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.