In the clinical diagnosis of pneumonia, particularly during the COVID-19 pandemic, individuals who progress to a critical stage requiring mechanical ventilation are classified as mechanically ventilated critically ill patients. Accurately predicting the discharge outcomes for this specific cohort, especially those with COVID-19, is of paramount clinical importance. Missing data, a common issue in medical research, can significantly impact the validity of analyses. In this work, we address this challenge by employing two missing data imputation techniques: multiple imputation and missForest, to enhance data completeness. Additionally, we utilize the smoothly clipped absolute deviation (SCAD) penalized logistic regression method to select significant features. Our real data analysis compares the predictive performances of extreme learning machines, random forests, support vector machines, and XGBoost using 10-fold cross-validation. The results consistently show that XGBoost outperforms the other methods in predicting discharge outcomes, making it a reliable tool for clinical decision-making in the treatment of severe pneumonia, including COVID-19 cases. Within this context, the random forest imputation method generally enhances performance, underscoring its effectiveness in managing missing data compared to multiple imputation.