Nonparametric inference for competing risks current status data with continuous, discrete or grouped observation times.

Marloes Maathuis and Michael Hudgens have a paper available at arXiv.org. This concerns nonparametric inference for competing risks current status data. They consider a naive estimator, which estimates each cumulative incidence function independently using the pooled-adjacent-violators algorithm. Additionally, the NPMLE is also considered. The naive estimator, while consistent, does not guarantee that the sum of CIFs is less than 1. Moreover, previous work by Groeneboom et al suggests it is less efficient. However, the naive estimator has the advantage (in addition to being computationally simpler) that the limiting distribution of the estimates of each CIF is known (being the same as standard current status survival data) and results regarding the likelihood ratio statistic (Banerjee and Wellner 2005) can be applied to get confidence intervals for the CIFs. These results are in the case of a smooth observation distribution. The authors note that if subjects can only be observed in a (finite) pre-defined grid of time points then obviously the CIFs can only be estimated at these time points but also, since the number of parameters cannot increase indefinitely, standard n^1/2 asymptotics apply.

Related to this work is the R package MLEcens developed by Marloes Maathuis. This computes the NPMLE for bivariate interval censored data. Special cases include competing risks data and standard survival data. Moreover the implementation seems to run considerably faster than the package Icens.

*Update: A video of Marloes Maathuis demonstrating MLEcens is available here.

**Update: The paper is now published in Biometrika.