A fast and stable algorithm for non-parametric maximum likelihood estimation of survival functions for left-truncated and interval-censored data

We present a fast and conceptually appealing product-limit style EM algorithm for calculating the non-parametric maximum likelihood estimator of the survival function for left-truncated and interval-censored (LTIC) data. By reparameterizing the estimator as a product-limit allows left-truncation and right-censoring to be accounted for analytically, while interval -censoring is still handled algorithmically. This reparameterization leads to a significant reduction in the number of iterations required to converge when applied to LTIC data compared to other EM algorithms. Combining this novel EM algorithm with a modified iterative convex minorant step (Pan 1999) allows the estimation of survival functions for larger and more complex LTIC data than was previously practical. We evaluate the performance of this algorithm through simulation and apply it to data from the Massachusetts Health Care Panel Study, demonstrating its effectiveness over other algorithms.