Author's Reply To: A Note on Competing Risks in Analyses of Cancer‐specific Mortality

Dear Sir, We have read the commentary by Dr Acuna and Dr Dossa in response to our article published in the International Journal of Cancer. We agree with the authors that competing risks analysis is indeed a topic that often leads to confusion and misinterpretation. As pointed out there are many such examples in the literature and we welcome their discussion that relates to our recent study on cancer survival after organ transplantation in Sweden. The primary objective of the study in question was to investigate if organ transplant recipients (OTR) have a worse cancer-specific survival as compared to cancer patients without a history of organ transplantation. There are several possible mechanisms that motivate such a hypothesis. For example, malignancies developing during immunosuppressive treatment may display more aggressive biological characteristics, or the possibility to administer full oncological therapy may be hampered due to risk of enhanced organ damage. To understand if these mechanisms play a combined role in the prognosis of OTR cancer patients, net survival was the underlying statistical quantity of interest in our study. In the context of cancer patient survival, net survival (also known as marginal survival) is defined as the survival that is associated with cancer in the hypothetical situation where the cancer in question is the only possible thing that can kill the patient. There are several approaches to estimating net survival, and we chose to apply a cause-specific survival analysis (whereby competing causes of death are censored). However, unless the risk of competing causes of death can be assumed to be independent of the risk of cancer death, Dr Acuna and Dr Dossa correctly point out that Kaplan–Meier estimates of survival will yield biased estimates of net survival. This is well-known and provides the rationale for not presenting such results in our study. The presented cause-specific hazard ratios, on the other hand, remain interpretable, also in situations when the independence assumption is violated. Under such situations, the cause-specific hazard quantifies the transition hazard to the event of interest in the real-world situation in which individuals may experience any type of event during follow-up. For the purposes of investigating how the rate of cancer-specific mortality among OTRs differs from that of transplantation-free patients, we therefore maintain that the cause-specific analysis performed in our study is the correct statistical approach. The issue that may have prompted the letter by Dr Acuna and Dr Dossa seems to stem from our use of the word prognosis and what the word itself entails. We argue that the word has a broader meaning than merely relating to the anticipated realworld risk of cancer death. In the context of our study, we use prognosis in the same manner as commonly used in clinical epidemiology and cancer control studies when, for example, investigating the impact of prognostic factors on (net) survival. We apologize if this usage of the word has indicated that the objective of the study was also to provide risk estimates that would have a closer clinically meaningful interpretation related to the proportion of affected patients. Studies that aim to estimate absolute risks of cancer death in the presence of competing risks among OTRs would, nevertheless, add an interesting extension to our study, as well as others who have arrived at similar conclusions regarding the net survival of these patients. We conclude our abstract by stating that “several but not all types of post-transplantation cancer diagnoses are associated with worse outcomes than in the general population. Reasons for this should be further explored to optimize posttransplantation cancer management.” Research directed toward this aim should further address the contribution of immunosuppression and selection to oncological treatment among OTRs, as well as the absolute risks of cancer deaths estimated in the presence of noncancer deaths. We fully support the authors in their argument that for the purposes of informing health care professionals, providing a basis for risk communication or planning health care services, competing risks methodology is required to estimate the proportion of patients who will suffer the event in the real world. Yours sincerely, Henrik Benoni Karin E. Smedby Sandra Eloranta