A fast and stable algorithm for calculating the non-parametric maximum likelihood estimate of left-truncated and interval-censored data

We present a fast and conceptually appealing product-limit style EM algorithmfor calculating the non-parametric maximum likelihood estimator (NPMLE) for left-truncated and interval-censored (LTIC) data. The reparameterization as a product-limit allows left-truncation and right-censoring to be accounted for in a pre-processing step, leading to an improvement in both time-per-iteration and number of iterations over other EM algorithms for interval-censored data. Combining this novel EM algorithm with a modified iterative convex minorant (ICM) step (Pan, 1999) allows for estimation of larger and more complex data than was previously practical for LTIC data. We evaluate the performance of this algorithm through simulation and apply it to data from the Massachusetts HealthCare Panel Study, demonstrating its effectiveness over other algorithms.