Choice of time-scale in time-to-event analysis: evaluating age-dependent associations

To compare hazard ratios obtained by using time on study (conventional) versus biological age as the time-scale in survival analyses for a known age-dependent association between an exposure and outcome.

We conducted a retrospective cohort study of 9 million people in Ontario, Canada who were followed from 2003 to 2018 to identify incident ischemic stroke using linked administrative health data. Using cause-specific hazards models, we calculated hazard ratios (HR) of ischemic stroke in women compared to men using the two different time scales. By using piecewise estimates and interaction terms, we evaluate the effect of sex on stroke incidence across age groups.

In unadjusted analyses, the reduction in the hazard of ischemic stroke in women compared to men was greater with age as time-scale (HR 0.77; 0.76-0.78) compared to conventional time-scale (HR 0.93; 0.92-0.93); however, the estimates were similar (HR 0.78 with age vs. 0.77 with conventional) in multivariable adjusted analyses. The estimates obtained by two methods across different age groups varied modestly, except in those under 30 years (HR 1.47; 1.19-1.83 with age vs. 1.08; 0.99-1.17 with conventional).

When evaluating age-dependent association between an exposure and outcome, estimates of association vary based on the time-scale used in survival analysis, requiring thoughtful consideration.