Estimation of the bivariate distribution function for censored gap times

ABSTRACT

In many medical studies, patients may experience several events during follow-up. The times between consecutive events (gap times) are often of interest and lead to problems that have received much attention recently. In this work, we consider the estimation of the bivariate distribution function for censored gap times. Some related problems such as the estimation of the marginal distribution of the second gap time and the conditional distribution are also discussed. In this article, we introduce a nonparametric estimator of the bivariate distribution function based on Bayes’ theorem and Kaplan–Meier survival function and explore the behavior of the four estimators through simulations. Real data illustration is included.

KEYWORDS:

• Gap times
• Kaplan–Meier
• Multi-state model
• Nonparametric estimation
• Simulation study

MATHEMATICS SUBJECT CLASSIFICATION:

• 62N02
• 62G05

Acknowledgment

Thanks to the anonymous referee for comments and suggestions which have improved the presentation of the article.

Funding

Ana Moreira acknowledges financial support by grant SFRH/BD/62284/2009 of the Portuguese Ministry of Science, Technology and Higher Education. This research was also financed by FEDER Funds through Programa Operacional Factores de Competitividade COMPETE and by Portuguese Funds through FCT - Fundação para a Ciência e a Tecnologia, within Projects PTDC/MAT/104879 and UID/MAT/00013/2013.