Presmoothing the transition probabilities in the illness-death model

Ana Paula Amorim, Jacobo de Una-Alvarez and Luis Meira-Machado have a new paper in Statistics & Probability Letters. This proposes an estimator for the transition probabilities in a three-state illness-death model under general (i.e. non-Markov conditions). A variant of the estimator by Meira-Machado et al (2006, Lifetime Data Analysis) is proposed, the difference here being the presence of "pre-smoothing". This involves replacing the censoring weights in the estimating equations with parametric estimates of the weights, for instance via a logistic model. They demonstrate that the method results in more efficient estimators of the transition probabilities and appear to be robust to some level of misspecification of the parametric model for the weights.