  We consider the problem of estimating the distribution of time-to-event data
that are subject to censoring and for which the event of interest might never
occur, i.e., some subjects are cured. To model this kind of data in the
presence of covariates, one of the leading semiparametric models is the
promotion time cure model \citep{yakovlev1996}, which adapts the Cox model to
the presence of cured subjects. Estimating the conditional distribution results
in a complicated constrained optimization problem, and inference is difficult
as no closed-formula for the variance is available. We propose a new model,
inspired by the Cox model, that leads to a simple estimation procedure and that
presents a closed formula for the variance. We derive some asymptotic
properties of the estimators and we show the practical behaviour of our
procedure by means of simulations. We also apply our model and estimation
method to a breast cancer data set.
