Modeling Negatively Skewed Survival Data in Accelerated Failure Time and Correlated Frailty Models

Negatively skewed survival data arise in public health and in statistical research. Commonly used distributions are not always well suited to this data. The reflected-shifted-truncated gamma (RSTG) distribution is effective in modeling negatively skewed survival data. In this paper, we examine the efficacy of the RSTG distribution in accelerated failure time (AFT) models with and without frailty and in the correlated frailty model. We derive the model functions and use maximum likelihood estimation and an expectation-maximization algorithm to estimate model parameters. We use simulated negatively skewed data to demonstrate the efficacy of the RSTG distribution as compared to the exponential, generalized F, generalized gamma, Gompertz, log-logistic, lognormal, Rayleigh, and Weibull distributions in the AFT model without frailty. Two real world negatively skewed data sets are used to demonstrate the flexibility and usefulness of the RSTG AFT model with frailty, the RSTG AFT model without frailty and the RSTG correlated frailty model. Model fit is assessed with information theoretic criteria and deviance residual plots.