Figure 5

Kaplan–Meier analysis of post-IS cumulative probability for 3 year mortality in the testing sample. Vertical Bar represents right-censored patients. Assuming three risk categories with different survival probability in the testing sample, features included in the multivariate Cox proportional-hazards regression model were selected for calculation of the risk score (\({Z}^{T}\widehat{\beta }\)) where \({Z}^{T}\) is a vector of covariates and \(\widehat{\beta }\) is a vector of estimate of effect size. P-value derived from Log-rank test provided a measure of how well the model stratified risk sets. For the entire analysis, p < 0.05 was considered statistically significant. For all the post-hoc pairwise tests, p-values were adjusted by Benjamin-Hochberg procedure. The number of patients at risk was listed in the table. We used candidate features with a p value < 0.05 from the univariate Cox regression model as an example for feature selection. We compared Kaplan–Meier curves developed from the base model (A) to the integrated model (B) with an additional 11 pathway-specific PRSs in the testing sample after the LASSO-based feature selection using the training sample (C). The forest plot demonstrated the effect size (HR) for the integrated multivariate Cox regression model in the training sample; (D). We calculated continuous Net Reclassification Index (NRI), Integrated Discrimination Improvement Index (IDI), and median improvement by R ‘survIDINRI’ package, as metrics to determine the improvement in prediction when comparing integrated model after additional features selected to the corresponding base model. The additional value of pathway-specific PRS is assessed by the paired difference of risk scores. The empirical distribution function of the paired difference (\(\widehat{D}\)) between the risk scores (on the probability scale) estimated at \({t}_{0}\) = 3 years using models with and without the inclusion of pathways-specific PRSs. The added value of these PRSs is proportional to the area of the shared region. The vertical difference at s = 0 (between the two black dots, where s scales the region between − 1 and + 1) is NRI (> 0), and the horizontal difference (between the two gray dots) equals the median risk-score difference. Y-axis, cumulative probability; X-axis, s = \(\widehat{D}\), the difference between two model risk scores.