Semiparametric efficient estimation in the generalized odds-rate class of regression models for right-censored time-to-event data

The generalized odds-rate class of regression models for time to event data is indexed by a non-negative constant rho and assumes that g(rho) (S(t\Z)) = alpha(t) + beta'Z where g(rho)(s) = log(rho(-1)(s(-rho) - 1)) for rho > 0, g(0)(s) = log(- logs), S(t\Z) is the survival function of the time to event for an individual with qx1 covariate vector Z, beta is a qx1 vector of unknown regression parameters, and alpha(t) is some arbitrary increasing function of t. When rho = 0, this model is equivalent to the proportional hazards model and when rho = 1, this model reduces to the proportional odds model. In the presence of right censoring, we construct estimators for beta and exp(alpha(t)) and show that they are consistent and asymptotically normal. In addition, we show that the estimator for beta is semiparametric efficient in the sense that it attains the semiparametric variance bound.