Semi-competing risks refer to the phenomenon where a primary outcome event (such as mortality) can truncate an intermediate event (such as relapse of a disease), but not vice versa. Under the multi-state model, the primary event is decomposed to a direct outcome event and an indirect outcome event through intermediate events. Within this framework, we show that the total treatment effect on the cumulative incidence of the primary event can be decomposed into three separable pathway effects, corresponding to treatment effects on population-level transition rates between states. We next propose estimators for the counterfactual cumulative incidences of the primary event under hypothetical treatments by generalized Nelson-Aalen estimators with inverse probability weighting, and then derive the consistency and asymptotic normality of these estimators. Finally, we propose hypothesis testing procedures on these separable pathway effects based on logrank statistics. We have conducted extensive simulation studies to demonstrate the validity and superior performance of our new method compared with existing methods. As an illustration of its potential usefulness, the proposed method is applied to compare effects of different allogeneic stem cell transplantation types on overall survival after transplantation.
This paper explores why Sinope may have shifted from its initial commemorative epoch of 45 BCE, suggesting that the city’s adoption of a new era might have been a modification rather than a complete overhaul, influenced by traditions or challenges related to Achaemenid-Seleucid periods. The analysis extends to the impact of regional externalities on Sinope’s decision-making processes, particularly whether the Lucullan era was adopted for better regional integration with northern Paphlagonia. This regional alignment, evident in cities like Amastris and Abonuteichos and facilitated through the “Koinon of the Cities in Pontus,” implies Amastris’s significant influence due to its long-standing use of the Lucullan era and its political stature. The paper attempts to advance two arguments. First, Sinope's era system alignment could be voluntary, aimed at regional conformity. Second, the intent to conform to regional norms may have been due to broader regional dynamics and potential gubernatorial pressures, and hence a decision informed by both local and global factors.