Maximum likelihood estimation for the proportional odds model with random effects

In this article we study the semiparametric proportional odds model with random effects for correlated, right-censored failure time data. We establish that the maximum likelihood estimators for the parameters of this model are consistent and asymptotically Gaussian. Furthermore, the limiting variances achieve the semiparametric efficiency bounds and can be consistently estimated. Simulation studies show that the asymptotic approximations are accurate for practical sample sizes and that the efficiency gains of the proposed estimators over those of Cai, Cheng, and Wei can be substantial. A real example is provided to illustrate the proposed methods.