Mechanical ventilation is a vital supportive measure for patients with acute respiratory distress syndrome (ARDS) in the intensive care unit. An important setting in the ventilator is the positive end-expiratory pressure (PEEP), which can reduce lung stress but may also cause harmful side effects. This research investigates the personalization of PEEP settings based on patient characteristics using three meta-learning algorithms (S-, T-, and X-learner) to estimate the conditional average treatment effect. Additionally, the hypothesis that the X-learner performs particularly well under a significant imbalance in patient numbers between treatment groups is tested. Results show that the X-learner slightly outperforms the S- and T-learners in terms of mean squared error under various unbalanced conditions in simulated data. However, the overall ability of these meta-learners to identify patients benefiting from high PEEP remains inconclusive. When using gradient boosted trees or random forest as base models, cumulative gain curves on MIMIC-IV data indicate potential overfitting. While the X-learner performs somewhat better on this data, the low area under the curve scores suggests a minimal distinction between high and low PEEP groups. External validation with data from a randomized control confirms that the models do not effectively distinguish between treatment groups. These findings suggest that further investigation with more complex models and real-world data is needed to validate the potential of meta-learning algorithms in personalizing PEEP settings for ARDS patients.