Applying Conventional and Saturated Generalized Gamma Distributions in Parametric Survival Analysis of Breast Cancer

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearlyall of the most commonly used distributions including the exponential, Weibull and log normal. A saturatedversion of the model allows covariates having effects through all the parameters of survival time distribution.Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates.
Methods: We fitted both the conventional GG model and the saturated form for each of its members includingthe Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selectedparameter distribution with log logistic distribution which is a famous distribution in survival analysis thatis not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). Allmodels were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer inBC during 1990-1999 and followed to 2010.
Results: In both conventional and saturated parametric models,the lognormal was the best candidate among the GG family members; also, the lognormal fitted better thanlog-logistic distribution. By the conventional GG model, the variables “surgery”, “radiotherapy”, “hormonetherapy”, “erposneg” and interaction between “hormone therapy” and “erposneg” are significant. In the AFTmodel, we estimated the relative time for these variables. By the saturated GG model, similar significant variablesare selected. Estimating the relative times in different percentiles of extended model illustrate the pattern inwhich the relative survival time change during the time.
Conclusions: The advantage of using the generalizedgamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormaldistributions. Alternatively, the generalized F family of distributions might be considered, of which thegeneralized gamma distribution is a member and also includes the commonly used log-logistic distribution.