# On some nonsense from Mishra et al

Warning: this is a draft, but since nobody reads my blog it shouldn’t matter.

In which a group at Imperial College try to find out how many people would have died in the UK if it had policies like Sweden.

Look at the following figure illustrating cumulative covid-19 deaths in different countries, shamelessly lifted from a recent paper appearing in Nature Scientific reports1

As you can see, Denmark, Sweden, and the UK had widely varying outcomes. They also had widely varying policies, so it’s natural to ask how much these are to blame. Luckily, epidemiologists have developed extremely precise tools to quantify this effect, the results of which are shown below:

The basic mathematical idea behind this approach is that obviously Sweden would have the same number of cumulative deaths as the other countries would have had if they had just used the same polices. Case closed.

This approach is used in Mishra et al., whose abstract states

We use two approaches to evaluate counterfactuals which transpose the transmission profile from one country onto another, in each country’s first wave from 13th March (when stringent interventions began) until 1st July 2020. UK mortality would have approximately doubled had Swedish policy been adopted, while Swedish mortality would have more than halved had Sweden adopted UK or Danish strategies.

Ok so Mishra et al. don’t actually just swap the labels, as far as I can tell they do something on the level of2 “take derivatives first, then swap labels, and then integrate again” but wrapped into the language of an SIR model. Here’s the relevant part of their paper:

If you’re not laughing/crying at the absurdity of actually publishing this kind of analysis, some more direct quotes:

We estimate that if Denmark had adopted Swedish policies, and introduced them at the same stage of its epidemic, mortality would have been between three and four (Table 1) times higher, and thus Denmark would have experienced similar per-capita mortality to Sweden

If Sweden had adopted Danish policies, both the absolute and relative approaches imply that there would have been approximately one fifth as many deaths.

The counterfactuals therefore demonstrate that small changes in the timing or effectiveness of intervention policies can lead to large changes in the resulting cumulative death toll

One fact I’ve noticed a few times from this group at Imperial College is the fact that they ascribe almost all outcomes to government policy when anybody who is following this at all should see that it isn’t even clear whether government policy is important. Thus, the article is full of the word “policy” whereas an astute reader should notice that none of the actual analysis looks at policies, it’s just comparing counts of infected/dead people, policy never actual enters the mix. This enters via phrasing like

the slightly lower effectiveness of Sweden’s policies

or

Denmark may have had marginally more effective and timely policies.

or

so that we might learn how best to control future waves, or indeed future pandemics

In fact, we might as well replace “policy” with weather everywher in the article and be no worse off for it. Or “population density”, or “trust in science” or “astrological favour”. Eventually do pay lip-service to non-policy factors also being of importance deep down in the discussion

Third, national-level Rt estimates average over a high level of geographic, social and demographic heterogeneity in transmission within each country. It is unclear how such heterogeneities between countries would determine the relative success of a country’s COVID-19 response, as opposed to differences in policy. This can be circumvented to some extent by interpreting each counterfactual scenario as an exchange of population behaviour as well as policy, although it is still true that not every country would respond in exactly the same way to each intervention.

so it all boils down to “if Sweden were the UK, it would have cases like the UK modulo initial values” which would – though not uncontroversial – be a better take than anything I’ve seen in their paper. Then again, this this was published in Nature Scientific reports, which is nice for all the grad students invovled as they now have a paper published.

Footnotes:

1. Not to be confused with Nature itself, twitter tells me Scieentific Reports is Nature‘s trash-basket but I have no opinion on whether or not this true apart from the fact that this particular paper belongs in the trash-basket.
2. Yes, I know this isn’t exactly what they do, but the analogy is pretty good though they wrap everything into a Bayesian mess.