Breast Cancer Survival Analysis: Applying the Generalized Gamma Distribution under Different Conditions of the Proportional Hazards and Accelerated Failure Time Assumptions

Background: the goal of this study is to extend the applications ofparametric survival models so that they include cases in which acceleratedfailure time (aft) assumption is not satisfied, and examine parametricand semiparametric models under different proportional hazards (ph)and aft assumptions.methods: the data for 12,531 women diagnosed with breast cancer inbritish columbia, canada, during 1990–1999 were divided into eightgroups according to patients’ ages and stage of disease, and each groupwas assumed to have different aft and ph assumptions. for parametricmodels, we fitted the saturated generalized gamma (gg) distribution,and compared this with the conventional aft model. using a likelihoodratio statistic, both models were compared to the simpler formsincluding the weibull and lognormal. for semiparametric models, eithercox’s ph model or stratified cox model was fitted according to the phassumption and tested using schoenfeld residuals. the gg family wascompared to the log-logistic model using akaike information criterion(aic) and baysian information criterion (bic).results: when ph and aft assumptions were satisfied, semiparametricand parametric models both provided valid descriptions of breastcancer patient survival. when ph assumption was not satisfied butaft condition held, the parametric models performed better than thestratified cox model. when neither the ph nor the aft assumptionswere met, the log normal distribution provided a reasonable fit.conclusions: when both the ph and aft assumptions are satisfied,the parametric and semiparametric models provide complementaryinformation. when ph assumption is not satisfied, the parametricmodels should be considered, whether the aft assumption is met ornot.