  We introduce a framework to build a survival/risk bump hunting model with a
censored time-to-event response. Our Survival Bump Hunting (SBH) method is
based on a recursive peeling procedure that uses a specific survival peeling
criterion derived from non/semi-parametric statistics such as the
hazards-ratio, the log-rank test or the Nelson-Aalen estimator. To optimize the
tuning parameter of the model and validate it, we introduce an objective
function based on survival or prediction-error statistics, such as the log-rank
test and the concordance error rate. We also describe two alternative
cross-validation techniques adapted to the joint task of decision-rule making
by recursive peeling and survival estimation. Numerical analyses show the
importance of replicated cross-validation and the differences between criteria
and techniques in both low and high-dimensional settings. Although several
non-parametric survival models exist, none addresses the problem of directly
identifying local extrema. We show how SBH efficiently estimates extreme
survival/risk subgroups unlike other models. This provides an insight into the
behavior of commonly used models and suggests alternatives to be adopted in
practice. Finally, our SBH framework was applied to a clinical dataset. In it,
we identified subsets of patients characterized by clinical and demographic
covariates with a distinct extreme survival outcome, for which tailored medical
interventions could be made. An R package `PRIMsrc` is available on CRAN and
GitHub.
