Some scale estimators and lack-of-fit tests for the censored two-sample accelerated life model

Some new scale estimators for the censored two-sample accelerated life model are introduced. They are zeros of some integrated weighted difference between the two cumulative hazard estimators. These estimators are asymptotically normal. The weight is chosen to result in estimators whose asymptotic variances do not involve the destiny functions and can be easily estimated. This provides a fast and simple means of statistical inference in the censored two-sample accelerated life model. Through investigating the asymptotic relative efficiency at some important censoring submodels and the finite example behaviors in various numerical studies, we obtain some estimators with very competitive performance. From the new class of scale estimators, some lack-of-fit tests for the accelerated life model are also derived. These tests are related to Gill-Schumacher type tests and require little extra computing time once the estimator is obtained. The estimators and tests are illustrated in two applications. For a vaginal cancer data set for rats, the effect of pretreatment regime was found to be well described by the two-sample accelerated life model. For a data set on progression of ovarian cancer, it was found that the effect of grade of disease could not be described either by the two-sample proportional hazards model or the two-sample accelerated life model.