A multiple imputation approach to distinguish curative from life-prolonging effects in the presence of missing covariates

Medical advancements have increased cancer survival rates and the possibility of finding a cure. Hence, it is crucial to evaluate the impact of treatments in terms of both curing the disease and prolonging survival. We may use a Cox proportional hazards (PH) cure model to achieve this. However, a significant challenge in applying such a model is the potential presence of partially observed covariates in the data. We aim to refine the methods for imputing partially observed covariates based on multiple imputation and fully conditional specification (FCS) approaches. To be more specific, we consider a more general case, where different covariate vectors are used to model the cure probability and the survival of patients who are not cured. We also propose an approximation of the exact conditional distribution using a regression approach, which helps draw imputed values at a lower computational cost. To assess its effectiveness, we compare the proposed approach with a complete case analysis and an analysis without any missing covariates. We discuss the application of these techniques to a real-world dataset from the BO06 clinical trial on osteosarcoma.