Many quantities of interest in survival analysis are smooth, closed-form
functionals of the law of the observations. For instance, the conditional law of a lifetime
of interest under random right censoring, and the conditional probability of being
cured. In such cases, one can easily derive nonparametric estimators for the quantities
of interest by plugging-into the functional the nonparametric estimators of the law of
the observations. However, with multivariate covariates, the nonparametric estimation
suffers from the curse of dimensionality. Here, a new dimension reduction approach
for survival analysis is proposed and investigated in the right-censored lifetime case.
First, we consider
√ a single-index hypothesis on the conditional law of the observations
and propose a n−asymptotically normal semiparametric estimator. Next, we apply
the smooth functionals to this estimator. This results in semiparametric estimators of
the quantities of interest that avoid the curse of dimensionality. Confidence regions for
the index and the functional of interest are built by bootstrap. The new methodology
allows to test the dimension reduction assumption, can be extended to other dimension

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• A dimension reduction approach for conditional Kaplan–Meier estimators