and NHS Improvement. Analysis within this secure environment took place using standard statistical software: Microsoft Excel (Microsoft Corp, Redmond, WA, USA), Stata (StataCorp LLC, College Station, TX, USA) and Alteryx (Alteryx Inc, Irvine, CA, USA).
In descriptive analysis, data were categorised as detailed above and summarised in terms of frequency and percentage. Length of stay was non-normally distributed, with a right-skew, and summarised using the median and inter-quartile range (IQR).
To explore variables associated with having a tracheostomy and the association between tracheostomy and in-hospital mortality and length of stay greater than the median (8 days) in critical care patients, a series of multilevel logistic regression models were fitted using themelogit command. Two-level intercept only models were used, allowing adjustment for clustering of patients within hospital trusts. Covariates were categorised as described above. Adjusted tracheostomy and mortality rates were calculated using the margins command in Stata based on the conditional probability across the entire dataset.
For the outcomes time from tracheostomy to hospital discharge and critical care discharge a multi-level linear model was fitted based on the natural logarithm of the outcome using the mixed command in Stata. The main exposure variable of interest (timing of tracheostomy post-critical care admission) was modelled as a binary variable with a threshold of ≤ 14 days with all covariates modelled as described previously.
Missing data were uncommon. No attempt was made to impute missing values. Where data were missing the numbers involved are given.