Comparative Analysis of Parametric Survival Models in HIV Patient Data

This study explores the efficacy of four key parametric survival models-Weibull, Gompertz, Lomax, and Exponential-in assessing mortality risk among HIV-positive patients undergoing antiretroviral therapy (ART). The research examined a retrospective cohort of 2,794 individuals, noting 124 deaths (4.4%) and 2,670 censored cases (95.6%), utilizing time-to-event data. Each model was estimated using maximum likelihood estimation (MLE) and assessed using various model selection criteria, including the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). The Gompertz distribution emerged as the best fit (AIC = 45,943.33; BIC = 45,961.58), followed by the Weibull model, while the Lomax and Exponential models showed higher AIC/BIC values and less stable fits. The optimized parameters for the Gompertz model were determined as l = 0.00316 and a = 1.77x10-6, indicating a gradually increasing hazard rate over time. Model adequacy was further confirmed using Cox-Snell residuals (via Nelson-Aalen cumulative hazard) and Cox-Snell residual Q-Q plots for diagnostic evaluation. The Gompertz model demonstrated the highest coefficient of determination (R2 = 0.9817), followed by the Weibull (R2 = 0.9168), while the Lomax and Exponential models both had lower R2 values (0.5989), underscoring the superior predictive capability of the Gompertz model. Additionally, Cox proportional hazards regression identified significant mortality predictors, such as age at ART initiation (HR = 1.05, p < 0.001), male sex (HR = 1.60, p < 0.01), and last recorded body weight (HR = 0.94, p < 0.001). In contrast, baseline CD4 count and WHO stage were not significant. The model’s concordance index (C = 0.85) indicated high predictive accuracy. This study is motivated by the ongoing variability in HIV survival outcomes despite the extensive use of ART. By comparing these parametric models, the research enhances the understanding of mortality dynamics, aiding clinicians and policymakers in selecting optimal model structures for precise survival prediction, improved ART program monitoring, and informed patient management.These findings highlight significant clinical implications for HIV care, identifying age at ART initiation, male sex, and lower body weight as mortality predictors,indicating where targeted actions are needed. The Gompertz model’s superior performance offers a robust method for the prediction of long-term survival, underlining the need for monitoring comorbidities and the management of treatment-related side effects. With this model, HIV programs will be better positioned to flag high-risk patients, time interventions more appropriately, and allocate resources to reduce preventable deaths among their aging populations.

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