Statistical inference for Kumaraswamy-G cure fraction competing risks models under unified progressive hybrid censoring

This study develops a statistical inference framework for a cure fraction based on a competing risks model from the Kumaraswamy-G family of distributions under the Unified Progressive Hybrid Censoring scheme. The latent failure times are assumed to be independent and identically distributed, where each individual is classified as either cured or susceptible to failure from competing causes. Classical and Bayesian inferential procedures are developed for parameter estimation. Maximum likelihood estimation is employed to obtain point estimates and asymptotic confidence intervals, while Bayesian estimation is performed using the Metropolis-Hastings Markov chain Monte Carlo algorithm to obtain posterior estimates and highest posterior density credible intervals. The finite-sample performance of the proposed estimators is evaluated through extensive Monte Carlo simulation studies under various sample sizes and censoring schemes, and levels of partially masking. The methods are compared in terms of bias, mean squared error, coverage probability, and average widths under both restricted and unrestricted parameter spaces. The proposed methodology is illustrated using the publicly available METABRIC breast cancer clinical dataset containing competing risks and long-term survivors. The proposed cure model sufficiently models the Cumulative incidence functions of two causes, particularly under moderate to heavy censoring. Moreover, it highlights the flexibility and effectiveness of the proposed framework for analyzing cure-fraction competing-risks data.