TITLE:
A Statistical Model with Non-Linear Effects and Non-Proportional Hazards for Breast Cancer Survival Analysis
AUTHORS:
Muditha Perera, Chris Tsokos
KEYWORDS:
Breast Cancer, Cox Model, Non-Linear Effects, Non-Proportional Hazards
JOURNAL NAME:
Advances in Breast Cancer Research,
Vol.7 No.1,
January
29,
2018
ABSTRACT: The Cox proportional hazard model is being used
extensively in oncology in studying the relationship between survival times and
prognostic factors. The main question that needs to be addressed with respect
to the applicability of the Cox PH model is whether the proportional hazard
assumption is met. Failure to justify the subject assumption will lead to
misleading results. In addition, identifying the correct functional form of the
continuous covariates is an important aspect in the development of a Cox
proportional hazard model. The purpose of this study is to develop an extended
Cox regression model for breast cancer survival data which takes
non-proportional hazards and non-linear effects that exist in prognostic
factors into consideration. Non-proportional hazards and non-linear effects are
detected using methods based on residuals. An extended Cox model with
non-linear effects and time-varying effects
is proposed to adjust the Cox proportional hazard model. Age and tumor
size were found to have nonlinear effects. Progesterone receptor assay status
and age violated the proportional hazard assumption in the Cox model. Quadratic
effect of age and progesterone receptor assay status had hazard ratio that
changes with time. We have introduced a statistical model to overcome the
presence of the proportional hazard assumption violation for the Cox
proportional hazard model for breast cancer data. The proposed extended model
considers the time varying nature of the hazard ratio and non-linear effects of the covariates. Our improved Cox model gives a
better insight on the hazard rates associated with the breast cancer
risk factors.