My research team suggested we use in a Cox regression the "lost disease-free years" as outcome measures. It works like this: we have the median age at which the general population gets cardiovascular disease, say 75 years. In my sample, I subtract the age that every subject got cardiovascular disease from that age; e.g. if somebody got cardiovascular disease at age 60, their lost disease-free years is 15. IF somebody got cardiovascular disease at age 81, their lost disease-free years is -6 (they "gained" disease-free years compared to the general population).
However, this is not a typical time-to-event variable to be modelled using Cox regression. We want a model in which our risk estimate is positive for positive lost disease-free years and increases with their absolute value; the earlier you get the disease before the population median, the higher the risk. Conversely, it should be negative for negative lost disease-years (protection effect) proportionally to their absolute values (-10 is more protective than -5).
How would you model this?
