Tuesday, March 23, 2021

History in the (re)making?

One year on and there's been a slew of articles revisiting the events of the past year. I was going to ask what has prompted this little flurry, but it's obviously the anniversary thing. With increasing pressure for a public inquiry, it seems that some of the key players have been trying to position themselves favourably, so let's have a look at what's been written, versus what the contemporaneous documentation actually says. SAGE minutes can be found here, I think (I downloaded the relevant docs a while back).

The first article I noticed was Laura Kuenssberg's “Inside Story”. She “talked to more than 20 of the people who made the life and death decisions on Covid”. The relevant passage that I am interested in concerns the decision making around mid-March:

“13 March, the government's Scientific Advisory Group for Emergencies (Sage) committee concluded the virus was spreading faster than thought.

But it was Downing Street "modellers in the building", according to one current official, who pored again over the numbers, and realised the timetable that had only just been announced was likely to result in disaster.

The next morning, a small group of key staff got together. Simple graphs were drawn on a whiteboard and the prime minister was confronted with the stark prediction that the plan he had just announced would result in the NHS collapsing under the sheer number of cases.

Several of those present tell me that was the moment Mr Johnson realised the urgency - that the official assumptions about the speed of the spread of this new disease had been wrong.


On 16 March, the public were told to stop all unnecessary social contact and to work at home if possible.


For many inside government, the pace of change that week was staggering - but others remain frustrated the government machine, in their view, had failed to move quickly enough.”

The narrative being presented here of ponderous government is significantly misleading.

The govt claimed at the time to be paying close attention to the scientific advice from SAGE, and the specific change to SAGE's assessment on the 13th March was not that the disease was spreading any more rapidly, but merely that the number of infections was higher than previously thought (due to greater importation from abroad). This is a key distinction that anyone numerate should be able to grasp readily. To quote from SAGE minutes on the 13th:

“Owing to a 5-7 day lag in data provision for modelling, SAGE now believes there are more cases in the UK than SAGE previously expected at this point, and we may therefore be further ahead on the epidemic curve, but the UK remains on broadly the same epidemic trajectory and time to peak. 
SAGE was unanimous that measures seeking to completely suppress spread of Covid- 19 will cause a second peak.”
Changing the estimate of the number of cases just brings the peak forward by a few days. Even a factor of 2 is only a single doubling time which they thought to be about 5-7 days at that time. Changing the estimate of the growth rate could (and in fact did) change the timetable and urgency much more significantly, but this didn't happen for another week and a half.

It is not clear who “the modellers in the building” refers to in Kuenssberg's piece, but they are clearly not SAGE. Maybe Cummings had run a few numbers on a spreadsheet but since SAGE was supposed to be an assembly of world-leading experts, it would hardly be appropriate to discard their analyses in favour of his. For that matter, I had also blogged that the mitigation plan was likely to overwhelm the NHS (a conclusion that I reached around the 9th March based on some very simple calculations) but I wouldn't expect Johnson to listen to me either. SAGE minutes are very clear that they still believed the doubling rate to be 5-7 days right up to the 18th March and had described any overload on the NHS as being some way off (albeit a looming problem that would need addressing at some time in the future). They were unanimously (see above) opposed to suppression at this point.

On the 16th, the SAGE meeting changed its advice somewhat and suggested that some social distancing measures (but not school closures) should be implemented promptly:

“SAGE advises that there is clear evidence to support additional social distancing measures be introduced as soon as possible.

SAGE will further review at its next meeting whether, in the light of new data, school closures may also be required to prevent NHS capacity being exceeded.”
Clearly there was some increased urgency here but NOT any indication that the NHS was under immediate threat, in direct contradiction to Kuenssberg's unattributed claim above that “the prime minister was confronted with the stark prediction that the plan he had just announced would result in the NHS collapsing under the sheer number of cases.” I'm not saying it is impossible that anyone said such a thing, but if they did, they were an isolated voice and certainly not representative of SAGE as a whole.

Immediately following the SAGE meeting on the 16th, the Govt did of course request that people avoid all unnecessary social contact. Admittedly, this instruction had neither legal force nor economic support at that point but SAGE was obviously reasonably satisfied with the adequacy of this plan as can be seen from their minutes of the 18th (at which time they also recommended school closures):
“SAGE advises that the measures already announced should have a significant effect, provided compliance rates are good and in line with the assumptions. Additional measures will be needed if compliance rates are low.”
So it was only in the case of poor compliance that additional measures would be required.

There was no SAGE meeting between 18th and 23rd, which was unfortunate in the circumstances (21-22 being a weekend). On the 23rd, SAGE finally realised that they had got the R number wrong and that as a result the doubling time was much shorter than had been previously believed, making the situation quite desperate. Specifically, the SAGE meeting of the 23rd concluded: “Case numbers could exceed NHS capacity within the next 10 days on the current trajectory” and this statement must be understood in the context of the immediately preceding 20th March SPI-M meeting which noted both: “Any measures enacted would take 2-3 weeks to have an impact on ICU admissions” and also: “If the higher reproduction number is representative of the longer term, then it is likely that additional measures will be required to bring it below one”.

Thus SAGE's underestimate of the R number didn't just mean that the epidemic was coming faster and harder than previously thought: another consequence is that actions that would have been adequate for R=2.4, might not be adequate for R=3. It is quite understandable that this caused alarm within SAGE, but it only happened on the 23rd.

The Govt imposed a legally-enforceable lockdown with much more far-reaching restrictions immediately that evening (23rd March).

Moving on to the next article, in the Guardian, a hagiography of Patrick Vallance:

“But it now seems clear that Boris Johnson, and his advisers, were slow to heed Vallance’s early advice.

Before the 16 March press conference, Vallance chaired a meeting of the Scientific Advisory Group for Emergencies (Sage) in which a collection of experts had advised that the first lockdown should begin immediately.

Johnson did not announce the unprecedented national lockdown until a week later on 23 March in a primetime TV address to the nation.”

This is simply not true as documented above. SAGE asked for relatively modest action around the 16-18th, and the Govt responded promptly. SAGE explicitly assessed on the 18th that the actions were probably adequate and it was only on the 23rd when they realised that they had got the doubling time wrong, that they suddenly realised they had a much larger and more urgent problem on their hands. Vallance also got this wrong in his appearance before the House of Commons Select Committee on Science and Technology

Most recently, a podcast on the Guardian consisting of an interview of Neil Ferguson. He points very firmly to the data about higher case numbers due to greater importation being what drove the accelerated decision making in mid-March (NB this view is very different from Vallance who very emphatically linked the change in policy advice to the revision of the estimated doubling time - it is simply not possible for both Ferguson and Vallance to both be correct about this). Ferguson mentions this being discussed in the “first weekend in March” which I'm sure must be a simple slip as this would be 7-8th March whereas on the 10th and even 13th SAGE seems pretty sanguine about the situation and does not suggest any need to take immediate action. Assuming he meant the 14-15th March instead, this is far more consistent with SAGE as the minutes of the 16th do certainly suggest some some action should be taken in the light of the new data:

“The science suggests additional social distancing measures should be introduced as soon as possible.”

When asked specifically (at 11m20 in the podcast) “were scientists telling ministers to go earlier?” Ferguson firstly points again to the surveillance data as escalating the decision making process, and then coyly says it was entirely in the Govt's hands as to what actions they took. He could have said, but chose not to, that the Govt followed SAGE's advice promptly and to the letter. And the interviewer didn't pursue the point. While the improved surveillance data undoubtedly played a role in the process, the urgent advice for the most stringent controls only came on the 23rd as a result of the revised estimate of doubling time. You only have to glance at the SAGE minutes to see that they were not shy about offering policy advice throughout the outbreak.

At 16m40 onwards the interviewer says, with reference to the situation in September after schools reopened: 

“...once again the advice from scientists was to lock down. But that advice was not heeded. Did that delay once again lead to a higher death rate than we might have seen?”

Without getting into the September story here, any delayed response from the Govt (which I don't dispute was evident in the autumn) could only “once again” have resulted in a higher death rate if there had also been a delayed response to advice to lock down in March. Which there was not, according to the evidence I have outlined.

Monday, March 01, 2021

BlueSkiesResearch.org.uk: Escape velocity

There is currently lot of debate on how and when we lift restrictions, and the risks of this. There are several unknowns that may affect the outcome. I have extended the model in a couple of simple ways, firstly by including a vaccination effect which both immunises people, and substantially reduces the fatality rate of those who do get ill, and also by including a loss of immunity over time which is potentially important for longer simulations. The magnitudes of these effects seem highly uncertain, I’ve just made what seems like plausible guesstimates. I use a vaccination rate of 0.5% per day which is probably in the right ballpark though my implementation is extremely simplistic (NB this is the rate at which people move from the vulnerable to the immune category, so it directly accounts for the imperfect performance of the vaccine itself). As well as this, I’m assuming the fatality rate for those infected drops down to 0.3% as vaccination progresses through the most vulnerable groups, since we’ve heard so many good things about vaccination preventing serious illness even in those who do get ill. This value must also account for the proportion of victims that have not been vaccinated at all, so it’s really a bit of a guess but the right answer has to be significantly lower than the original fatality rate. The loss of immunity in this model occurs on a 1 year time scale, which in practice due to model structure means 1/365 = 0.27% of the immune population return to the vulnerable state each day. I don’t claim these numbers are correct, I merely hope that they are not wrong by a factor of more than about 2. In the long term in the absence of illness, the balance between vaccination and loss of immunity loss would lead to about 1/3rd of the population being vulnerable and 2/3rds being immune at any given time. This is just about enough to permanently suppress the disease (assuming R0=3), or at least keep it at a very low level.

The model simulates the historical trajectory rather well and also matches the ONS and REACT data sets, as I’ve shown previously, so I think it’s broadly reasonable. The recent announcements amount to an opening of schools on the 8th March, and then a subsequent reopening of wider society over the following weeks and months. In the simulations I’m about to present, I’m testing the proposition that we can open up society back to a near-normal situation more quickly. So after bumping the R number up on the 8th March I then increase it again more substantially, putting the underlying R0 number up to 2.5 in the ensemble mean, close to (but still lower than) the value it took at the start of last year, with the intention being to simulate a return to near-normal conditions but with the assumption that some people will still tend to be a bit on the cautious side. So this is a much more ambitious plan than the Govt is aiming for. I’m really just having a look to see what the model does under this fairly severe test. Here is the graph of case numbers when I bump the R number up at the end of April:

And here is the equivalent for deaths, which also shows how the R number rises:

So there is another wave of sorts, but not a terrible one compared to what we’ve seen. In many simulations the death toll does not go over 100 per day though it does go on a long time. Sorry for the messy annotations on the plots, I can’t be bothered adjusting the text position as the run length changes.

If we bring the opening forward to the end of March, it’s significantly worse, due to lower vaccination coverage at that point:

Here the daily deaths goes well over 100 for most simulations and can reach 1000 in the worse cases. On the other hand, if we put off the opening up for another couple of months to the end of July, the picture is very much better, both for cases:

and deaths:

While there are still a few ensemble members generating 100 deaths per day, the median is down at 1, implying a substantial probability that the disease is basically suppressed at that point.

I have to emphasise the large number of simplifications and guesstimates in this modelling. It does however suggest that an over-rapid opening is a significant risk and there are likely benefits to hanging on a bit longer than some might like in order that more people can be vaccinated. My results seems broadly in line with the more sophisticated modelling that was in the media a few days ago. To be honest it’s not far from what you would get out of a back-of-the-envelope calculation based on numbers that are thought to be immune vs vulnerable and the R0 number you expect to arise from social mixing, but for better or worse a full model calculation is probably a bit more convincing.

While the Govt plan seems broadly reasonable to me, there are still substantial uncertainties in how things will play out and it is vitally important that the govt should pay attention to the data and be prepared to shift the proposed dates in the light of evidence that accrues over the coming weeks. Unfortunately history suggests this behaviour is unlikely to occur, but we can live in hope.