Generalized Gamma Distributions in Parametric Breast Cancer Survival Analysis

When a parametric survival analysis is considered, we assume that the survival time (or a function of it) follows a given theoretical distribution (or model) and has an explicit relationship with the covariates (Lee and Wang, 2003). Survival time models that can be linearized by taking logs are called ‘accelerated failure time’ (AFT) models. In AFT models the effect of covariates is multiplicative over time (Hosmer and Lemeshow, 1989). The acceleration factor is a ratio of survival times corresponding to any fixed value of S(t).The acceleration factor describes the “stretching out” or contraction of survival functions when comparing one group to another (Kleinbaum and Klein, 2005). The underlying AFT assumption, for comparing two levels of covariates, is that the ratio of times to any fixed value of S(t) = q is constant for any probability q (Kleinbaum and Klein, 2005). The application of a constant relative time implies the assumption that the treatment only has an effect on one