A note on proportional hazards and proportional odds models

The proportional hazards model has been used as a major model for analyzing survival data. When there are heavy ties, the proportional odds model is often recommended as an alternative. In this paper, we explore theoretical properties of these two models. We obtain a necessary condition for the discrete proportional odds model. We study the relationship between the proportional hazards and proportional odds models when the continuous times are discretized. Using this relationship, we derive a characterization result for the proportional hazards model, showing that the proportional hazards model is only related to the geometric distribution, a special case of the proportional odds model. We highlight this important difference between the two models that seems to be ignored in the analysis of real data. Using small numerical studies, we show that caution should be taken in using a proportional odds model in place of a proportional hazards model.