The Reflected-Shifted-Truncated-Gamma Distribution for Negatively Skewed Survival Data with Application to Pediatric Nephrotic Syndrome
Date of Award
Open Access Dissertation
Epidemiology and Biostatistics
The Norman J. Arnold School of Public Health
Negatively skewed survival data arise occasionally in public health fields and in statistical research. Standard distributions such as the exponential, generalized F, generalized gamma, Gompertz, log-logistic, lognormal, Rayleigh, and Weibull distributions are not always well suited to this data. The primary goal of this dissertation is to find a viable alternative for modeling negatively skewed survival data such as the time to first remission for pediatric patients with frequently relapsing or steroid dependent nephrotic syndrome.
We begin with a brief introduction of survival analysis and the nature of pediatric nephrotic syndrome. A meta-analysis on atopy and pediatric nephrotic syndrome using worldwide studies is performed. We introduce the reflected-shifted-truncated-gamma (RSTG) distribution as an alternative model for survival data whose event times arise from a negatively skewed distribution. Explicit expressions are provided for the mean, variance, hazard function, survival function and quantile function of the RSTG distribution. A simulation study verifies the consistency of maximum likelihood estimates of model parameters. Using maximum likelihood methods, we compare the RSTG distribution to the exponential, generalized F, generalized gamma, Gompertz, log-logistic, lognormal, Rayleigh, and Weibull distributions for modeling negatively skewed complete (uncensored) data, right-censored data and interval-censored data using well-known data sets. We then apply the RSTG distribution to pediatric nephrotic syndrome data from the Clinical Data Warehouse from Health Sciences of South Carolina and from the Robert Wood Johnson Medical School in New Jersey using covariate adjusted accelerated failure time (AFT) models with and without frailty. We include a brief example of the RSTG distribution applied to a 1972 study on diabetic retinopathy.
Our research shows that the RSTG distribution is superior to the eight aforementioned distributions for modeling negatively skewed survival data. The results from applications of this distribution and future goals are discussed.
Waymyers, S. D.(2016). The Reflected-Shifted-Truncated-Gamma Distribution for Negatively Skewed Survival Data with Application to Pediatric Nephrotic Syndrome. (Doctoral dissertation). Retrieved from https://scholarcommons.sc.edu/etd/3736