Estimation of Hazard, Density and Survivor Functions for Randomly Censored Data

• Published in: Journal of applied statistics Vol. 31; no. 10; pp. 1211 - 1225
• Main Authors: Reineke, David, Crown, John
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.12.2004; Taylor and Francis Journals; Taylor & Francis Ltd
• Series: Journal of Applied Statistics
• Subjects: competing risks; Estimates; goodness-of-fit; maximum likelihood estimation; Maximum likelihood method; net and crude lifetimes; Randomly censored data; semi-parametric models; Theory
• ISSN: 0266-4763; 1360-0532
• DOI: 10.1080/0266476042000285521

Maximum likelihood estimation and goodness-of-fit techniques are used within a competing risks framework to obtain maximum likelihood estimates of hazard, density, and survivor functions for randomly right-censored variables. Goodness-of- fit techniques are used to fit distributions to the crude lifetimes, which are used to obtain an estimate of the hazard function, which, in turn, is used to construct the survivor and density functions of the net lifetime of the variable of interest. If only one of the crude lifetimes can be adequately characterized by a parametric model, then semi-parametric estimates may be obtained using a maximum likelihood estimate of one crude lifetime and the empirical distribution function of the other. Simulation studies show that the survivor function estimates from crude lifetimes compare favourably with those given by the product-limit estimator when crude lifetimes are chosen correctly. Other advantages are discussed.