Saturday, April 17, 2021

Modelling the effect of lockdowns

Covid and the lockdown effect: a look at the evidence | The Spectator - Simon Wood: 

April 14, 2021 - "What forces Covid into reverse? To many, the obvious answer is lockdown.... It’s often said that all else failed. The Prime Minister said on Tuesday that lockdown, far more than vaccines, explains the fall in hospitalisations, deaths and infections. But how sure are we that only lockdown caused these falls — in the first, second and third wave? Or were other interventions, plus people’s spontaneous reactions to rising cases, enough to get R below one?...

"Let’s start with the events of last March. Imperial’s Neil Ferguson, whose modelling inspired the government’s decision to go into lockdown in March, told MPs in June that ‘had we introduced lockdown measures a week earlier, we would have reduced the final death toll by at least a half’. Last December, a paper called Report 41 was published by Imperial College along these lines. It said: 'Among control measures implemented, only national lockdown brought the reproduction number [the "R number"] below 1 consistently. Introduced one week earlier, it could have reduced first wave deaths from 36,700 to 15,700'....

"Ferguson’s Imperial team had developed a simple model of the spread of Covid-19 and fitted it to data on the daily deaths ... to tell them how, when and by how much the R number changed.... [T]he Imperial team’s model assumed that they knew when and how R was changing. They only needed the data to tell them by how much it changed. I repeated Imperial’s analysis, but with one important difference: the data were used to also determine when and how R changed. The Imperial model then gives a very different result. It suggests that R was already below 1 before lockdown. If that is the case then, rather than surging, new infections were already in decline.... I also used a different approach, bypassing the Imperial model altogether, to directly estimate the daily number of new fatal infections from the data on daily deaths and fatal disease duration. This direct approach also strongly suggests that infections were in substantial decline before lockdown, and that R was already below one. The graph below shows what this second approach found around the time of the first lockdown.

"The same approach can be used again at the second and third lockdowns. Before the second lockdown it was argued that the tier system was ineffective and that cases were surging. But the reconstructions suggest that fatal infections — and by implication Covid infections generally — were not surging. They were in decline having peaked earlier. The third peak is between Christmas and New Year.... It is possibly worth noting that although the estimated fatal infections were in retreat before each lockdown, the daily deaths were surging each time that a lockdown was called. The psychological pressure that this puts on the decision makers is obvious....

"This brings us back to Imperial’s Report 41.... With professor Ernst Wit of Universit√† della Svizzera Italiana in Switzerland, I repeated the Report 41 analysis as reported in a pre-print (a not yet peer-reviewed study) on medRxiv. The Report 41 assumptions around the first lockdown are even more restrictive than in Imperial’s earlier study, and we again replaced them with an approach that allows the data to tell us when and how R changed, as well as by how much. Because far more data are involved this time, the scope for our own assumptions to bias our results is lessened, but we nonetheless took an approach designed to minimise such problems.

"As we went through Report 41 we also noticed some unusual things: Imperial’s model was using key input measures that were shorter than the times given in the published papers cited as sources.

  • The time Imperial used from infection to symptoms (the ‘incubation period’). It’s stated as 4.6 days, citing Lauer et al. But that study says ‘the estimated mean incubation period was 5.5 days.’ A careful subsequent analysis by McAloon et al combining several studies, including Lauer et al, gives 5.8 days.
  • The time Imperial gave from symptoms to hospitalisation. Imperial give a mean of 4 days, citing Docherty et al. But that paper gives 4 days as the median time. For the model they use, the corresponding mean days from onset to hospital is 6, not 4.

These two changes subtract three days from the model time between Covid infection and hospitalisation, compared to the values given in the cited literature. This is not a small issue if so much is to be made about every day mattering. Two other points from Imperial’s Report 41 were troubling:

  • The model structure forced the average time from infection to infection to be quite a bit longer than the times reported in the literature.
  • The model-fitting appeared to be set up in a way that attributed unusually low weight to the actual data, relative to assumptions built into the model.

"We tried to correct each of these four issues. The resulting model and analysis are very far from perfect, but we think that the results can give a somewhat more accurate picture of what the data imply than the original. Below is the picture we got for infections, by region and in total, around the time of first lockdown. Again the results imply that infections were in retreat before lockdown was called....

"So even taking the most negative view of our work, and the most positive view of the Imperial study, it is hard to see the latter as providing robust evidence for lockdown having caused R to drop below 1. Let alone as providing a reasonable basis on which to compute the number of lives that an earlier lockdown might have saved.  Even if our study’s assumptions are no better than Imperial’s, just different (which we would dispute), we have clearly shown that the Report 41 results are too strongly dependent on the model assumptions to provide reasonable evidence for the life-saving potential of earlier lockdowns claimed in the press."

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