Fig. 3

Bayesian inference of the CTEs of chemotherapy for the optimal subgroup. a Win probability distribution of the optimal subgroup. In subgroup 30, the patients who were treated with chemotherapy exhibit a significantly greater probability of survival compared to the untreated patients (lower bound of 95% CI > 0.5). b Kaplan–Meier survival curves of optimal subgroups. The treated patients exhibit significantly better prognoses than the untreated patients in the subgroups (p = 0.003). c Kaplan–Meier survival curves of other subgroups outside the optimal subgroup. The treated patients do not exhibit significantly better prognoses than the untreated patients in these subgroups (p = 0.352). d Bivariate win probability distribution for visualizing treatment benefits. To compare the distributions of win probabilities between the optimal and control subgroups, we visualized the joint distribution of these two groups. The blue contour represents the density of probability and the end of the contour (margin of the graph) represents a 95% CI. The upper triangle represents the area of treatment benefit