Fig. 1

Workflow of gene-level and pathway-level models. Gene-level data matrix of GE/SPM/CNV is input into the workflow. Genes are pre-filtered either by intersecting with the pathway collection (shown as ‘Path’) or further filtering the genes by intersecting with COSMIC genes (shown as ‘COSMIC’) or significant genes (p-value less than 0.05) in univariable Cox models (shown as ‘Cox’). Then, for the pathway-level models, gene set enrichment is conducted to transform the gene-level matrix into a pathway-level matrix. For GE and CNV data, GSVA is applied and for SPM, odds ratio is applied to conduct gene set enrichment. While for the gene-level models, this step is skipped. With the filtered gene-level data matrix or the transformed pathway-level data matrix as the predictor matrix, we conducted nested cross validation to test the predictive performance of gene-level and pathway-level models. A 5-fold cross validation separates the data into training and test sets. In the training set, a Lasso (least absolute shrinkage and selection operator) or L1-penalized Cox model is fit with the shrinkage parameter chosen by a nested 10-fold cross validation. With the selected predictors and coefficient estimates, the estimated model is applied to the test set and three metrics are adopted to measure the prediction: i) the predictive performance is measured by the concordance index, ii) the model robustness is measured by Fleiss Kappa, iii) the model parsimony is measured by average model size