Modeling Right-skewed Heavy-tail Right-censored Survival Data with Application to HIV Viral Load

Right-skewed heavy-tailed survival data commonly arise in health-related studies, and the probability distributions proposed to model such survival data are not adequately described in the literature. Although a wide selection of survival distributions is available, applied researchers often face the challenge of choosing a right model for analyzing survival data with these special features in distributional shape. In this article, we evaluated some of the most popular parametric families of distributions as well as nonparametric approaches to model right-censored data using several goodness of fit measures. We carried out extensive simulation studies with different censoring rates to compare the performance of survival models using sixteen different parametric families and the Bernstein polynomials-based nonparametric model to analyze right-skewed heavy-tailed survival data. We also illustrated the use of both parametric and nonparametric approaches to model observed viral load (VL) data from HIV/AIDS patients where we defined the survival outcome as transitioning from an undetectable VL status to a detectable VL status over time. In addition, we used bootstrap samples drawn from the observed VL data and evaluated the estimation properties of all sixteen parametric distributions and the Bernstein polynomial-based method. Finally, results from simulation, observed VL data, and the bootstrap samples were compared using four different divergence-based information criteria. Overall, among the parametric families, the power generalized Weibull model was found to provide adequate fit under several scenarios (censoring rates, choice of information criterion, etc.). The other two families to be competitive with power generalized Weibull were the Burr XII and generalized Gamma distributions.

Duke Scholars

Author Hrishikesh Chakraborty Biostatistics & Bioinformatics, Division of Biostatistics