Friday, 12 June 2020

Looking past the headline statistics

Referring to his track and trace strategy in the press briefing yesterday, the English Health Minister said that the numbers of people and contacts being contacted and advised to self-isolate had exceeded his expectations. The only possible conclusion from that is that his expectations must have been extremely low to start with. Statistics can be spun to show different pictures, of course, and the claim that 85% of contacts had been traced certainly sounds impressive. But the obvious question to any mathematician, is ‘85% of what?’. It turns out that it means 85% of the contacts of the subset of confirmed cases which the tracers were able to contact; and the number of confirmed cases is itself a subset of the total number of infections.
To put some numbers on that: according to the government’s own figures, there were 8,117 confirmed cases during the week in question, although everyone knows that the actual number of cases is considerably higher. None of us knows the actual total, although the Office for National Statistics estimates that it is around 23,000. Of the 8,117, the government’s figures claim that 5,407 (or around 67%) were traced and asked for details of their contacts and it is 85% of those contacts which forms the basis of the headline ‘success’ rate. Assuming that all those infected had roughly the same number of contacts, and infected roughly the same number of people (both reasonable assumptions), then the proportion of people contacted out of the total number of people potentially infected was only around 20%. (85% of 5,400/23,000). Looking at it another way, if it takes 25,000 contact tracers to pursue the details of 5,400 people, that’s equivalent to almost one week's work for 5 tracers per confirmed case. If it were possible to identify all 23,000 cases (a job which would require a significant workforce and expenditure in itself), then it would need perhaps 100,000 contact tracers rather than the 25,000 currently in post to talk to them, establish a contact list, and contact just 85% of the people on that list. Improving on that figure of 85% adds more to the total.
As far as I’m aware, we don’t have comparable figures available for Wales at present – I hope that the government will make them available, although the deficiencies exposed by the English figures may create an understandable desire to avoid revealing the same failings. We do know that the number of confirmed cases is currently around 5-600 per week, or about 6-8% of the total in England. If the performance level of the two teams is roughly the same, then even matching the current extremely poor English performance would require more like 1,800-2,000 people.  Whilst the more cautious approach to lockdown should see the number of infections in Wales reducing faster, it’s still a large disparity.
In fairness, it’s early days and two things could and should happen as we move forward: the number of infections should decline further (although the rush to ease the lockdown in England may make that less likely there), and the productivity of the team should improve (5 tracers for one week per confirmed case certainly looks excessive, based solely on ‘gut feel’). However, even allowing for both of those factors, it appears that both governments have significantly underestimated the scale and complexity of the task which needs to be undertaken if they are serious about using track and trace as the main control mechanism. And they’re both about three months late in setting up a system the need for which was entirely foreseeable.

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