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.
Bibliographical noteFunding Information:
The first author would like to thank Yunlei Zhang and Xiwu Lin for their stimulating discussions. We are very grateful to two anonymous referees and the Editor for many insightful comments which have dramatically improved our presentation. This research was supported by NIH grant EY10769.
- EM algorithm
- Gradient projection
- ICM algorithm
- Isotonic regression
- Proportional hazards model