Sparse supervised principal component analysis for survival models

Abstract

Survival prediction plays a vital role in biomedical research, but the large number of patient characteristics considered as covariates raises the concern about overfitting leading to poor prediction accuracy. To address this, we propose a sparse supervised PCA method for censored Accelerated Failure Time models (SSPCA-AFT), which formulates sparse principal components with maximum dependency on the survival outcome of interest, through the optimisation of a penalised negative log-likelihood and PCA loss function. An adaptive sparse regularisation on the principal component loadings is also proposed through the adaptive SSPCA-AFT (aSSPCA-AFT) method, which was shown to incorporate sparsity more effectively than SSPCA-AFT. The proposed methods were illustrated with simulation studies and two real datasets - the Primary Biliary Cirrhosis (PBC) and Systolic Heart Failure (Peak VO2) datasets. The empirical results show that our proposed method is competitive with existing methods in terms of variable selection and prediction accuracy, with the added advantage of interpretability. Overall, we have proposed a suitable and effective method to overcome the problem of overfitting in survival prediction.