Analysis of Gamma and Weibull lifetime data under a general censoring scheme and in the presence of covariates

• Published in: Communications in statistics. Theory and methods Vol. 46; no. 5; pp. 2277 - 2289
• Main Authors: Bennett, Nathan, Iyer, Srikanth K., Jammalamadaka, S. Rao
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 04.03.2017; Taylor & Francis Ltd
• Subjects: Accelerated failure time model; Economics; EM algorithm; Gamma distribution; Intervals; Lifetime; maximum-likelihood estimators; middle censoring; Natural resources; Samples; Statistical methods; Statistics; Survival; Weibull distribution
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2015.1041981

We consider the problem of estimating the lifetime distributions of survival times subject to a general censoring scheme called "middle censoring". The lifetimes are assumed to follow a parametric family of distributions, such as the Gamma or Weibull distributions, and is applied to cases when the lifetimes come with covariates affecting them. For any individual in the sample, there is an independent, random, censoring interval. We will observe the actual lifetime if the lifetime falls outside of this censoring interval, otherwise we only observe the interval of censoring. This censoring mechanism, which includes both right- and left-censoring, has been called "middle censoring" (see Jammalamadaka and Mangalam, 2003 ). Maximum-likelihood estimation of the parameters as well as their large-sample properties are studied under this censoring scheme, including the case when covariates are available. We conclude with an application to a dataset from Environmental Economics dealing with ContingentValuation of natural resources.