Nonparametric estimation in an "illness-death" model when the transition times are interval-censored and one transition is not observed.

Frydman, Gerds, Groen and Keiding have a paper available as a research report from the Department of Biostatistics, Copenhagen. The paper develops previous work on the non-parametric estimation of interval-censored multi-state data. Here the data in question follow a progressive three-state "illness-death" model but the ill to death transition is never observed. This is because the data arise from clinical observation and the trial ceases if a patient is observed to be in the illness state. Such an observation scheme has strong similarities with data considered by Duffy et al relating to breast cancer screening where a three-stage unidirectional model was assumed and the intermediate state was pre-clinical detectable breast cancer. No data on pre-clinical to clinical breast cancer transitions were available as interest was in the natural progression of the disease. Duffy et al analysed the data parametrically, assuming a time homogeneous Markov model. In contrast Frydman et al fit a non-homogeneous Markov model non-parametrically. Since all transitions are interval censored, they model the process in discrete time.
Update: A paper broadly based upon the research report has now been published in Biometrical Journal. The supplementary materials also includes R code to implement the proposed algorithm.