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

François Lefebvre,Roch Giorgi

doi:10.1186/s12874-021-01273-2

Abstract

BackgroundIn 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.MethodsThis 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).ResultsThe 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.ConclusionsSurvival 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.

Highlights

In survival analysis, data can be modeled using either a multiplicative hazards regression model or an additive hazards regression model
The aim of this study is to propose a strategy for the optimal fitting of multiplicative and additive hazards regression models in survival analysis
The Methods section begins by detailing our 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

Summary

Introduction

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). We propose a strategy for optimal fitting of multiplicative and additive hazards regression models in survival analysis. The most commonly used models for this purpose focus directly on the hazard function and Lefebvre and Giorgi BMC Medical Research Methodology (2021) 21:100 statistical software. This model is based on two assumptions that must be satisfied to ensure correct fitting of the data, and, correct interpretation of covariate effects. One typically uses an extended Cox model with time-varying effects when the first assumption is not met [3, 4] and an extended Cox model with nonlog-linear effects when the second assumption is not respected [4]

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Methods

Results

Conclusion