Likelihood ratio inference for mean residual life

Abstract

One of the basic parameters in survival analysis is the mean residual life M ₀. For right censored observation, the usual empirical likelihood based log-likelihood ratio leads to a scaled ${\chi_1^2}$ limit distribution and estimating the scaled parameter leads to lower coverage of the corresponding confidence interval. To solve the problem, we present a log-likelihood ratio l(M ₀) by methods of Murphy and van der Vaart (Ann Stat 1471–1509, 1997). The limit distribution of l(M ₀) is the standard ${\chi_1^2}$ distribution. Based on the limit distribution of l(M ₀), the corresponding confidence interval of M ₀ is constructed. Since the proof of the limit distribution does not offer a computational method for the maximization of the log-likelihood ratio, an EM algorithm is proposed. Simulation studies support the theoretical result.