Residual-based model diagnosis methods for mixture cure models

Model diagnosis, an important issue in statistical modeling, has not yet been addressed adequately for cure models. We focus on mixture cure models in this work and propose some residual-based methods to examine the fit of the mixture cure model, particularly the fit of the latency part of the mixture cure model. The new methods extend the classical residual-based methods to the mixture cure model. Numerical work shows that the proposed methods are capable of detecting lack-of-fit of a mixture cure model, particularly in the latency part, such as outliers, improper covariate functional form, or nonproportionality in hazards if the proportional hazards assumption is employed in the latency part. The methods are illustrated with two real data sets that were previously analyzed with mixture cure models.