Assessing the Fit of Parametric Cure Models

• Activity Number: 88
• Type: Invited
• Date/Time: Sunday, August 3, 2014 : 8:30 PM to 10:30 PM
• Sponsor: Health Policy Statistics Section
• Author(s): E. Paul Wileyto*+ and Yimei Li and Jinbo Chen and Daniel F. Heitjan
• Companies: University of Pennsylvania and Children's Hospital of Philadelphia and University of Pennsylvania Perelman School of Medicine and University of Pennsylvania
• Keywords: Accelerated failure time ; Long-term survivors ; Proportional hazards ; Residual analysis

Abstract

Survival data often contain an unknown fraction of subjects who are "cured" in the sense of not being at risk of failure. "Cure-mixture models" describe these data, which model both cure status and the hazard of failure among non-cured subjects with separate linear predictors. No diagnostic currently exists for evaluating the fit of such models; the popular Schoenfeld residual (Schoenfeld (1982) Biometrika 69, 239-241) is not applicable to data with cures. In this article, we develop a pseudo-residual, based 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 demonstrate our approach using time to failure data from a smoking cessation drug trial.