A Bayesian Approach for Competing Risks Model Using Power Ailamujia Distribution

Abstract

A Bayesian risk analysis technique based on power Ailamujia (PA) distribution has been developed in this work, which helps in identifying various types of risk factors with their specific utility. Prior distributions have been used in the models while Bayesian estimations have been done with the help of the use of standard squared error loss functions, such as the mean square error function together with a quadratic loss function. Analysis is then performed with the help of Markov chain Monte Carlo (MCMC) approaches and time and sensitivity analyses can be done precisely in the process. For practical demonstration of this technique, real-life data are analyzed and a comparison of our proposed technique is made with the classical method of prediction. Also, we apply the proposed methodology to two distinct real-world datasets: the biomedical AIDSSI dataset from the Amsterdam Cohort Studies on HIV infection, and a sports dataset comprising UEFA Champion’s League goal-scoring times. Crucially, we present a comprehensive goodness-of-fit analysis for both datasets to validate the suitability of the PA distribution before conducting the competing risks analysis.