This paper proposes a discrete-time hazard regression approach based on the relation between hazard rate models and excess over threshold models, which are frequently encountered in extreme value modelling. The proposed duration model employs a flexible link function and incorporates the grouped-duration analogue of the well-known Cox proportional hazards model and the proportional odds model as special cases. The theoretical setup of the model is motivated, and simulation results are reported to suggest that it performs well. The simulation results and an empirical analysis of US import durations also show that the choice of link function in discrete hazard models has important implications for the estimation results, and that severe biases in the results can be avoided when using a flexible link function as proposed in this study.