Cure model analysis in cancer: an application to data from the Children's Cancer Group

The most commonly used statistical methods for evaluating treatment or prognostic effects on cancer outcome--the logrank test and Cox regression analysis--rely on the proportional hazards (PH) assumption in that they have maximal power in this circumstance. Implicitly, these methods emphasize covariate effects on failure times rather than their effects on the proportion of long-term survivors ('cures'), which may be of equal or primary interest. In paediatric cancer, treatment has progressed dramatically in recent decades, and in many diagnoses cures are obtained in a large fraction of patients. A primary focus of clinical research is therefore the achievement of cure. Parametric cure model (PCM) analysis, introduced 50 years ago, is arguably better suited to the analytic requirements of clinical research in paediatric and other cancers where cure is achieved. In this paper two classes of PCMs are described and used to analyse examples from the Children's Cancer Group. These are compared to analyses using Cox regression analysis. Results from PCM analyses are similar or identical to Cox regression analysis when the PH assumption is appropriate. When it is not, PCMs can provide a coherent way to investigate and report covariate effects on the proportion cured separately from their effect on time to failure. Despite their reliance on explicit parametric forms, PCMs often provide a good description of cancer outcome, and are insensitive to lack of fit provided that follow-up is sufficient.