Rank-based inference in the proportional hazards model for interval censored data

A marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed; this approach maximises a likelihood that is the sum over al rankings of the data that are consistent with the observed censoring intervals. As in the usual proportional hazards model, the method does not require specification of the baseline hazard function. The score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model, with respect to a certain distribution of rankings. A Gibbs sampling scheme is given to generate rankings from this distribution, and stochastic approximation is used to solve the score equations. Simulation results under various censoring schemes give-point estimates that are close to estimates obtained using actual failure times.