Correcting the bias due to dependent censoring of the survival estimator by conditioning

Abstract

We consider the conditional estimation of the survival function of the time T₂ to a second event as a function of the time T₁ to a first event when there is a censoring mechanism acting on their sum T₁+T₂. The problem has been motivated by a treatment interruption study aimed at improving the quality of life of HIV-infected patients. We base the analysis on the survival function of T₂ given that T₁∈I, where I represents a period of scientific interest (1 trimester, 1 year, 2 years, etc.) and propose a non-parametric estimator for the survival function of T₂ given that T₁∈I, which takes into account both the selection bias and the heterogeneity due to the dependent censoring. The proposed estimator for the survival function uses the risk group of T₂ conditioned on the categories of T₁ and corrects for the dependent censoring using weights defined by the observed values of T₁. The estimator, properly normalized, converges weakly to a zero-mean Gaussian process. We estimate the variance of the limiting process via a bootstrap methodology. Properties of the proposed estimator are illustrated by an extensive simulation study. The motivating data set is analysed by means of this new methodology.

Keywords:

• AIDS
• conditional survival
• dependent censoring
• inverse probability of censoring weighted estimators
• ordered survival times

MSC 2000:

• Primary: 62N02
• Secondary: 62G05

Acknowledgements

This work has partially been supported by grant MTM2008–06747–C02-01 from the Ministerio de Ciencia y Tecnología. Authors are indebted to the GRASS group for fruitful discussions and to the Fundació Lluita contra la SIDA for providing the data set and, in particular, to Lidia Ruiz for her contributions in the initial steps of this work. Authors also thank the constructive comments of the reviewers.