Analysis of the primary outcome
VAE
REGRESSION, SECONDARY
In the primary outcome analysis (VAE rate), we used repeated measures mixed modeling (generalized linear and mixed model [GLMM]) with a Poisson distribution for the monthly number of VAEs, including an offset term for the number of ventilator days to account for variation due to lengths of time. The ICU and hospital were considered as random effects and the standardized study month as a fixed effect in the model. Results were expressed as incidence risk ratio (IRR) for each additional month in the project with 95%CI.Diagnostic checking of residuals was performed for the parameter estimates. The over-dispersion of parameters was also assessed by calculating the ratio of the Pearson chi-square statistic and its degrees of freedom. If this ratio exceeded 1, it indicated that the variability in data was not properly modeled and that there was residual over-dispersion due to misspecification of the conditional distribution. When the Poisson regression model deviated from the assumption of equi-dispersion (average = variance), the negative binomial regression model was adopted. The model was selected as the best model with a unique covariance structure that produced the lowest Bayesian Information Criterion value. The covariance structures which were considered in the model were: first order of autocorrelation covariance structure, unstructured covariance structure, Toeplitz covariance structure and variance component structure. The random coefficients were modeled using G-side random effects and obtained the unit-specific estimates by defining the appropriate variance-covariance structure. The Newton-Raphson optimization technique with ridging option was used whenever the model failed to converge. We conducted a secondary analysis of VAE per 100 episodes of mechanical ventilation [