title: Assessing the fit of parametric cure models.
abstract: Survival data can contain an unknown fraction of subjects who are "cured" in the sense of not being at risk of failure. We describe such data with cure-mixture models, which separately model cure status and the hazard of failure among non-cured subjects. No diagnostic currently exists for evaluating the fit of such models; the popular Schoenfeld residual (Schoenfeld, 1982. Partial residuals for the proportional hazards regression-model. Biometrika 69, 239-241) is not applicable to data with cures. In this article, we propose a pseudo-residual, modeled on Schoenfeld's, to assess the fit of the survival regression in the non-cured fraction. Unlike Schoenfeld's approach, which tests the validity of the proportional hazards (PH) assumption, our method uses the full hazard and is thus also applicable to non-PH models. We derive the asymptotic distribution of the residuals and evaluate their performance by simulation in a range of parametric models. We apply our approach to data from a smoking cessation drug trial.
authors.affiliation: Department of Biostatistics & Epidemiology, University of Pennsylvania, Philadelphia, PA 19104, USA. epw@upenn.edu
authors.forename: E Paul
authors.initials: EP
authors.lastname: Wileyto
authors.forename: Yimei
authors.initials: Y
authors.lastname: Li
authors.forename: Jinbo
authors.initials: J
authors.lastname: Chen
authors.forename: Daniel F
authors.initials: DF
authors.lastname: Heitjan
mesh_terms: D056808:Biostatistics; D003198:Computer Simulation; D006801:Humans; D053208:Kaplan-Meier Estimate; D015233:Models, Statistical; D016016:Proportional Hazards Models; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data; D016540:Smoking Cessation / Q000379:methods / Q000706:statistics & numerical data; D016019:Survival Analysis