Semiparametric transformation models with random effects for clustered failure time data

We propose a general class of semiparametric transformation models with random effects to formulate the effects of possibly time-dependent covariates on clustered or correlated failure times. This class encompasses all commonly used transformation models, including proportional hazards and proportional odds models, and it accommodates a variety of random-effects distributions, particularly Gaussian distributions. We show that the nonparametric maximum likelihood estimators of the model parameters are consistent, asymptotically normal and asymptotically efficient. We develop the corresponding likelihood-based inference procedures. Simulation studies demonstrate that the proposed methods perform well in practical situations. An illustration with a well-known diabetic retinopathy study is provided.