This research investigates the use of Causal Multi-task Gaussian Process (CMGP) for estimating the individualized treatment effect (ITE) of low versus high Positive End-Expiratory Pressure (PEEP) regimes on ICU patients requiring mechanical ventilation. The study addresses the complexities of determining ITE due to the inability to observe counterfactual outcomes and the confounding bias in observational studies. By employing Conditional Average Treatment Effect (CATE) estimators, such as S-Learner, T-Learner, and CMGP, the research evaluates the impact of different PEEP settings on patient survival across varied patient characteristics. The precision of these estimators is assessed using simulated data, real-world observational data from the MIMIC-IV dataset, and an external RCT dataset. The findings of this study are inconclusive, highlighting the need for further research to refine these methods and explore larger, more balanced datasets.