Performance and Prediction for Varying Survival Time Scales

The Cox proportional hazards model is widely used for analyzing associations between risk factors and occurrences of events. One of the essential requirements of defining Cox proportional hazards model is the choice of a unique and well-defined time scale. Two time scales are generally used in epidemiological studies: time-on-study and chronological age. The former is the most frequently used time scale, both in clinical studies and longitudinal observation studies. However, there is no general consensus on which time scale is the most appropriate for a given question or study. In this article, we address the question of robustness of the results using one time scale when the other is actually the correct one. We use three criteria to measure the performances of these models through simulations: magnitude of the bias of the regression coefficients, mean square errors, and the measure of overall predictive discrimination of the models. We conclude that the time-on-study models are more robust to misspecification of the underlying time scale.