The purpose of this paper is to present the development of the Proportional Odds Model for discrete time-to-event data in a survival analysis context. In this work, inferences about the model parameters considering the discrete Weibull as baseline distribution are presented, obtaining the point and interval estimates of the model parameters. In addition, procedures for checking the proportional odds assumption were proposed. Simulation studies were performed to evaluate the asymptotic properties of the estimators. The proposed model is illustrated using a dataset on the survival time of patients with Leukemia.