Potential bias introduced by not including multiple time-scales in survival analysis: a simulation study

When analyzing cohort data, we rarely consider potential simultaneous effects of multiple time-scales on estimated survival proportions and hazard ratios. Instead, often, only one time-scale, such as time-on-study or attained age, is taken as the main time-scale and the other time-scale(s) included in the model as time-fixed covariate(s). In this simulation study, we investigate the potential bias in estimated survival proportions and hazard ratios by not modeling multiple time-scales. We simulate data with two time-scales, under various scenarios, and a binary covariate as the exposure of interest. Flexible parametric models with one time-scale were fitted to the simulated data, including the exposure variable of interest and the other time-scale as a fixed covariate. For many of our simulated scenarios, the models with one time-scale showed small bias for the survival proportions. Bias in the log hazard ratios (for the covariate of interest) was observed when there were non-proportional hazards on the second time-scale. If one is modeling only one time-scale it is advisable to include non-proportional hazards and interactions with the time-scale. Exploration of approaches to modeling multiple time-scales is outside the scope of this study.