  In survival analysis it often happens that some subjects under study do not
experience the event of interest; they are considered to be `cured'. The
population is thus a mixture of two subpopulations: the one of cured subjects,
and the one of `susceptible' subjects. When covariates are present, a so-called
mixture cure model can be used to model the conditional survival function of
the population. It depends on two components: the probability of being cured
and the conditional survival function of the susceptible subjects. In this
paper we propose a novel approach to estimate a mixture cure model when the
data are subject to random right censoring. We work with a parametric model for
the cure proportion (like e.g. a logistic model), while the conditional
survival function of the uncured subjects is unspecified. The approach is based
on an inversion which allows to write the survival function as a function of
the distribution of the observable random variables. This leads to a very
general class of models, which allows a flexible and rich modeling of the
conditional survival function. We show the identifiability of the proposed
model, as well as the weak consistency and the asymptotic normality of the
model parameters. We also consider in more detail the case where kernel
estimators are used for the nonparametric part of the model. The new estimators
are compared with the estimators from a Cox mixture cure model via finite
sample simulations. Finally, we apply the new model and estimation procedure on
two medical data sets.
