Modelling multiple time-scales with flexible parametric survival models

Background: There are situations when we need to model multiple time-scales in survival analysis. A usual approach in this setting would involve fitting Cox or Poisson models to a stacked time-split dataset. However, this leads to large datasets and can be computationally intensive, especially if interest lies in displaying how the hazard rate or survival change along multiple time-scales continuously. Methods: We propose to use flexible parametric survival models on the log hazard scale as an alternative method when modelling data with multiple time-scales. By rewriting one of the time-scales as a function of the other time-scale, there is no need to split the data into categories of time along one or both of the time-scales. Result: Through case-studies we demonstrate the usefulness of this method and provide examples of graphical representations of estimated hazard rates and survival proportions. The model gives nearly identical results to using a Poisson model, without requiring time-splitting. Conclusion: Flexible parametric survival models are a powerful tool for modelling multiple time-scales. This method does not require splitting the data into small time-intervals, and therefore saves time, helps avoid technological limitations and reduces room for error.