Table 2.

Summary of methods discussed for predicting survival

Method	Sparsity	Description	Reference
Cox prop. hazards	No	Only applies if columns of X not multicollinear	Kalbfleisch and Prentice16
Univariate selection	Yes	Does not find best multivariate model	Klein and Moeschberger63
Stepwise selection	Yes	Computationally intensive; not global optimum	Klein and Moeschberger63
L2 shrinkage	No	Resulting coefficients can be small, but non-zero	Verweij and van Houwelingen28
L1 shrinkage	Yes	Dimension reduction and feature selection are integrated into one step	Tibshirani29
Covariance-regularised regression	Yes	Sparsity results if p2 = 1	Witten and Tibshirani36
Tree harvesting	Maybe	In general, not sparse; depends on clusters included in model	Hastie et al.39
Principal component regression	No	Outcome is regressed onto high-variance subspace of features	Massy40
SIR + PC	No	PC is followed by SIR44in order to reduce dimension before fitting survival model	Li and Li43
Supervised PC	Yes	PC is performed only on the features with highest Cox scores	Bair and Tibshirani41
PLS + Cox prop. hazards	No	PLS used to reduce dimension before fitting a survival model	Nguyen and Rocke47
PCR (PLS for Cox model)	No	PLS regression adapted to the survival setting	Park et al.48