## An urn model in the simulation of interval censored failure time data.(English)Zbl 0951.62087

Summary: A self-consistent algorithm was proposed by B.W. Turnbull [J. Am. Stat. Assoc. 69, 169-173 (1974; Zbl 0281.62044)] 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 urn model, consistent estimates can be obtained by using the self-consistency algorithm. A simulation example is provided to illustrate the procedure.

### MSC:

 62N05 Reliability and life testing 65C60 Computational problems in statistics (MSC2010) 62N99 Survival analysis and censored data

Zbl 0281.62044
Full Text:

### References:

 [1] Cox, D.R., Oakes, D., 1984. Analysis of Survival Data. Chapman & Hall, New York. [2] De Gruttola, V; Lagakos, S.W, Analysis of doubly-censored survival data, with application to AIDS., Biometrics., 45, 1-11, (1989) · Zbl 0715.62223 [3] Finkelstein, D.M, A proportional hazards model for interval-censored failure time data., Biometrics., 42, 845-854, (1986) · Zbl 0618.62097 [4] Finkelstein, D.M; Wolfe, R.A, A semiparametric model for regression analysis of interval-censored failure time data., Biometrics., 41, 933-945, (1985) · Zbl 0655.62101 [5] Gomez, G; Lagakos, S.W, Estimation of the infection time and latency distribution of AIDS with doubly censored data., Biometrics., 50, 204-212, (1994) · Zbl 0826.62088 [6] Lawless, J.F., 1982. Statistical Models and Methods for Lifetime Data. Wiley, New York. · Zbl 0541.62081 [7] Leiderman, P.H; Babu, D; Kagia, J; Kraemer, H.C; Leiderman, G.H, African infant precocity and some social influence during the first year., Nature., 242, 247-249, (1973) [8] Sun, J, A non-parametric test for interval-censored failure time data with application to AIDS studies., Statist. med., 15, 1387-1395, (1996) [9] Turnbull, B.W, Nonparametric estimation of a surviorship function with doubly censored data., J. amer. statist. assoc., 69, 169-173, (1974) · Zbl 0281.62044
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.