Maximization of the marginal likelihood of grouped survival data

Abstract

Grouped failure time data occur in studies where subjects are monitored periodically to determine whether failure has occurred in the intervening interval. Here the model under consideration is Cox's (1972, 1975) proportional hazards model, but the commonly used method of partial likelihood needs modification with grouped data due to a potentially large number of ties. This paper demonstrates how the Monte Carlo em algorithm (Wei & Tanner, 1990) can be used on grouped data to find the maximum likelihood estimate from the marginal likelihood based on the incomplete ranks of the event times. The methodology is exemplified with a data set with precise failure times after artificially introducing grouping.