  We consider linear transformation models applied to right censored survival
data with a change-point based on a covariate threshold. We establish
consistency and weak convergence of the nonparametric maximum lieklihood
estimators. The change-point parameter is shown to be $n$-consistent, while the
remaining parameters are shown to have the expected root-$n$ consistency. We
show that the procedure is adaptive in the sense that the non-threshold
parameters are estimable with the same precision as if the true threshold value
were known. We also develop Monte-Carlo methods of inference for model
parameters and score tests for the existence of a change-point. A key
difficulty here is that some of the model parameters are not identifiable under
the null hypothesis of no change-point. Simulation students establish the
validity of the proposed score tests for finite sample sizes.
