Along with the analysis of time-to-event data, it is common to assume that
only partial information is given at hand. In the presence of right-censored
data with covariates, the conditional Kaplan-Meier estimator (also referred as
the Beran estimator) is known to propose a consistent estimate for the
lifetimes conditional survival function. However, a necessary condition is the
clear knowledge of whether each individual is censored or not, although, this
information might be incomplete or even totally absent in practice. We thus
propose a study on the Beran estimator when the censoring indicator is not
clearly specified. From this, we provide a new estimator for the conditional
survival function and establish its asymptotic normality under mild conditions.
We further study the supervised learning problem where the conditional survival
function is to be predicted with no censorship indicators. To this aim, we
investigate various approaches estimating the conditional expectation for the
censoring indicator. Along with the theoretical results, we illustrate how the
estimators work for small samples by means of a simulation study and show their
practical applicability with the analysis of synthetic data and the study of
real data for the prognosis of monoclonal gammopathy