Further details on inference under right censoring for transformation models with a change-point based on a covariate threshold

TL;DR

This paper develops methods for inference in transformation models with right censored survival data, focusing on change-points based on covariate thresholds, establishing estimator properties, and proposing Monte Carlo inference techniques.

Contribution

It introduces consistent estimators for change-points in transformation models and develops Monte Carlo methods and score tests for inference, addressing non-identifiability issues.

Findings

Change-point parameter is n-consistent.

Remaining parameters have root-n consistency.

Score tests are valid for finite samples.

Abstract

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.