Modeling Cure from Cancer Accounting for Inevitable Mortality

Cancer remains the second most prevalent cause of death in the United States, claiming 605,213 lives in 2021, surpassing COVID-19 deaths. The cancer mortality rate continued to decline between 2019 and 2020, dropping by 1.5%, marking a significant 33% decrease since 1991. This ongoing improvement primarily mirrors advances in treatment, allowing patients to achieve clinical remission and recovery. Now, a cancer patient is simultaneously exposed to the risk of primary cancer as well as other risks, such as other cancer(s) or other diseases, leading to a competing risks scenario. Analysis of survival data under competing risks and the presence of cured patients have been extensively studied individually, but there is limited work in the current literature that models the possibility of cure from one risk in the presence of competing risks. Moreover, such a model should allow for the possibility of cure from the cause-specific risk of the primary cancer; however, the overall survival probability should eventually approach zero, thereby incorporating the prevalent belief of eventual failure with certainty. We propose a novel unified competing risks cure model, based on the cause-specific hazard approach, that satisfies the aforementioned desired properties. The conditions required to establish model identifiability are studied in detail. To find the maximum likelihood estimates of the model parameters, a computationally efficient expectation maximization algorithm is developed. An extensive simulation study is carried out to demonstrate the performance of the proposed model and estimation method under different parameter settings and in the presence of multiple competing risks. Finally, an application is illustrated using breast cancer data from the SEER cancer database.