  This paper investigates the (in)-consistency of various bootstrap methods for
making inference on a change-point in time in the Cox model with right censored
survival data. A criterion is established for the consistency of any bootstrap
method. It is shown that the usual nonparametric bootstrap is inconsistent for
the maximum partial likelihood estimation of the change-point. A new
model-based bootstrap approach is proposed and its consistency established.
Simulation studies are carried out to assess the performance of various
bootstrap schemes.
