mrc-ide / EpiEstim

A tool to estimate time varying instantaneous reproduction number during epidemics
https://mrc-ide.github.io/EpiEstim
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Combine backimputation_window & aggregated incidence #168

Open abriz97 opened 2 months ago

abriz97 commented 2 months ago

Hi @annecori and @rebeccanash.

In my latest PR, I added backimputation as a solution to early over-estimation of the reproduction number. However, my implementation doesn't cover all cases of interest, for example it is currently not supported together with incidence disaggregation as in @rebeccanash 's paper. It could be interesting to explore how to best combine the two methods.

abriz97 commented 2 months ago

I have a suggestion to approch the combination of the methods.

If I remember correctly, and based on Fig.1, the gist of Rebecca's paper involved combining EM techniquest to a local assumptions of exponential growth to disaggregate incidence cases and subsequently fit EpiEstim on the inferred time series.

To think about a specific example, let me consider a week-day disaggregation problem . Let me denote with $wi$ the cases in the i-th week, and the disaggregated daily cases with $d{i, j}$ for week $i$ and day $j$ of the week.

The method computes weekly estimate $R^_{w}$, then imputes cases within the weekly window. I believe it would make sense to use that same estimate for the first week $R^_{w=1}$ (translated to a growth rate), to then perform backimputation when calculating daily cases.