A model-based approach to estimate the cure fraction in the population of colon cancer patients

Estimating the cure fraction in a diseased population, especially in the presence of competing mortality causes, is essential for both patients and clinicians. It offers a critical measure for understanding and interpreting trends in disease outcomes. The Relative Survival (RS) framework is particularly useful in situations where cause-of-death information is unavailable or unreliable, and it is an alternative way to estimate net survival, survival solely due to the disease of interest. In cancer survival analysis, net survival often plateaus over time, indicating that a subset of diagnosed individuals is statistically cured, meaning they face the same mortality risk as a comparable group of healthy individuals with similar demographic characteristics. On the other hand, the group of fatal patients is often heterogeneous, and identifying subgroups with different characteristics is a key goal from both epidemiological and clinical perspectives. In this paper, we propose a model-based approach to estimate the cure fraction in a diseased population, while also distinguishing different groups among fatal cases according to disease severity. We derive an Expectation-Maximization (EM) algorithm for the proposed RS cure model, we explore the performance of the model in a simulation study, and we apply our methodology to a real-world dataset from a historical Italian cancer registry. The results are consistent with previous analyses which reported reduction in colon cancer mortality.