Comparison of procedures to assess non-linear and time-varying effects in multivariable models for survival data

The focus of many medical applications is to model the impact of several factors on time to an event. A standard approach for such analyses is the Cox proportional hazards model. It assumes that the factors act linearly on the log hazard function (linearity assumption) and that their effects are constant over time (proportional hazards (PH) assumption). Variable selection is often required to specify a more parsimonious model aiming to include only variables with an influence on the outcome. As follow-up increases the effect of a variable often gets weaker, which means that it varies in time. However, spurious time-varying effects may also be introduced by mismodelling other parts of the multivariable model, such as omission of an important covariate or an incorrect functional form of a continuous covariate. These issues interact. To check whether the effect of a variable varies in time several tests for non-PH have been proposed. However, they are not sufficient to derive a model, as appropriate modelling of the shape of time-varying effects is required. In three examples we will compare five recently published strategies to assess whether and how the effects of covariates from a multivariable model vary in time. For practical use we will give some recommendations.