Data are presented with figures and percentages for categorical variables and median (interquartile range) for continuous variables. Normality was investigated using graphical methods for continuous variables. Non-parametric Kruskal-Wallis test was used to compare non-normal quantitative variables and ANOVA was used for normally distributed variables. Qualitative variables were compared with the Chi-squared test unless expected counts were less than 10, in which case Fischer’s exact test was used.
We faced an indication bias as the three groups were constituted retrospectively. In order to consider indication bias and potential confounders, covariates that might influence both timings of surgery and clinical outcomes were analyzed using a Directed Acyclic Graph (DAG). The first step consisted in the choice of the covariates to analyze (mechanism of trauma (motor vehicle crash, pedestrian/bicycle collision, fall from a height, other), uncontrolled pain as an indication to surgery, SAPS II, ISS, presence of hemothorax, presence and number of non-thoracic lesions, chest deformation as indication to surgery, CTS (less than 5 vs. 5 or more). The hypotheses of association were based on the literature and on pathophysiological knowledge. The second step was to identify covariates whose effect can be mediated by others and, then these new hypotheses were investigated by the monitoring and steering committee. Finally, all the direct associations were used to construct the DAG using the DAGitty software (25 (link)). A multivariable logistic regression model was used to calculate the odds ratio of main outcomes and covariates selected using the DAG. Sensitivity analyses were performed to analyze timing for surgery divided into two groups (within 48 vs. 48 h and more). Analyses were performed on complete data.
Then, an exploratory analysis was conducted to determine factors associated with early pneumonia. A first selection of the variables of interest was carried out with a univariable logistic regression model. Then, the variables of interest with a threshold of P<0.25 were implemented in a multivariable logistic regression model. Then, using a backward stepwise selection of covariates, the covariates were selected until the most appropriate model, defined by the lowest Akaike Information Criterion. A threshold of α= 0.05 was considered for significance for the final model. Analyses were performed with R software version 3.5.1.