Models for convolution inference

[athowes]

This issue is drawn from conversation with @zsusswein and @SamuelBrand1 at https://github.com/cdcent/cfa-parameter-estimates/issues/22.

Topline

• We could look to add new models to estimate delays more indirectly where components of the overall delay are observed then one needs to combine estimates of delays together
• This would leverage existing infrastructure and good practises we have for estimation of delays with censoring and truncation biases so could be a good fit for the package

Problem background

Let person A be the infector and person B be the infectee in an infector-infectee pair.

• Generation interval (GI): infection of A to infection of B
• Serial interval (SI): time from symptoms of A to symptoms of B
• Incubation period (IP): time from infection to symptoms

Assume that we would like to estimate the GI. However, we do not have direct observations of infection times for person A and person B. Instead we have:

1. Data on time of symptom onset for person A and person B (i.e. data on the SI)
2. Auxiliary data on the IP

Using these two sources of data, one can try to estimate the GI. This supposes that the auxiliary data for the IP can be reasonably applied to estimate the IP of person A and person B. Both sources of data are going to be subject to censoring and truncation biases (like the other data that epidist aims to handle). See Ferretti et al. 2020 for an example of doing this.

Why is could be a good fit for this package

• Builds on existing strengths of package We can already handle censoring and truncation well. This is an extension which builds on our core strengths
• Similar workflow In Ferretti et al. they fit 3 possible delay distribution families, then use AIC to choose a model. We can support this workflow using what I think are best practise tools for estimation and model comparison (brms into tidybayes with loo and all other Stan infra etc.). We could make it easy for a user to run this analysis, setting the family argument, running inference, then using loo
• Support for model structures We have a set-up where you can fit distributional regression models and specify the model on each distributional parameter. This would allow for quite sophisticated modelling approaches. For example, with this auxilitary data, I can imagine that you might want to fit space-time-demographic specific models such that you can reasonably apply it in the transmission chains you have.

Other thoughts

• With the Bayesian framework, I think another natural extension that you'd want is to incorperate probabilites of transmission pairs. Even further to link into phylogenetic analysis. This is probably really hard. You could use brms::make_stancode then start to build towards this without the constraints of brms. I know people are working on this type of thing but don't know the state-of-the-art

Next steps

• It'll become clearer how this might fit in as the package matures I think. Maybe it could be quite easy at some point if we do a good enough job with the infrastructure
• I think this is probably a good research project, so might be a good fit for someone in an academic role. It could also be a project for a student

[seabbs]

@parksw3 I think this is in your wheelhouse and is a good fit

[seabbs]

Models for deconvolution inference

Also is it not convolution

[athowes]

Also is it not convolution

Don't know / mind. Copied from @SamuelBrand1 👼

[seabbs]

I feel like we always want to be talking about forward processes hence trying to avoid "deconvolution".

[SamuelBrand1]

pdf of $X + Y$ is a convolution... so in my head back inferring to get pdf of $X$ from data on $X + Y$ is a deconvolution.

[SamuelBrand1]

From f2f I think @seabbs was a bit radicalised by some actual deconvolution techniques that used to be used... so I'm happy to go with his naming conventions.