Mechanical ventilation with positive end-expiratory pressure (PEEP) is a critical intervention for patients in intensive care units (ICUs) with acute respiratory failure. Identifying the optimal PEEP level is challenging due to conflicting evidence from studies comparing low and high PEEP regimes. This research explores machine learning methods for estimating individualized treatment effects (ITE) in ICU patients on different PEEP levels using the observational MIMIC-IV dataset. Various conditional average treatment effect (CATE) estimators, including S-, T-, and DR-learners, are applied to control for confounders and identify PEEP effects on patient subgroups. This research aims to compare the performance of the aforementioned CATE estimators, with a focus on the doubly-robust (DR) learner, and determine which one is best suited for causal inference in this context. The DR-learner offers increased resilience to model errors since it integrates two models. Simulations using mean squared error (MSE) show the DR-learner performs well with confounded data and differing linear response functions between control and treatment groups. However, when looking at the performance on the MIMIC-IV dataset, the predictions are unstable, failing to reliably identify the optimal PEEP for increasing patient survival. This trend is also observed in a randomized controlled trial (RCT) dataset, with the area under the Qini curve (AUQC) close to zero, indicating difficulties in identifying the effects of PEEP settings. Despite promising simulation results, real-world application shows limitations in these machine learning methods for optimal PEEP identification.