Transformation models with informative partly interval-censored data

Partly interval censoring is frequently encountered in clinical trials when the failure time of an event is observed exactly for some subjects but is only known to fall within an observed interval for others. Although this kind of censoring has drawn recent attention in survival analysis, available methods typically assume that the observed interval is independent of the failure time and that all potential predictors can be fully observable. However, the above assumptions may not be valid in practice. This paper considers a new joint modeling approach to simultaneously model the failure and observation times and correlate these two stochastic processes through shared latent factors. The proposed model comprises a transformation model for the failure time of interest, a proportional hazards model for the length of censoring interval, and a factor analysis model for characterization of the latent factors. A multi-stage data augmentation procedure is introduced to tackle the challenges posed by the complex model and data structure. A Bayesian approach coupled with monotone spline approximation and Markov chain Monte Carlo techniques is developed to estimate the unknown parameters and nonparametric functions. The satisfactory performance of the proposed method is demonstrated through simulations, and it is then applied to a Framingham Heart study.