Computation of the NPMLE of distribution functions for interval censored and truncated data with applications to the Cox model

The iterative convex minorant (ICM) algorithm (Groeneboom and Wellner, 1992) is widely believed to be much faster than the EM algorithm (Turnbull, 1976) in computing the NPMLE of the distribution function for interval censored data. Our formulation of the ICM helps to explore its connection with the gradient projection (GP) method that is commonly used in the constrained optimization area. Difficulties in extending the ICM to left truncated and interval censored data are also explained. Simulations were conducted to assess the performance of these methods. In particular, the GP is shown to be much faster than the EM. Due to its generality and simplicity the GP method is easily applied to the Cox proportional hazards model with left truncated and interval censored data. The methodology is illustrated by using the Massachusetts Health Care Panel Study dataset.