University of Wisconsin Department of Biostatistics and Medical Informatics University of Wisconsin Department of Biostatistics and Medical Informatics

We consider linear transformation models applied to right censored survival data with a change-point in the regression coefficient based on a covariate threshold. We establish consistency and weak convergence of the nonparametric maximum likelihood estima-tors. 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 studies establish the validity of the proposed score tests for finite sample sizes.