# Subdistribution hazard ratios: incidence of different events

As I understand it, the subdistribution hazard model gives hazard ratios which tell you the direction of the effect of a covariate on the event occurrence, as defined in the paper below. If the SD hazard ratio for age is 1.2 for event type 1, an increase of a year means the probability of event type 1 (at any particular time) increases.

• "the covariates in [the subdistribution hazard] model can be interpreted as having an effect on the cumulative incidence function or on the probability of events occurring over time."

Now, what I'm massively confused about is that the paper below uses an example where there are 2 event types (cardiovascular and noncardiovascular).

They say the following:

• "we conclude that a 10‐year increase in age is associated with an increase in the incidence of cardiovascular death"

AND

• "similarly, we conclude that a 10‐year increase in age is associated with an increase in the incidence of noncardiovascular death".

How is it possible, with only 2 event types, that the same variable increases the probability of BOTH event types? If one probability goes up, the other has to come down, right? The only thing getting in the way of event 1 occurring is if event 2 occurs first. Of course there's a probability that neither occur at any given moment, but one event occurring would prevent the other from occurring, so how can the same variable have a SD hazard ratio > 1?

Austin PC, Fine JP. Practical recommendations for reporting Fine-Gray model analyses for competing risk data. Stat Med. 2017 10.1002/sim.7501