Applying deep learning to medical research with limited data is challenging. This study focuses on addressing this difficulty through a case study, predicting acute respiratory failure (ARF) in patients with acute pesticide poisoning. Commonly, out-of-distribution (OOD) data are overlooked during model training in the medical field. Our approach integrates OOD data and transfer learning (TL) to enhance model performance with limited data. We fine-tuned a pre-trained multi-layer perceptron model using OOD data, outperforming baseline models. Shapley additive explanation (SHAP) values were employed for model interpretation, revealing the key factors associated with ARF. Our study is pioneering in applying OOD and TL techniques to electronic health records to achieve better model performance in scenarios with limited data. Our research highlights the potential benefits of using OOD data for initializing weights and demonstrates that TL can significantly improve model performance, even in medical data with limited samples. Our findings emphasize the significance of utilizing context-specific information in TL to achieve better results. Our work has practical implications for addressing challenges in rare diseases and other scenarios with limited data, thereby contributing to the development of machine-learning techniques within the medical field, especially regarding health inequities.