Computational Algorithms for Censored Data Problems Using Intersection Graphs

In this paper methods for nding 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 combinato-rial algorithms can be used to nd the important structures, namely the maximal cliques. When viewed in this framework there is no fundamental diierence 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 simpliied through the graph{theoretic representation of the data.