The nonparametric location-scale mixture cure model

We propose completely nonparametric methodology to investigate location-scale modelling of two-component mixture cure models, where the responses of interest are only indirectly observable due to the presence of censoring and the presence of so-called long-term survivors that are always censored. We use covariate-localized nonparametric estimators, which depend on a bandwidth sequence, to propose an estimator of the error distribution function that has not been considered before in the literature. When this bandwidth belongs to a certain range of undersmoothing band-widths, the asymptotic distribution of the proposed estimator of the error distribution function does not depend on this bandwidth, and this estimator is shown to be root-n consistent. This suggests that a computationally costly bandwidth selection procedure is unnecessary to obtain an effective estimator of the error distribution, and that a simpler rule-of-thumb approach can be used instead. A simulation study investigates the finite sample properties of our approach, and the methodology is illustrated using data obtained to study the behavior of distant metastasis in lymph-node-negative breast cancer patients