A modified generalized hazard model with time-varying effects for survival analysis of Tuberculosis patients

Abstract

Classical survival models often fall short when applied to tuberculosis (TB) data, which involve heterogeneous patient risks, non-linear hazard patterns, substantial censoring, and the presence of long-term survivors. This study developed and evaluated a Modified Generalized Hazard Model (MGHM) that integrates generalized hazard structures, accelerated failure time components, and time-varying covariate effects into a single unified modelling framework. The analysis was based on a retrospective dataset comprising 500 TB patients drawn from Nasarawa State, Nigeria, complemented by simulated survival data generated under a range of hazard structures, sample sizes, censoring proportions to rigorously test model performance. Descriptive statistics of Kaplan–Meier survival estimation, log-rank testing, and smoothed hazard function assessment. The performance of MGHM was benchmarked against several models, including the Cox proportional hazards model, Weibull proportional hazards model, log-logistic accelerated failure time model, and standard Generalized Hazard Models, using evaluation metrics such as AIC, BIC, HQIC, bias, RMSE, and coverage probability. Among the 500 patients studied, 64% were male, 30% were HIV-positive, 40% were classified as underweight, and 72% experienced right censoring. Both HIV status (log-rank χ² = 12.45, p = 0.0004) and BMI (χ² = 9.87, p = 0.002) were significant predictors of survival. HIV-positive patients faced elevated mortality risk (HR = 2.12), higher BMI was protective (HR = 0.56). While the MGHM model fit (AIC = 1955, BIC = 2015, HQIC = 1980) and simulation performance, achieving the lowest bias (0.02), lowest RMSE (0.10), and highest coverage probability (0.97), confirming its value for modelling complex biomedical survival data.