A strategy for optimal fitting of multiplicative and additive hazards regression models

Abstract

Background: In survival analysis, data can be modeled using either a multiplicative hazards regression model (such as the Cox model) or an additive hazards regression model (such as Lin’s or Aalen’s model). While several diagnostic tools are available to check the assumptions underpinning each type of model, there is no defined procedure to fit these models optimally. Moreover, the two types of models are rarely combined in survival analysis. Here, we propose a strategy for optimal fitting of multiplicative and additive hazards regression models in survival analysis. Methods: This section details our proposed strategy for optimal fitting of multiplicative and additive hazards regression models, with a focus on the assumptions underpinning each type of model, the diagnostic tools used to check these assumptions, and the steps followed to fit the data. The proposed strategy draws on classical diagnostic tools (Schoenfeld and martingale residuals) and less common tools (pseudo-observations, martingale residual processes, and Arjas plots). Results: The proposed strategy is applied to a dataset of patients with myocardial infarction (TRACE data frame). The effects of 5 covariates (age, sex, diabetes, ventricular fibrillation, and clinical heart failure) on the hazard of death are analyzed using multiplicative and additive hazards regression models. The proposed strategy is shown to fit the data optimally. Conclusions: Survival analysis is improved by using multiplicative and additive hazards regression models together, but specific steps must be followed to fit the data optimally. By providing different measures of the same effect, our proposed strategy allows for better interpretation of the data.