ROC-based methods for comparing two survival curves under non-proportional hazards with right, left, and doubly censored data

Studies comparing two survival curves to assess treatment differences are commonplace. The widely used log-rank test assumes proportional hazards (PH) and may yield misleading results when this assumption is violated. Alternative methods, such as the Fleming-Harrington weighted log-rank tests, rely on prior knowledge of survival patterns, which is often difficult to specify before a study. The recently developed MaxCombo test does not require such prior information; however, it leaves substantial room for power improvement, particularly when survival curves cross. To address these issues, we propose new nonparametric and semiparametric methods for comparing two survival curves based on the receiver operating characteristic (ROC) curve length and the overlap coefficient, along with a joint inference approach combining both measures. Our methods are applicable under non-PH settings and can accommodate right, left, and double censoring. We evaluate our methods through extensive simulation studies under different non-PH configurations. Our results show improved performance of the proposed methods compared to existing nonparametric methods, particularly under early and crossing effects. Real-world examples involving various non-PH scenarios are provided, illustrating the superiority of our methods in detecting survival differences. We further provide an R package named ''ROCsurvcomp" that implements all our proposed approaches and is available on CRAN.