In this article, we present the development of the proportional odds hazard model for discrete time-to-event data. In this work, inferences about the model’s parameters were formulated considering the presence of right censoring and the discrete Weibull and log-logistic distributions. Simulation studies were carried out to check the asymptotic properties of the estimators. In addition, procedures for checking the proportional odds assumption were proposed, and the proposed model is illustrated using a dataset on the survival time of patients with low back pain.