Extending Buckley–James method for heteroscedastic survival data

The Buckley–James method for the classical accelerated failure time model has been extended to accommodate heteroscedastic survival data in two ways. The first is the weighted least squares method [Yu et al. Weighted least-squares method for right-censored data in accelerated failure time model. Biometrics. 2013;69:358–365], which estimates the heteroscedasticity nonparametrically, while the second is the local Buckley–James method [Pang et al. Local Buckley–James estimation for heteroscedastic accelerated failure time model. Stat Sin. 2015;25:863–877], which uses local Kaplan–Meier method to estimate the heteroscedasticity. However, no comparisons have been done for these two methods. Furthermore, there is no hypothesis testing procedure for this heteroscedastic accelerated failure time model. This paper is then aimed to fill these two gaps to compare the two methods theoretically and numerically with extensive simulation studies. In addition, we propose a class of hypothesis tests for the parameters to provide a complete procedure for analysing heteroscedastic survival data. Two real data examples are used for practical illustration of the comparison and the new proposed tests.