In this paper, we propose a methodology for deriving a new kind of approximate temporal functional dependencies, called Approximate Predictive Functional Dependencies (APFDs), based on a three-window framework and on a multi-temporal relational model. Different features are proposed for the Observation Window (OW), where we observe predictive data, for the Waiting Window (WW), and for the Prediction Window (PW), where the predicted event occurs. We then consider the concept of approximation for such APFDs, introduce new error measures, and discuss different strategies for deriving APFDs. We discuss the quality, i.e., the informative content, of the derived AFDs by considering their entropy and information gain. Moreover, we outline the results in deriving APFDs focusing on the Acute Kidney Injury (AKI). We use real clinical data contained in the MIMIC III dataset related to patients from Intensive Care Units to show the applicability of our approach to real-world data.