Limitation: perfect observation of primary events

[seabbs]

In our current simulation setup we are assuming that we have perfect observation of primary events (apart from daily censoring). In reality this would not be the case and the delay from primary to secondary events would not be exactly observed.

This is perfectly fine as a simplification but we need to be aware that it biases us towards concluding that approaches that condition on primary observations (vs approaches that jointly model) are better (as easier to estimate and with no observation error they have no downsides.

For now I'd suggest we do nothing about this apart from discuss it as a limitation. The only thing I think we could consider doing is including a joint model (i.e epinowcast as I don't think we can easily implant in brms) in our comparison to show as this will help our discussion of the trade-offs.

[seabbs]

This relates to our discussion in #24 and elsewhere. I think we need to discuss this in the draft and perhaps use it to motivate links between the various ways of estimating delays.

Note that in some sense a censoring window for the primary event is an adjustment for this. I still haven't quite worked out the settings where there might be a problem and so this is perhaps(?) a fairly minor point.

[parksw3]

I think we discussed on our last call, but I never wrote anything here (I should've).

I think we have to be more careful about talking about observation error. When we model epidemic trajectories, we include observation error in population-level incidence largely because there's under-reporting in both primary and secondary event incidence and mismatch between two cohorts. If we had individual-level data, we wouldn't have to do this because we can just model each delay separately without using a population-level model. I kind of feel like the observation error is a feature of population-level data in this sense.

More to be discussed...

[seabbs]

I'm still not entirely sure I agree though I do agree that it is less of an issue. There is still some sense in which the date we see has observation error, under-reporting, censoring etc we don't know about and don't adjust for. In my view that unmeasured structure is what we would want an observation error model for.

That being said as we reduce the amount of things that are unmeasured (as we do here) we are travelling towards a world where we don't need additional observation error.

[parksw3]

the date we see has observation error

This is a good point. Not sure why I didn't think about this (to be honest, I can't remember what I was thinking 2 weeks ago). I think this is something we can bring up when we talk about implicit censoring and back in discussion.

unmeasured structure is what we would want an observation error model for.

Good point.

we are travelling towards a world where we don't need additional observation error.

To me, this is a philosophically interesting point because we still need "observation error" to fit the model even if we simulate a model without observation error. For example, if we simulate a deterministic SIR ODE model and want to fit the SIR model to the simulation, we still need some kind of an error term to fit the model... weird, isn't it? practically not useful or relevant but just an interesting thought..