Competing Risks Modelling via Multistate System Methodology under a Generalized Family of Distributions

Abstract This paper develops a competing risks model within the framework of Multi-State Systems (MSS) methodology, focusing on statistical inference when sojourn times (waiting times) are from a general closed-under-minima family of distributions. The proposed family includes a broad class of time-to-event distributions and thus is highly applicable to reliability theory, survival analysis and other fields of study. We set up a consistent statistical framework for inference and evaluate its performance through large-scale simulation studies. The findings validate the flexibility and accuracy of the proposed method, signifying its potential in modeling advanced failure mechanisms. The contribution of this study lies in presenting a new, holistic approach to competing risks analysis with its wide applications in various disciplines.