In the intensive care unit (ICU), optimizing mechanical ventilation settings, particularly the positive end-expiratory pressure (PEEP), is crucial for patient survival. This paper investigates the application of neural network-based machine learning methods to personalize PEEP settings in the ICU, aiming to improve patient survival outcomes. The research focuses on two specific algorithms, TARNet and CFR, evaluating their ability to estimate individualized treatment effects of lower versus higher PEEP regimes. The study is structured into three phases: controlled simulations, application to the MIMIC-IV dataset, and validation using a randomized control trial dataset. TARNet and CFR showed potential for estimating the individualized treatment effects but required large datasets for optimal performance. In the case where limited data is available, these models are upstaged by simpler learners, such as the S- and T-learners. The study concludes that while neural network-based methods hold promise for personalizing ICU treatment, their efficacy is heavily influenced by data availability and quality.