Fig. 4: Survival Prediction.

a The C-index of different methods on six cancers. BEPH exhibits a higher C-index compared to weakly supervised models and baseline models across six different cancer subtypes (n = 5). The black solid line indicates the median and the red dashed line represents the mean. The whiskers extend from the box to the smallest and largest values within 1.5 times the IQR, while points outside the whiskers are considered outliers. All results are from 5-fold cross validation. Two-side paired t-test (p-value < 0.5 is considered significant) and Cohen’s d (Small effect size when 0.2 < Cohen’s d < 0.5, Medium effect size when 0.5 ≤ Cohen’s d < 0.8, Large effect size when Cohen’s d ≥ 0.8) to evaluate model differences across six cancer types. All data are presented as mean values ± SD. b Survival curves for patient stratification are depicted using Kaplan–Meier analysis. These curves illustrate the true survival rates of patients classified as high or low risk. The number of patients who survived in each risk group is shown below the survival curves. The log-rank test calculates the p-value, indicating the significance of the difference in survival between the two groups. Source data are provided with this paper.