Abstract
Semiparametric hazard function regression models are among the well studied risk models in survival analysis. The Cox proportional hazards model has been a popular choice in modelling data from epidemiological settings. The Cox-Aalen model is one of the tools for handling the problem of non-proportional effects in the Cox model. We show an application on Piedmont cancer registry data. We initially fit standard Cox model and with the help of the score process we detect the violation of the proportionality assumption. Covariates and risk factors that, on the basis of clinical reasoning, best model baseline hazard are then moved into the additive part of the Cox-Aalen model. Multiplicative effects results are consistent with those of the Cox model whereas only the Cox-Aalen model fully represents the timevarying effect of tumour size.
Highlights
In survival analysis, regression models are employed to explain the occurrence of events over a period of time taking various explanatory variables into consideration
The semiparametric Cox (1972) proportional regression model is the cornerstone of modern survival analysis and even if many alternatives exist in statistical literature, like the additive
In this paper we present an application of the Cox-Aalen model on a breast cancer cohort identified by the population-based Piedmont Cancer Registry
Summary
Regression models are employed to explain the occurrence of events over a period of time taking various explanatory variables into consideration. Some covariates may initially decrease the hazard rate, but the long-term effect might be adverse as that of treatment in malignant lymphoma Both Cox and Aalen models were extended in several directions. Multiplying the additive and multiplicative hazards models, Scheike and Zhang (2002) studied the model which will be referred to as Cox-Aalen. The prognosis for breast cancer is relatively good, with 5-year relative survival exceeding 75% in most countries of Western Europe (80% in Italy) (see Sant et al, 2003) For this cancer site, covariates measured at diagnosis may eventually change their influence on survival during the follow-up period as a consequence of treatments (such as surgery, chemotherapy and radiation).
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