Decision support systems based on clinical notes have the potential to improve patient care by pointing doctors towards overseen risks. Predicting a patient's outcome is an essential part of such systems, for which the use of deep neural networks has shown promising results. However, the patterns learned by these networks are mostly opaque and previous work revealed flaws regarding the reproduction of unintended biases. We thus introduce an extendable testing framework that evaluates the behavior of clinical outcome models regarding changes of the input. The framework helps to understand learned patterns and their influence on model decisions. In this work, we apply it to analyse the change in behavior with regard to the patient characteristics gender, age and ethnicity. Our evaluation of three current clinical NLP models demonstrates the concrete effects of these characteristics on the models' decisions. They show that model behavior varies drastically even when fine-tuned on the same data and that allegedly best-performing models have not always learned the most medically plausible patterns.