Before revision:  The proposed tests are based on two-step Kaplan-Meier integrals , and do not rely on parametric distributional assumptions, shape restrictions, nor on restricting the potential treatment effect heterogeneity across different subpopulations.
After revision:  The proposed tests are based on two-step Kaplan-Meier integrals and do not rely on parametric distributional assumptions, shape restrictions, nor on restricting the potential treatment effect heterogeneity across different subpopulations.