Cumulative hazard ratio estimation for adverse events data from two-stage dynamic treatment regimes

Accurate analysis of adverse events in two-stage dynamic treatment regimes is complicated by the presence of competing risks, such as death, which can preclude the observation of an adverse event and introduce bias into standard survival estimates. To address these challenges, this study employs cumulative hazard functions to compare the safety profiles of different treatment policies, offering a more precise quantification of adverse event risk in the context of competing outcomes. The Nelson-Aalen estimator is utilized to decompose the overall hazard into cause-specific components, enabling a nuanced assessment of both mortality and adverse event risks. By appropriately censoring for competing events, the proposed approach ensures unbiased estimation of cumulative hazards, thereby facilitating robust and interpretable comparisons between treatment strategies. Our methodology is demonstrated through the estimation of the cumulative hazard ratio for adverse events in a real world data set for leukemia.