Fascinating Application in Medicine Using Mixture Cure Models and Martingale Difference Correlation

Rheumatoid arthritis (RA) is a chronic systemic inflammatory disease that leads to joint inflammation, functional disability, deformities, and reduced life expectancy. The goal of RA treatment is to achieve remission in the early stages of the disease, before permanent deformities develop. Therefore, identifying predictors of relapse is crucial, allowing physicians to tailor treatment plans. This need gives rise to the development of predictive models capable of processing large amounts of information and considering relapse of RA as the event of interest. Since not all individuals will experience this event, some will be classified as 'long-term survivors' or 'cured individuals.' Cure models enable direct modeling of the cure proportion and the effect of covariates on this proportion. This study introduces a new methodology to test the effect of covariates on patients who do not experience relapse, using a database provided by the Rheumatology-Health research group (GIR-S, by its acronym in Spanish).