Primary outcome
The primary outcome is intubation (or death, for patients who died
before intubation) after randomisation. This will be assessed in a time
to event analysis and a regression analysis of the proportion of
patients receiving intubation by day 28 after randomisation.
Because of the meta-trial design, we use regression modelling (patients
nested in sites nested in trials), with site as a random effect and
trial as a fixed effect, along with testing the effect of other
covariates as collected in the common variable set. The fixed effect of
dose and device will also be estimated across the sites which use
different combinations. The fixed effect of country can also be assessed
amongst the trials which use the same dose-device combination.
We analyse binomial outcomes using multilevel logistic regression,
reported as odds ratios and 95% confidence intervals. We analyse time
to death using multilevel Cox proportional-hazards regression, reported
as hazard ratios and 95% confidence intervals. For time to intubation,
death will be treated as a competing risk. The analysis will compare the
cause-specific hazard in the treatment groups using the same multilevel
Cox proportional hazards model.[12] Continuous outcomes will be
analysed using multilevel linear regression, reported as differences in
means and 95% confidence intervals.
We will present intubation to 28 days using a Kaplan–Meier survival
curve and compare groups using a stratified log-rank test.
Prior distributions will be placed on all parameters in the regression
models described. Three types of priors will be employed: sceptical,
neutral and enthusiastic.[9] For example, the neutral prior will be
centred at 0, the enthusiastic prior at the clinically important effect
mentioned in the sample size calculation and the sceptical priors at the
negative of that clinically important effect.