RANK-BASED INFERENCE IN THE PROPORTIONAL HAZARDS MODEL FOR INTERVAL CENSORED-DATA

A marginal likelihood approach to fitting the proportional hazards mod el to interval censored or grouped data is proposed; this approach max imises 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 m aximum marginal likelihood estimator can be written as the expected va lue of the score of the usual proportional hazards model, with respect to a certain distribution of rankings. A Gibbs sampling scheme is giv en to generate rankings from this distribution, and stochastic approxi mation is used to solve the score equations. Simulation results under various censoring schemes give-point estimates that are close to estim ates obtained using actual failure times.