Cross‐validation and peeling strategies for survival bump hunting using recursive peeling methods

Abstract

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.

Machine Learning Approaches to Identify Thresholds in a Heat-Health Warning System Context

“…The process is carried out until the proportion of observations left in the box is below . The final box is then chosen as the one yielding the largest rate of increase compared to the previous larger box as (Dazard et al, 2016):where is the risk and is the proportion of remaining observations in the box at step of the peeling. The largest rate of increase (4) thus represents the best change point in the relationship between and .…”

“…The process is carried out until the proportion of observations left in the box is below 0 . The final box is then chosen as the one yielding the largest rate of increase compared to the previous larger box as (Dazard et al, 2016):…”

Cross-validation and Peeling Strategies for Survival Bump Hunting using Recursive Peeling Methods

“…• The (two-sample) log-rank test can be used at a peeling step pm, lq to compare estimates of the hazard functions from each child box-defined subgroups ("in-box" and its "out-of-box" complement). We recently proposed to use it as a survival-specific box peeling criterion [14]. Using the (two-sample) log-rank test statistic is actually a natural candidate for survival decision-box, having been a wellestablished concept for splitting trees in survival decision-trees [1,45,46,62,69] and for being robust in non-proportional hazard settings [46].…”

“…Recently, we described a cross-validation technique for recursive peeling methods in a survival/risk setting [14]. The subject of this section is to give a more in-depth development of this strategy and compare it to standard cross-validation techniques.…”

“…In all our performance analyses below, we used LRT in both peeling and optimization criteria and RCCV as our cross-validation technique. Comparisons include (i) Survival Bump Hunting by our PRSP method (Algorithm 1 and [14]), (ii) Regression Survival Trees (RST) by recursive partitioning [1,11,13,32,45,46,62], (iii) Random Survival Forest (RSF) by ensemble tree-based method [40], (iv) Cox Proportional Hazard Regression (CPHR) [12], (v) Survival Supervised PCA (SSPCA) [4], (vi) Survival Supervised Clustering (SSC) [5]. The simulated survival model was according to simulated model #1b, that is, by generating a boxshaped region R of the input covariate space with higher hazards than a uniform background (see 4.1).…”