Recent medical prognostic models adapted from high data-resource fields like language processing have quickly grown in complexity and size. However, since medical data typically constitute low data-resource settings, performances on tasks like clinical prediction did not improve expectedly. Instead of following this trend of using complex neural models in combination with small, pre-selected feature sets, we propose EffiCare, which focuses on minimizing hospital resource requirements for assistive clinical prediction models. First, by embedding medical events,we eliminate manual domain feature-engineering and increase the amount of learning data. Second, we use small,but data-efficient models, that compute faster and are easier to interpret. We evaluate our approach on four clinical prediction tasks and achieve substantial performance improvements over highly resource-demanding state-of-the-art methods. Finally, to evaluate our model beyond score improvements, we apply explainability and interpretability methods to analyze the decisions of our model and whether it uses data sources and parameters efficiently.