Inference under hybrid censoring for the quadratic hazard rate model: Simulation and applications to COVID-19 mortality
Moustafa N. Mousa, M. E. Moshref, N. Youns, Mahmoud M. M. Mansour
Abstract
This study implements Bayesian along with non-Bayesian approaches to estimate the parameters of the three-parameter quadratic hazard rate distribution using hybrid Type-II censoring. The model expands upon linear hazard rate, exponential, and Rayleigh distributions. In the non-Bayesian framework, point estimates and survival and hazard functions are calculated using maximum likelihood estimation (MLE). Asymptotic confidence intervals are derived, with a focus on the delta method. By applying independent normal and gamma priors, Bayesian inference produces point estimates and credible intervals using different symmetric and asymmetric loss functions. The analytical intractability of posterior distributions makes Markov chain Monte Carlo (MCMC) methods necessary for sampling purposes. The evaluation of point and interval estimates depends on root mean squared error (RMSE) in combination with mean relative absolute bias (MRAB), average confidence interval length (AL), and coverage probability (CP). The performance evaluation through different sample sizes and censoring schemes is conducted by simulation studies, while real-world data from COVID-19 mortality demonstrates the practical implementation of methods. Graphical and numerical analyses confirm the existence and uniqueness of the estimates. Results indicate that Bayesian methods deliver superior accuracy and more robust estimates than their non-Bayesian counterparts for survival analysis purposes in clinical and medical research.