Date of Award


Document Type

Open Access Thesis




The Norman J. Arnold School of Public Health

First Advisor

Hrishikesh Chakraborty


Left censoring is generally a rare type of censoring in time-to-event data, however there are some fields such as HIV related studies where it commonly occurs. Currently, there is no clear recommendation in the literature on the optimal model and distribution to analyze left-censored data. Recommendations can help researchers apply more accurate models for this type of censoring. This study derives the Parametric Reversed Hazards (PRH) Model for a variety of distributions which may be appropriate for left censored data. The performance of these derived PRH models to analyze HIV viral load data are compared using extensive simulations and a guideline is established for which distribution/s are most appropriate. Each simulation setup is varied by sample size and proportion of censoring to find a consistently high performance distribution. The best distribution is determined using the information criteria: AIC, AICC, HQIC, and CAIC. The South Carolina Enhanced HIV/AIDS Reporting Surveillance System (SC eHARS) data were utilized and a bootstrap study provided further insights towards appropriateness of the distributions in analyzing HIV viral load data. Results from simulation studies point to the Generalized Inverse Weibull distribution to outperform all others across censoring rates and sample sizes. The bootstrap study, however, contradicts this and suggests the Marshal-Olkin distribution to be the superior performer. This disagreement may have resulted from the special heavy tail nature of viral load data that demands further attention. Application of the best performing models on the SC eHARS database revealed important effects explaining trends of viral load over time.

Included in

Biostatistics Commons