We address the problem of predicting when a disease will develop, i.e., medical event time~(MET), from a patient's electronic health record~(EHR). The MET of non-communicable diseases like diabetes is highly correlated to cumulative health conditions, more specifically, how much time the patient spent with specific health conditions in the past. The common time-series representation is indirect in extracting such information from EHR because it focuses on detailed dependencies between values in successive observations, not cumulative information. We propose a novel data representation for EHR called cumulative stay-time representation~(CTR), which directly models such cumulative health condition. We derive a trainable construction of CTR based on neural networks, which has the flexibility to fit the target data and scalability to handle high-dimensional EHR. Numerical experiments using synthetic and real-world datasets demonstrate that CTR alone achieves a high prediction performance, and it enhances the performance of existing models when combined with them.