Nonparametric inference and uniqueness for periodically observed progressive disease models

Beth Griffin and Stephen Lagakos have a new paper in Lifetime Data Analysis. They consider panel observed progressive disease model (chain-of-events) data. The NPMLE estimator under a discrete-time semi-Markov assumption was developed by Sternberg and Satten (Biometrics, 1999). For datasets where individuals are observed at different times, some discretization of the data is required. An issue with the NPMLE is that it is not guaranteed to be unique and therefore reporting a single NPMLE may be misleading. The paper develops procedures for determining which components of the NPMLE are unique based on considering various re-parameterizations of the likelihood. The method is demonstrated on three example datasets including one on bronchiolitis obliterans syndrome in post-lung transplantation patients and one on primary HIV infection. In addition, the authors also provide a more intuitive algorithm for obtaining the NPMLE than the self-consistency algorithm of Sternberg and Satten.