Novel Regression Model for Investigating the Survival Times of HIV Patients in Gombe State, Nigeria

Abstract

Conventional survival models often lack the flexibility required to capture the complex hazard structures observed in biomedical data. This study proposes a survival regression model based on the log-DUS Topp–Leone Burr–Hatke exponential (LDUSTLBHE) distribution for modeling censored survival times among patients with HIV in Gombe State, Nigeria. The model extends the Burr–Hatke exponential framework by incorporating additional shape flexibility to accommodate diverse survival patterns. Its probability density function, survival function, and regression structure were derived, and the parameters were estimated using maximum likelihood estimation under censoring. The model was applied to data from 200 patients with HIV, with age, gender, CD4 count, World Health Organization disease stage, and number of opportunistic infections included as explanatory variables. Its performance was compared with the log-Topp–Leone Burr–Hatke exponential, log-alpha-power Burr–Hatke exponential, and log-Burr–Hatke exponential regression models using the log-likelihood, Akaike information criterion, Bayesian information criterion, consistent Akaike information criterion, and Hannan–Quinn information criterion. The LDUSTLBHE model provided the best fit among the competing models, while diagnostic assessments based on Cox–Snell residuals and Kaplan–Meier survival comparisons further supported its adequacy. Advanced disease stage, a greater number of opportunistic infections, and older age were associated with shorter survival times. The proposed model therefore offers a flexible framework for analyzing censored survival data and provides clinically relevant insights into HIV survival dynamics.