The sample size calculation (GPower Software Version 3.1.3 , University of Düsseldorf, Germany) was based on the Wilcoxon-Mann-Whitney-Test (two groups, two tailed). The calculation was based on the expectation that the primary endpoint variable “time from randomization to successful extubation” shows a difference of 2 days between the two treatment groups. Based on the study by Lellouche et al. ¹⁾ the standard deviation (SD) is estimated being 5 days for both groups, yielding an effect size (d) of 0.4. Accordingly, 104 patients per group would allow detecting differences between groups with a power of 80% and a type one error of 5%. Assuming that 10 dropouts per group may occur, 228 patients in total are necessary.

The descriptive analysis will include mean and standard deviation for normally distributed variables. Not normally distributed variables will be expressed by their medians and interquartile ranges. Categorical variables will be expressed as n (%). Differences in the primary endpoint variable “time from randomization to successful extubation” between the two treatment groups will be analyzed by a Wilcoxon-Mann-Whitney-Test. To decide on the proper comparison method for the exploratory analysis of the secondary endpoints, we will test whether the variables are normally distributed. To test groups of independent continuous normally distributed variables, Student’s t-test will be used. For continuous not normally distributed variables the Mann-Whitney U test will be used. Categorical variables will be compared with the Chi–square test or Fisher’s exact test. Paired data will be analyzed using the Student’s t-test for continuous normally distributed variables, the Wilcoxon test for continuous not normally distributed variables and the McNemar or Bowker test, as appropriate, for categorical variables. To evaluate differences in overall survival, Kaplan–Meier survival curves will be computed. Survival curves will be compared by log-rank test and multivariable analysis will be accomplished by the Cox regression model. If there is any case of “lost to follow-up” or consent withdrawal from the trial, the causes will be reported. The intention-to-treat analysis (ITT) and per protocol (PP) analysis will be conducted to test whether the result of this trial is reliable. Missing data will be handled by means of the last-observation-carried-forward method. For the intention-to-treat analysis, data will be processed of all trial patients in the groups to which they were randomized, regardless of whether they received or adhered to the allocated intervention. It is assumed that the majority of patients in the two triage arms will receive the appropriate study intervention. The per protocol analysis will be performed as a secondary analysis if there are sufficient patients in the triage arms who do not receive study therapy or are lost to outcome assessment. Data from participants who do not violate the treatment protocols will be included in the per-protocol analysis.