A Novel Three Parameter Modified Cox Frailty Model For Noncompeting Risk Patients with Breast Cancer Malignality

Abstract

The typical Cox proportional hazard (PH) model will provide erroneous estimates if the PH assumption is broken, which is quite prevalent in medical research. We have developed an expanded version of the basic Cox Model that includes a time-lag function and a frailty parameter to account for time-variant covariates, heterogeneity and unobserved components in this study. Secondary data from 558 Breast cancer (BC) patients diagnosed at Korle Bu teaching hospital were analyzed. The dataset was divided into two parts: training (which had 70% of the data) and validation (30 percent). Tests for the functional form of continuous covariates and outliers were included in the model diagnostics. The Shoenfeld residual test and the graphical test served as the foundation for the PH assumption test. In a noncompeting risk environment, the PH assumption was violated by progesteron receptor status, molecular subtype, and tumor grade at diagnosis. Frailty component was revealed to be a significant contributor to the developed model, accounting for around 15% of all fatalities attributable to heterogeneity and unobserved variables. Our model outperformed current models such as the Exponential AFT model, stratified Cox (interaction) model, the standard Cox PH Model and Park and Qiu (2017) model in terms of AIC, BIC, likelihood ratio test and area under the ROC curve. Breast cancer survival in Ghana is influenced by stage at diagnosis, metastatic status, lymph node involvement, and HER2 overexpression, according to our model. Among other findings, BC patients who develop metastasis are 41.264 times more likely to die from the disease than individuals who do not develop metastasis. Individuals with higher stages of BC (III and IV) are 6.89 times more likely to die from the disease than patients with lower stages (I and II). To improve BC care and prognosis, it was suggested that medical officers and diagnosticians take into account the identified significant determinants regulating survival as well as the estimated risk and survival probability.

Keywords: Breast Cancer, Frailty, Heterogeneity, Cox Proportional Hazard Model, Stratified Cox (interaction), Extended Cox.