Cox proportional hazards models with left truncation and time-varying coefficient: Application of age at event as outcome in cohort studies

When analyzing time-to-event cohort data, two different ways of choosing a time scale have been discussed in the literature: time-on-study or age at onset of disease. One advantage of choosing the latter is interpretability of the hazard ratio as a function of age. To handle the analysis of age at onset in a principled manner, we present an analysis of the Cox Proportional Hazards model with time-varying coefficient for left-truncated and right-censored data. In the analysis of Northern Manhattan Study (NOMAS) with age at onset of stroke as outcome, we demonstrate that well-established risk factors may be important only around a certain age span and less established risk factors can have a strong effect in a certain age span.