2.2.6 Time-varying nature of covariates

In survival analysis, particularly when using the Cox hazards model, it is common to encounter time-varying covariates. These are covariates whose values may change over time for each individual firm in the study. These covariates change over time and may influence the hazard rate at different time points.

To understand better the time-varying nature of covariates, we will use Aalen’s (1989) additive regression method. This is a statistical approach used for analysing survival data, particularly when covariate effects may change over time. It is based on the additive model for the cumulative hazard function.

Aalen’s model is particularly useful in situations where the effects of covariates on survival may vary over time and can provide a more nuanced understanding of these relationships. The figures below show how the covariates change over time (Age).

_{Aalen, O.O. (1989). A linear regression model for the analysis of life times, Statistics in Medicine, 8(8), 907-925. https://doi.org/10.1002/sim.4780080803}