Handling negative delays between reference and report

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Porting the discussion started here.

@samabbott wrote:

There is some interest in linking events where the report happens before the reference. An example of this is test positivity and symptom onset.

Potentially this could be handled by changing the indexing of the delay distribution (i.e add a negative delay_min which defaults to 0).

However, I am not sure this really strictly makes sense, especially when considering partially observed data. How do you know if something observed in real-time will eventually convert to a reference? If you don’t (which seems likely) then I assume you can’t use this information and hence this has no real-time benefit? Or you have to make a censoring adjustment of some kind.

Regardless there is demand so worth thinking about or at least thinking about documenting a solution that doesn’t require model changes (i.e updating the user on the definition of reference and report).

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Note some work on this includes the Epiline (GitHub - BDI-pathogens/EpiLine: Bayesian Modelling in Epidemiology Case Line Lists) package from Robert Hinch at Oxford BDI.

They make use of a Johnson SU distribution (which has negative support) to handle this and model delays jointly but independently from case counts (i.e with counts as a convolution based on the delay but with delays treated as truncated but known).

I am not sure this can be ported as is into the epinowcast framework but is worth checking out.