Standard errors for the Cox proportional hazards cure model

Standard errors for tile maximum likelihood estimates of tile regression pa rameters in the logistic-proportional-hazards cure model are proposed using an approximate profile likelihood approach and a nonparametric likelihood. Two methods are given and are compared with the standard errors obtained f rom the inverse of the joint observed information matrix of tile regression parameters and tile nuisance hazard parameters. The observed information m atrix is derived and is shown to be all approximation of the conditional in formation matrix of the regression parameters given the hazard parameters. Simulations indicate that the standard errors obtained from the inverse of the observed information matrix based oil the profile likelihood and the fu ll likelihood are comparable and appropriate. The coverage rates for the lo gistic regression parameter are generally good. Tile proportional hazards r egression parameter show reasonable coverage rates under ideal conditions b ut lower coverage rates when the incidence proportion is low or when censor ing is heavy. Tile three methods are applied to a data set to investigate t he effects of radiation therapy on tonsil cancer. (C) 2001 Elsevier Science Ltd. All rights reserved.