Choice of time scale and its effect on significance of predictors in longitudinal studies

Time-to-event regression is a frequent tool in biomedical research. In clinical trials this time is usually measured from the beginning of the study. The same approach is often adopted in the analysis of longitudinal observational studies. However, in recent years there has appeared literature making a case for the use of the date of birth as a starting point, and thus utilize age as the time-to-event. In this paper, we explore different types of age-scale models and compare them with time-on-study models in terms of the estimated regression coefficients they produce. We consider six proportional hazards regression models that differ in the choice of time scale and in the method of adjusting for the years before the study. By considering the estimating equations of these models as well as numerical simulations we conclude that correct adjustment for the age at entry is crucial in reducing bias of the estimated coefficients. The unadjusted age-scale model is inferior to any of the five other models considered, regardless of their choice of time scale. Additionally, if adjustment for age at entry is made, our analyses show very little to suggest that there exists any practically meaningful difference in the estimated regression coefficients depending on the choice of time scale. These findings are supported by four practical examples from the Framingham Heart Study.