A comparison of presmoothing methods in the estimation of transition probabilities

Abstract

One major goal in clinical applications of multi-state models is the estimation of transition probabilities. Estimators based on subsampling were recently introduced by de Uña-Álvarez and Meira-Machado to estimate these quantities, and their superiority with respect to the competing estimators has been proved in situations in which the Markov condition is violated. The idea behind the proposed estimators is to use a procedure based on (differences between) Kaplan-Meier estimators derived from a subset of the data consisting of all subjects observed to be in a given state at a given time. Subsampling, also referred to as landmarking, leads to small sample sizes and high percentage of censoring for which more efficient estimators are essential. Preliminary smoothing, also known as presmoothing, is a good alternative to these situations. The presmoothed estimators are obtained by replacing the censoring indicator variables in the classical definitions by values of a regression estimator. The behavior of the presmoothed landmark estimators for the transition probabilities is explored through simulation studies when different ways to estimate the conditional probability of uncensoring are used. Real data illustration is included.