Nonparametric estimation in the illness-death model using prevalent data.

We study nonparametric estimation of the illness-death model using left-truncated and right-censored data. The general aim is to estimate the multivariate distribution of a progressive multi-state process. Maximum likelihood estimation under censoring suffers from problems of uniqueness and consistency, so instead we review and extend methods that are based on inverse probability weighting. For univariate left-truncated and right-censored data, nonparametric maximum likelihood estimation can be considerably improved when exploiting knowledge on the truncation distribution. We aim to examine the gain in using such knowledge for inverse probability weighting estimators in the illness-death framework. Additionally, we compare the weights that use truncation variables with the weights that integrate them out, showing, by simulation, that the latter performs more stably and efficiently. We apply the methods to intensive care units data collected in a cross-sectional design, and discuss how the estimators can be easily modified to more general multi-state models.