epiforecasts / eval-germany-sp-nowcasting Goto Github PK

Currently, a negative binomial error model is used with a single overdispersion parameter. This is problematic because data with little truncation (and hence well known) is treated equally with data that is highly truncated (and hence poorly known). To some degree this uncertainty is modelled in the truncation distribution but having a single overdispersion parameter does allow additional model flexibility for which there is not much justification.

A potential option, that has been partially explored with quite poor results, would be to have an overdispersion parameter for each day of truncation. Alternatively, the simplest solution may be to assume a Poisson error model.

The effect of the single overdispersion can be seen in the posterior prediction plots where the model is quite uncertain about data with very little truncation even though these data should be very well known.

Currently, the model as implemented assumes a log-normal distribution for the reporting delay prior to applying report day effects. It would be sensible to explore other the non-parametric variant of this model where report day effects are not assumed to be log normal. This would also help us understand the benefit/disadvantages of these approaches in a comparable context. This is related to epinowcast#

This project started as an extension of a very simple model. It may make sense to include an evaluation of this model.

A daily random effects model cannot recover simulated data. Initially, I thought this was a bug but further thinking has led me to the conclusion that when the model has sufficient flexibility for the target date it will arrive at a posterior for the truncation distribution that assumes no truncation (as this gives the best fit to the observed truncated data).

This is an extreme example of this issue but potentially other flexible models in which the latest data is given to much weight will also show this issue and therefore perform poorly.

The workflow proposed here should be fully reproducible and generic. Given this, it would make sense to explore the models as defined here (or a related set) on another case study where nowcasting is required. An example of this is reporting of cases, deaths, and hospitalisations in the UK.

Models that are hierarchical across age groups, and particularly flexible ones, appear to perform poorly in hold out evaluation. This is somewhat surprising as models that are independent across age groups but otherwise flexible perform very well (which is not perhaps what would be expected if overfitting was the root cause). This may be attributable to a range of factors. To start exploring this potential options are:

• Check in sample performance to understand possible overfitting
• Check model formulation and model backend in epinowcast for issues.
• Visualise and explore the observations in case
• Potentially explore a hierarchical structure across locations rather than age groups to see if location differences are the key factor.

The decomposition into a hospitalisation and probability vector model used here is not the only possible nowcasting approach. A very sensible approach, though one that has slightly less nice theoretical properties is to model hospitalisations and delays jointly in a regression framework (with the outcome being new cases by time and delay). Summing over these then gives the nowcast.

Comparing these two approaches in a context where the models are otherwise the same would make it easier to understand their differences.

Similarly, the model evaluated here can also be phrased as a non-linear regression problem, for example in brms. It would be interesting to explore this implementation as it would allow a much large suite of models to be formulated though at the potential cost of some efficiency.