A flexible, computationally efficient method for fitting the proportional hazards model to interval censored data.
The proportional hazards model (PH) is currently the most popular regression model for analyzing time to event data. Despite its popularity, the analysis of interval censored data under the PH model can be challenging using many available techniques. This article presents a new method for analyzing interval censored data under the PH model. The proposed approach uses a monotone spline representation to approximate the unknown nondecreasing cumulative baseline hazard function. Formulating the PH model in this fashion results in a finite number of parameters to estimate while maintaining substantial modeling flexibility. A novel expectation maximization (EM) algorithm is developed for finding the maximum likelihood estimates of the parameters. The derivation of the EM algorithm relies on a two stage data augmentation involving latent Poisson random variables. The resulting algorithm is easy to implement, robust to initialization, enjoys quick convergence, and provides closed form variance estimates. The performance of the proposed regression methodology is evaluated through a simulation study, and is further illustrated using data from a large population based randomized trial designed and sponsored by the United States National Cancer Institute.
Biometrics