Analysis of Unified Hybrid Hjorth Competing Risk Data and Its Application to Multiple Myeloma and Electrical Appliances

In many survival analysis studies, it is common to observe failures caused by multiple factors. The data obtained in such instances are referred to as competing risk data. This work focuses on the analysis of a competing risks model where the underlying population distribution follows the Hjorth distribution. The data are collected using a unified hybrid censoring scheme, which generalizes several existing censoring mechanisms. Our study explores the estimation of parameters for the Hjorth competing risks model, along with two key survival metrics, namely survival and hazard rate functions. The estimation process incorporates both classical likelihood-based methods and Bayesian techniques, addressing both point and interval estimation. Within the Bayesian framework, the squared error loss function is employed, and the Markov Chain Monte Carlo procedure is utilized for computation. Additionally, the study includes both approximate confidence intervals from the classical approach and highest posterior density credible intervals from the Bayesian point of view. To evaluate the performance of the proposed estimation methods, a simulation study is conducted to assess their accuracy. Furthermore, two real-world applications from clinical and industrial sectors are presented to highlight the practical relevance and effectiveness of the proposed methodologies.