Efficient estimation of semiparametric transformation models for counting processes

A class of semiparametric transformation models is proposed to characterise the effects of possibly time-varying covariates on the intensity functions of counting processes. The class includes the proportional intensity model and linear transformation models as special cases. Nonparametric maximum likelihood estimators are developed for the regression parameters and cumulative intensity functions of these models based on censored data. The estimators are shown to be consistent and asymptotically normal. The limiting variances for the estimators of the regression parameters achieve the semiparametric efficient bounds and can be consistently estimated. The limiting variances for the estimators of smooth functionals of the cumulative intensity function can also be consistently estimated. Simulation studies reveal that the proposed inference procedures perform well in practical settings. Two medical studies are provided.