On Estimating Survival and Hazard Ratios Using One Time-Scale When Cohort Data Have Multiple Time-Scales: A Simulation Study

Abstract Background: When estimating survival functions and hazard ratios during theanalysis of cohort data, we often choose one time-scale, such as time-on-study, asthe primary time-scale, and include a xed covariate, such as age at entry, in themodel. However, we rarely consider the possibility of simultaneous effects ofmultiple time-scales on the hazard function. Methods: In a simulation study, within the framework of exible parametricmodels, we investigate whether relying on one time-scale and xed covariate asproxy for the second time-scale is sucient in capturing the true survivalfunctions and hazard ratios when there are actually two underlying time-scales. Result: We demonstrate that the one-time-scale survival models appeared toapproximate well the survival proportions, however, large bias was observed in thelog hazard ratios if the covariate of interest had interactions with the secondtime-scale or with both time-scales. Conclusion: We recommend to exercise caution and encourage tting modelswith multiple time-scales if it is suspected that the cohort data have underlyingnon-proportional hazards on the second time-scale or both time-scales.