We investigate the problem of finding confidence sets for a threshold in the baseline hazard function of the Cox proportional hazards model. The aim is to find an effective way of condensing information in the baseline into a small number of estimable parameters. A binary decision tree is used as a working model, with the jump point (threshold) representing a time at which baseline risk changes abruptly between two levels. We find the asymptotic distribution of estimators of best-fitting parameters under an arbitrary misspecification of the working model. The estimators converge at cube-root rate to a non-normal limit distribution. Two alternate ways of constructing confidence intervals for the threshold are compared. Results from a simulation study and an example concerning a threshold for the age of onset of schizophrenia in a large cohort study are discussed.
Banerjee, Moulinath and McKeague, Ian W., "Decision trees for instantaneous hazard rates with adjustment for covariate effects" (June 2006). Columbia University Biostatistics Technical Report Series. Working Paper 5.