Standard errors for the Cox proportional hazards cure model

Standard errors for the maximum likelihood estimates of the regression parameters 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 from the inverse of the joint observed information matrix of the regression parameters and the nuisance hazard parameters. The observed information matrix is derived and is shown to be an approximation of the conditional information 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 on the profile likelihood and the full likelihood are comparable and appropriate. The coverage rates for the logistic regression parameter are generally good. The proportional hazards regression parameter shows reasonable coverage rates under ideal conditions but lower coverage rates when the incidence proportion is low or when censoring is heavy. The three methods are applied to a data set to investigate the effects of radiation therapy on tonsil cancer.