  We consider survival data in the presence of a cure fraction, meaning that
some subjects will never experience the event of interest. We assume a mixture
cure model consisting of two sub-models: one for the probability of being
uncured (incidence) and one for the survival of the uncured subjects (latency).
Various approaches, ranging from parametric to nonparametric, have been used to
model the effect of covariates on the incidence, with the logistic model being
the most common one. We propose a monotone single-index model for the incidence
and introduce a new estimation method that is based on the profile maximum
likelihood approach and techniques from isotonic regression. The monotone
single-index structure relaxes the parametric logistic assumption while
maintaining interpretability of the regression coefficients. We investigate the
consistency of the proposed estimator and show through a simulation study that,
when the monotonicity assumption is satisfied, it performs better compared to
the non-constrained single-index/Cox mixture cure model. To illustrate its
practical use, we use the new method to study melanoma cancer survival data.
