An urn model in the simulation of interval censored failure time data

A self-consistent algorithm was proposed by Turnbull (J. Amer. Statist. Assoc. 69 (1974) 169-173) to estimate the distribution of X on the basis of interval censored data of X. An interval censored X means that X is known either to lie inside an interval (X-L,X-R], or to lie below X-L or above X-R. The calculation of the estimates is not an easy task. In this article, an urn model is constructed to sample the random intervals and to calculate relevant probabilities. It is proved that using the interval data obtained from the um model, consistent estimates can be obtained by using the self-consistency algorithm. A simulation example is provided to illustrate the procedure. (C) 1999 Elsevier Science B.V. All rights reserved.