In Reply We greatly appreciate Yin and Zhang’s comments and the opportunity to further elaborate on the interpretation of our findings,1 and more generally, to describe a fitted Cox model for competing risk data and standard survival data if the proportional hazard (PH) assumption is in doubt.
The Cox regression model is developed at the level of hazard, and a hazard ratio (HR) is, strictly speaking, a ratio between the instantaneous rates of event occurrence among patients who are still event free. In a standard survival analysis, an HR less than 1 implies a reduction in hazard and cumulative incidence by exploiting their 1-to-1 relationship. Such correspondence does not hold in competing risks analysis; for example, we evaluated the association between prophylactic cranial irradiation (PCI) and occurrence of brain metastases (BM) in RTOG 0214 because patients who died without BM can no longer experience BM, and death was treated as a competing event. In an effort to elucidate the role of PCI, we reported findings from a cause-specific hazard Cox model2,3 of BM, where the HR was the ratio of the instantaneous rates of BM occurrence in participants who were both alive and free of BM, and a reduction in HR does not guarantee a reduction in the incidence of BM. We were imprecise and should have been more explicit in our language in this regard.
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Sun A, Hu C. Reanalysis of Data Comparing Prophylactic Cranial Irradiation vs Observation in Patients With Locally Advanced Non–Small Cell Lung Cancer—In Reply. JAMA Oncol. 2019;5(11):1638–1639. doi:10.1001/jamaoncol.2019.3602
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