Baseline age effect on parameter estimates in Cox models

The Cox proportional hazards model is widely used in time-to-event analysis. Two time scales are used in practice: time-on-study and chronological age. The former is the most frequently used time scale in clinical studies and longitudinal observation studies. However, there is no general consensus about which time scale is the best. It has been asserted that if the cumulative baseline hazard is exponential or if the age-at-entry is independent of the covariate, then the two models are equivalent. We show that neither of these conditions leads to equivalency. Variability in the age-at-entry of individuals in the study causes the models to differ significantly. This is shown both analytically and through a simulation study. Additionally, we show that the time-on-study model is more robust to changes in age-at-entry than the chronological age model.