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Robert C Gentleman and Alain Vandal (2001)
Computational Algorithms for Censored Data Problems Using
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In this paper methods for finding the non-parametric maximum likelihood estimate (NPMLE) of the distribution function of time to event data will be presented. The basic approach is to use graph theory (in particular intersection graphs) to simplify the problem.
Censored data can be represented in terms of their intersection graph. Existing combinatorial algorithms can be used to find the important structures, namely the maximal cliques. When viewed in this framework there is no fundamental difference between right censoring, interval censoring, double censoring or current status data and hence the algorithms apply to all types of data.
These algorithms can be extended to deal with bivariate data and indeed there are no fundamental problems extending the methods to higher dimensional data.
Finally we will show how to obtain the NPMLE using convex optimization methods and methods for mixing distributions. The implementation of these methods is greatly simplified through the graph-theoretic representation of the data.
KeyWords: Censored data, interval censoring, current status, doubly censored, nonparametric maximum likelihood, graph theory.
