Empirical likelihood for linear transformation models with interval-censored failure time data

For regression analysis of interval-censored failure time data, Zhang et al. (2005) [40] proposed an estimating equation approach to fit linear transformation models. In this paper, we develop two empirical likelihood (EL) inference approaches for the regression parameters based on the generalized estimating equations. The limiting distributions of log-empirical likelihood ratios are derived and empirical likelihood confidence intervals for any specified component of regression parameters are obtained. We carry out extensive simulation studies to compare the proposed methods with the method discussed by Zhang et al. (2005) [40]. The simulation results demonstrate that the EL and jackknife EL methods for linear transformation models have better performance than the existing normal approximation method based on coverage probability of confidence intervals in most cases, and they enable us to overcome an under-coverage problem for the confidence intervals of the regression parameters using a normal approximation when sample sizes are small and right censoring is heavy. Two real data examples are provided to illustrate our procedures.