Empirical likelihood analysis for accelerated failure time model using length-biased data

Abstract

Length-biased data arise when the probability of observing a subject in a sample is proportional to its corresponding value. The statistical tools that should be applied to analyse such sets of data differ from those used for random samples. Ignoring this issue in an investigation results in a biased inference. In this paper, we propose an empirical likelihood-based method to draw inference on covariate effects in an accelerated failure time model while the observations are subject to length-bias. The asymptotic distribution of the empirical log-likelihood ratio statistic is derived to be a weighted sum of independent chi-square distributions. Hence, we then extend the results by an exploration into the adjusted empirical likelihood. We derive an asymptotic standard chi-square distribution for the adjusted log-likelihood statistic. The limiting distributions are applied to obtain confidence regions for the regression parameters. A simulation study is carried out to evaluate and compare the performance of the proposed procedures with an existing method based on the normal approximation approach. Finally, the procedures are illustrated by modelling the regression parameter and estimating confidence intervals for a set of real data on widths of shrubs.