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 proposed approach is
illustrated on a Calcification data set.