Assessing the fit of parametric cure models

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.