Sepsis is a leading cause of death in intensive care, and early detection is needed for timely intervention. However, methods to identify the time of sepsis onset from health records vary, which is critical in retrospective studies. Using the Sepsis-III criteria, we determine three potential onset times for sepsis against which we apply three representative predictive models: a tree-based model (LGBM), a sequential neural network model (LSTM), and the Cox proportional-hazard model (CoxPHM). Here we consider the static demographic factors and the signature feature of physiological time series of the patients for feature extraction.  The models were trained on MIMIC-III critical care database. We show that machine-learning models (LGBM and LSTM) consistently outperformed the classical approach (CoxPHM). The signature feature set can improve the performance of the predictive model significantly, especially the CoxPHM model.