Statistical analysis Data are expressed as median (interquartile range (IQR)) and absolute and relative frequencies, as appropriate. A non‐parametric test (Kruskal‐Wallis) was used to compare median ventilation durations. We first calculated cause‐specific hazards using univariate Cox regression models, adjusted for hospital as a fixed effect. Time‐fixed, non‐linear, or continuous covariates as well as duration of participation were modelled categorically in separate models using dummy variables. Separately for each time‐dependent covariate, we fitted four regression models to determine if, and in which form, the covariate should be included in a multivariate analysis. The four models included three Cox models (current effects and delayed effects of one or two days) and one flexible Cox model using the WCE approach[22]. The WCE approach estimates not only the current effect of a covariate, but also the cumulative delayed effects of past exposures, and provides the timeframe for which a covariate is significantly associated with the studied event. See Box 1 for more details[25]. We assessed which of these four models fitted best using the Akaike information criteria (AIC)[26]. A difference of less than four suggested that the models fit the data equally well, a difference between four and ten suggested a slight difference, and a difference greater than ten suggested a major difference in model fit[27]. We chose the WCE model as the best‐fitting model when it yielded a slight or major improvement in model fit to all of the three non‐cumulative models. All risk factors with p‐value<0.2 in the univariate analysis were included in the initial multivariate Cox PH model, using the best‐fitting univariate models. The final multivariate model was selected manually by backward selection using the likelihood ratio test. At each iteration, we removed from the model the variable that was associated with the highest p‐value>0.05, except when the 95% CI for that variable did not include the null. The WCE model requires complete data for the entire follow‐up of each admission. Since some time‐dependent data were missing for only 32 ventilation days (0.4%) in 24 admissions (2.6%), we used the last observation carried forward approach to fill in these values for missing days in our regression analyses. The sensitivity of our results to this approach for completing missing data was assessed by removing admissions with missing time‐varying data from the dataset and rerunning the multivariate model. Admissions with data missing on time‐fixed patient or ventilation period characteristics were excluded from the specific analysis. Analyses were done with SAS 9.4 and R 3.4.1 software using the survival and WCE packages[28‐30]. 64 Chapter 4
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