Nonparametric analysis of interval censored and doubly truncated data

Abstract

Doubly truncated data appear in a number of applications, including astronomy and survival analysis. For double-truncated data, the lifetime T is observable only when U≤T≤V, where U and V are the left-truncated and right-truncated time, respectively. In some situations, the lifetime T also suffers interval censoring. Using the EM algorithm of Turnbull [The empirical distribution function with arbitrarily grouped censored and truncated data, J. R. Stat. Soc. Ser. B 38 (1976), pp. 290–295] and iterative convex minorant algorithm [P. Groeneboom and J.A. Wellner, Information Bounds and Nonparametric Maximum Likelihood Estimation, Birkhäuser, Basel, 1992], we study the performance of the nonparametric maximum-likelihood estimates (NPMLEs) of the distribution function of T. Simulation results indicate that the NPMLE performs adequately for the finite sample.

Keywords:

• double truncation
• interval censoring
• nonparametric maximum-likelihood estimation

Acknowledgements

The author would like to thank the associate editor and referees for their helpful and valuable comments and suggestions.