The bivariate defective Marshall-Olkin Weibull distribution based on Clayton Copula and its application to medical survival data

Traditional survival analysis models assume that all individuals will eventually experience the event, while cure models account for subsets that remain "cured" or immune. These models estimate cure rates and have been applied extensively, particularly in cancer research. Recent advancements have introduced defective distributions as a novel approach in cure rate modeling. In defective models, the total probability mass is less than one, and the survival function approaches a constant value, referred to as time progresses toward infinity. In this context, p represents the cure rate. This innovative method is particularly beneficial in real-world applications involving correlated time-to-event outcomes. A significant gap exists in the study of defective models, which fundamentally contradict probability theory. We proposed a new bivariate cure model using a copula-based approach to address dependencies between survival outcomes, introducing the use of defective distributions in multivariate survival analysis as a novel topic. We investigated the behavior of the defective Marshall-Olkin Weibull distribution in bivariate survival analysis using Clayton copula through a simulation study and on real-world datasets. The simulation study confirmed the model's adequacy, with estimations improving as the sample size increased. Our model demonstrated exceptional flexibility compared to previous models in the literature; its correlation estimates (Kendall and Spearman) closely matched empirical values, achieved lower AIC and BIC values, and accurately identified significant covariates. The model performed well even without a cure fraction, highlighting its robustness and potential for various scenarios.