Application of additive hazards models for analyzing survival of breast cancer patients

Survival rates for breast cancer (BC) are often based on the outcomes of this disease. The aim of this study was to compare the performance of three survival models, namely Cox regression, Aalen's, and Lin and Ying's additive hazards (AH) models for identifying the prognostic factors regarding the survival time of BC patients.

This study was a historical cohort study which used 1025 females' medical records that underwent modified radical mastectomy or breast saving. These patients were admitted to Besat and Chamran Hospitals, Tehran, Iran, during 2010-2015 and followed until 2017. The Aalen's and Lin and Ying's AH models and also traditional Cox model were applied for analysis of time to death of BC patients using R 3.5.1 software.

In Aalen's and also Lin and Ying's AH models, age at diagnosis, history of disease, number of lymph nodes, metastasis, hormonal therapy, and evacuation lymph nodes were prognostic factors for the survival of BC patients (P < 0.05). In addition, in the Lin and Ying's AH model tumor size (P = 0.048) was also identified as a significant factor. According to Aalen's plot, metastasis, age at diagnosis, and number of lymph nodes had a time-varying effect on survival time. These variables had a different slope as the times go on.

AH model may yield new insights in prognostic studies of survival time of patients with BC over time. Because of the positive slope of estimated cumulative regression function in Aalen's plot, metastasis, higher age at diagnosis, and high number of lymph nodes are important factors in reducing the survival BC, and then based on these factors, the therapists should consider a special therapeutic protocol for BC patients.