A Comparison between Accelerated Failure Time Models in Analyzing the Survival of Breast Cancer Patients

Background: Female breast cancer (BC) has surpassed lung cancer as the most prevalent reason for cancer-related diagnosis in the world. BC has geographical disparities in the intensity of effect of its associated risk factors on patients’ survival. Several models can be employed to determine the effect of risk factors on patients’ survival. The present study aims at evaluating these models.

Methods: The secondary data of 558 BC patients diagnosed at Korle Bu teaching hospital during 2010-2015 and followed-up (right censored) to the end of 2015 were analysed. The survival status, demographic and tumour characteristics of these patients were determined by event history analysis. To compare various models of survival, Akaike Information Criterion (AIC) , Bayesian Information Criteria (BIC) and Receiver Operation Characteristic (ROC) curve were used. R software was used for data analyses. The data consisted of BC patients in the age range of 13 to 97 years. The dataset was partitioned into training (holding 70%) and validation set (30%).

Results: Based on AIC, BIC and ROC curve values the Gompertz (AIC=2322, BIC=2391) was the best model fit for the survival data. Generalised Gamma (AIC=2378, BIC=2451) and Weibull (AIC=2382, BIC=2452) models were respectively the next alternatives among the nine (9) accelerated failure time (AFT) models considered in our study. Results from the three best fitted AFT models showed that covariates such as Age at diagnosis, Progesterone receptor, Molecular Subtype, Grade, Stage, Metastasis, number of Lymph nodes involved and genetic status were the significant factors that have an effect on the survival time of BC patients in Ghana (P<0.05). The Area under the ROC curve (AUC=0.945) shows an outstanding performance of the Gompertz AFT model to discriminate the true disease status of patients.

Conclusion: Although the Cox proportional hazard model has seen wide usage and remains a robust approach in survival analyses for the past four decades; its proportional hazards assumption is most often violated by some covariates in medical research. Under such violations, AFT models are a strong alternative.