Spring Seminar Series  January 29, 2008
University of Minnesota
School of Statistics
College of Liberal Arts

Change-Point Cox Model with Current Status Data

Rui Song
Department of Biostatistics
The University of North Carolina at Chapel Hill

Tuesday, January 29, 2008
3:30 PM, 115 Ford Hall
Minneapolis, East Bank Campus
Social at 3:00 PM, 300 Ford Hall

Abstract

Current status data arise when only random censoring time and event status at censoring are observable. We 
investigate the inference of the change-point Cox model with an unknown covariate threshold for current 
status data. The parameters of interest consist of a threshold parameter and other regression parameters. We 
study the consistency and weak convergence of the nonparametric maximum likelihood estimators. The 
change-point parameter is shown to be $n-$consistent, while the finite-dimensional regression parameters 
are root-$n$ consistent and the baseline cumulative hazard function is cubic-root consistent. 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 score tests for the existence 
of a change-point, along with a Monte Carlo method of obtaining critical values. 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 our inference procedures for finite sample sizes. The calcification 
data is analyzed with the proposed approach.