Estimating and presenting hazard ratios and absolute risks from a Cox model with complex nonlinear interactions

Abstract

Abstract Interaction analysis is a critical component of clinical and public health research and represents a key topic in precision health and medicine. In applied settings, however, interaction assessment is usually limited to the test of a product term in a regression model and to the presentation of results stratified by levels of additional covariates. Stratification of results often relies on categorizing or making linearity assumptions for continuous covariates, with substantial loss of precision and of relevant information. In time-to-event analysis, moreover, interaction assessment is often limited to the multiplicative hazard scale by inclusion of a product term in a Cox regression model, disregarding the clinically relevant information that is captured by the absolute risk scale. In this paper we present a user-friendly procedure, based on the prediction of individual absolute risks from the Cox model, for the estimation and presentation of interactive effects on both the multiplicative and additive scales in survival analysis. We describe how to flexibly incorporate interactions with continuous covariates, which potentially operate in a nonlinear fashion, provide software for replicating our procedure, and discuss different approaches to deriving CIs. The presented approach will allow clinical and public health researchers to assess complex relationships between multiple covariates as they relate to a clinical endpoint, and to provide a more intuitive and precise depiction of the results in applied research papers focusing on interaction and effect stratification.