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 (Patient Rule Induction Method in Survival,
Regression and Classification settings) is available on CRAN (Comprehensive R
Archive Network) and GitHub.
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