Parametric Regression Model Based on Reversed Hazard Rate: An Application to left censored heavy tailed HIV Viral Load Data

The parametric survival model with Weibull distribution can be used to model a wide range of practical lifetime data. While there have been several studies comparing the fit of various distributions to right-censored and interval censored data, there are no recommendations in the literature on optimal distributions to use for left-censored heavy-tailed data. Parametric Reverse Hazards (PRH) has gained considerable attention from time-to-event data researchers for its excellent properties and appropriateness to analyzing left-censored survival data. To analyze left-censored with heavy-tailed data, we derived the PRH model for a variety of distributions including the Exponential, Log-normal, Inverse Gaussian, Log-logistic, Gompertz–Makeham, Gamma, Generalized Gamma, Inverse Gamma, Generalized Inverse Gamma, Weibull, Inverse Weibull, Generalized Inverse Weibull, Modified Weibull, Flexible Weibull, Power Generalized Weibull, and Marshal–Olkin distributions. Extensive statistical simulations were used to assess the performance of the derived PRH models and compare these to establish a guideline for which distribution/s would “best” fit for left-censored heavy-tailed data. We then applied the best performing model to the South Carolina Enhanced HIV/AIDS Reporting Surveillance System data to explain the effects of different demographic, social, and treatment factors on patients’ viral load transition from detectable-to-undetectable levels.