Clarify when time-varying CFR applies

[sbfnk]

It might be good to clarify (in the vignette / docs) when the time-varying CFR applies as it affects the interpretation. If it's due to e.g. a new variant or cases moving into different age groups this would apply at the time at which cases appear. If it's e.g. due to hospital capacity issues it's more likely to apply at the time of death. If I understand the methods correctly in cfr_time_varying the application is at the time of death.

[pratikunterwegs]

Thanks @sbfnk, happy to add these clarifications, but I must admit I haven't really understood the distinction - could you point me to a reference where I could learn more about this?

[sbfnk]

I'm not aware of a reference so I'll try to express myself more clearly: Say there is a delay distribution from case to death $p_i$, the probability of the delay from case to outcome (death or recovery) being $i$ time units.

The question I'm asking is: out of the two time points considered (case vs. death), is your risk of dying determined at the time that you become a case (e.g., because of your age) or at the time at which you die or not (e.g., because there is no space in intensive care unit where your life otherwise would have been saved).

In the first case (risk determined at the risk of becoming a case):
$$D_t = \sum_{i=0}^T C_{t-i} p_i f_{t-i}$$
where $D_t$ is the number of deaths at time $t$, $C_{t-i}$ is the number of cases at time $t-i$, and $f_{t-i}$ is the CFR at time $t-i$.

In the second case (risk determined at the risk of dying) this becomes
$$D_t = f_t \sum_{i=0}^T C_{t-i} p_i$$

If the CFR does not change this makes no difference, but if it does then these are different.

[pratikunterwegs]

Thanks for explaining @sbfnk - I think the way the vignettes are currently written the risk determination is at the point of becoming a case, as we reference new variants and vaccination. I can clarify this in the vignette; would it make a difference to the time-varying CFR calculation we have currently implemented?

[pratikunterwegs]

After discussion, the CFR method as implemented applies at the time of death. When there's a change in variants or a change in vaccination coverage, we would expect the CFR method to reflect the (implicit) weighted average for infections by each variant, or for vaccinated/non-vaccinated individuals. I can add this to the docs and vignettes if this makes sense.

[pratikunterwegs]

Just thinking about this a bit more, in the vignette we currently mention factors that change risk at the time of infection/case reporting. But as health systems are overwhelmed, we could potentially see changes driven by that which apply at the time of death as well. So I suppose it's a bit of both, although much more focused on the former - is that a suitable way of explaining this in the vignettes?