The EG-Lindley Distribution: A Flexible Model for Non-Communicable and Chronic Disease Survival Analysis.

Abstract

This study introduces and evaluates the EG-Lindley (EG-L) distribution as a flexible model for analyzing survival data. The EG-L distribution is shown to capture a wide range of hazard rate behaviors - including increasing, decreasing, and bathtub-shaped patterns, making it highly adaptable to biomedical and reliability data analysis. A comprehensive analysis of the statistical properties of the EG-L distribution is presented, including the probability density function, cumulative distribution function, survival function, and hazard function, supported by detailed graphical interpretations. To assess the empirical performance of the EG-L distribution, three real-world datasets were analyzed: (1) bladder cancer patient survival times, (2) acute bone cancer survival data, and (3) head and neck cancer cases treated with radiotherapy and chemotherapy. The proposed model was compared with several existing generalizations of the Lindley distribution - namely, the New Generalized Two-Parameter Lindley Distribution, and the four other Generalized Lindley Distributions. Model performance was evaluated using goodness-of-fit criteria, including the -2log-likelihood, Akaike Information Criterion, Bayesian Information Criterion, Hannan–Quinn Information Criterion, and the Corrected Akaike Information Criterion. Across all datasets, the EG-L distribution consistently achieved the best or most competitive fit, as evidenced by the lowest information criteria values. These results underscore the robustness and adaptability of the EG-L distribution in capturing complex survival patterns and support its application as a valuable tool in the analysis of time-to-event data in clinical and epidemiological research.