When should the current Lockdown finish? How about 3rd April

All the previous charts have simply taken the England in-hospital death rates and plotted them. I have then postulated what the charts might look like if the peaks were reached sooner. Nothing more, nothing less. The following chart depends on two assumptions:

1. The peak of new-infections is 13 days prior to the peak in deaths.

2. The IMR was 0.7% in the spring and 0.4% in the autumn. 

If you want to model all this out properly it would be simply a matter of plotting several charts with different input values and seeing what the charts look like. I have no doubt that part of the expert advice to the government is to run these kinds of numbers and therefore generating a range of potential dates to relax the Lockdown.

(Click on the image to see a bigger version).

There is without a doubt a temporal relationship between new infections and deaths. The exact nature of this relationship is not known for sure but 13 days is a reasonable estimate. It is based simply on the time from initiation of lockdown to peak of deaths (on average). Thus this figure will be reasonable accurate.

The IFR is the Infection Fatality Rate put simply that is the number of people who die as a proportion of the total number who get infected. In principle, it is possible to measure this number directly. In practice that is extremely difficult. In order to do so, you either need to be testing (accurately) the whole population and thus you know the total number of infections (the total number of deaths being a robust figure as well) - or you need a representative cohort that can be followed prospectively to see how many of those who are infected (not necessarily symptomatic) end up dying from Covid-19.

I took the IFR's that I used to generate this chart from here: https://www.cebm.net/covid-19/estimating-the-infection-fatality-ratio-in-england/

This is one of several estimates around. There are lots of caveats with this data. The one thing that is clear (although we'll have to wait for detailed publications on this point) is that,  of those who present with Covid-19, fewer people are dying. We seem to have made several incremental improvements in supportative care such that the mortality from Covid-19 is lower. This is really good news. 

However, in terms of tracking the pandemic, it makes things more complex. If the mortality rate is fixed then using the death rate to track the pandemic is easy. The number of new infections is simply derrived accurately by multiplying the number of deaths by the IFR. If the IFR estimate is wrong it doesn't matter for our purposes here as the key to understanding the pandemic (and how we respond, to this is the timing of the peak. It doesn't directly matter here whether the IFR is 2% or 1% or 0.5% or 0.1% the peak will still correspond to the peak in deaths - just ~ 2 weeks earlier. I.e. if the IFR is constant it changes the numbers but allows east comparison between spring and autumn. If it's not, then an adjustment is needed.

To point of a lockdown is to reduce new infections. (Unless you are able to test everyone or at least a representative cohort then the best way to track new infections is to track back from the death rate. In the Spring of 2020, the only accurate figure we had was the daily death rate). However we know that the IFR is different between the spring and the autumn we just don't know for sure how different.

All I have done here is to use these two figures to estimate infection rates based on the known death rates. The point here is that because the IFR is different the number of infections implied by a death rate of x in May 2020 would be less that the number implied the the same deathrate of x in January 2021.

What I am getting at is that if we assume the relaxation on 30th May 2020 makes sense, then we need to acheive the same level of infection in the community in Feb-April 2021 to relax the current lockdown. The number of daily deaths in Jan '21 appears to be about the same as April '20 but because the IFR is now lower (again this is good news!) it does reflect a much higher infection rate in the community and thus we have further to go to be in a position to relax lockdown.

This is just one chart. There are other ways to derive these estimates and the potential that the estimate of the IFR being wrong is important as that will change the graph and move the target level of ~8000 infections a day to a different point in time and thus change when is the right time to relax the Lockdown.

Two more things need to be said though. Firstly I think ~8000/day is still too high a level to be relaxing. We need to be at a point where the numbers are low enough that Track & Trace can work. So maybe, we need to wait a bit longer?

The other unknown here is the effect of vaccination. The vaccines were passed as safe and effective based on the trials that showed they reduced the risk of people getting ill. That's not the same as saying they stop people from passing the virus on (whilst remaining well themselves). Increasingly we are seeing early evidence that the vaccines are also effective at stopping the spread. As more people are vaccinated, it does become easier to relax restrictions.⁰

Lots of unknowns but based on what we have so far; beginning - middle of April would be my target. If I find more data on IFR estimates which enable me to refine this further and/or fixed estimate on time from infection to death I will modify the chart accordingly.

AFZ

The Night is Dark but the Dawn is Coming...

 Here's an update as to where we are as of 14th February 2021. (See previous posts for details of the methodology).

The horizontal line represents the death rate (and thus by inference a proxy for infection prevalence) when the Lockdown was relaxed in May 2020. This is the earliest it would be safe to relax this Lockdown (I would argue for another week beyond this point). There is one caveat to this that the inferred infection rate may be different in March '21 compared with May '20 as the Case Fatality Rate is lower and thus the death rate corresponds to a higher infection level. Conversely large sections of the population will be vaccinated so it's not clear what the correct point is. However, as always in this pandemic, erring on the side of caution seems very wise.

AFZ

Covid-19 and How Johnson's Government has failed totally and completely.

And thousands have died unnecessarily as a consequence.

 

This post builds on these two previous ones:

http://alienfromzog.blogspot.com/2021/01/covid-data-january-2021.html

http://alienfromzog.blogspot.com/2020/09/covid-19-and-why-timing-of-lockdown.html

In the previous posts I have laid out the caveats that exist around these charts. This is a simple method of estimating the effect of the timings of key decisions but 1) it is in line with much more complex modelling (reference in first post) and 2) it is intuitive and easy to understand: When you lockdown, around 2 weeks later you will see death rates start to fall. Because the growth rates are exponential a week's difference in timing makes a huge difference in the total number of deaths.

In this post I am going to lay out three scenarios. None of which support the government's managment of this crisis. They have failed. Many thousands more people died than needed to. That is the inescapable conclusion of all this. 

Firstly, I will lay out the effect in the Autumn of not learning the lessons of the Spring. This was the major thrust of my post in September - by refusing to acknowledge the mistakes of the past - the government doomed us to the consequences of making the same mistakes again. That is exactly what happened.

Secondly I want to show the effect of acting sooner in the spring - there was a point in mid-march when it was inescapable that prompt and drastic action was needed. It is probably unfair to blame the government for what went before then (in terms of the Lockdown decision-making, although not in terms of PPE planning or other decisions but I am not going to write about that here).

And thirdly I will look at a 'perfect' response. The point here is that the government has claimed - and continues to do so - that the UK government has done an amazing job responding to this 'unprecedented crisis.' In this section I will hold the government to their own standard - this is what was possible if things had been done right from the very beginning. 

For me, the second scenario is, I think, fair criticism. Any government can make honest mistakes and that is a good arugment for using my second model rather than the third as a true comparitor with the sad reality we are living. However, when the government claims to be 'World-beating' or 'proud' of their response, then the honest mistake arugment runs into trouble. The on-going issue is an absolute and total refusal by the government to admit mistakes were made. Without accepting that mistakes were made, it is impossible to learn from them. And the consequence of that is measured in thousands of lives.

Covid Data - January 2021

In September I wrote about the timings of lockdowns. That is this post here. In that post I discussed the various measures of mortality and what they mean. Put simply, the best measure of the overall effect of the pandemic is the excess mortality and the best way of tracking the pandemic in real time is with the daily in-hospital deaths published by NHS England here.

When I wrote in September, I was simply exploring the first wave from the Spring. The assumption that underlies all of this is that the lockdowns work. There is a lot of international data to support this assumption; and it is very reproducible. Basically the peak of deaths occurs around 2 weeks after lockdowns are instituted. Hence the arugment is very simple - if you change the time of the lockdown you change the time when the peak is reached. Because of exponetional growth of the virus, moving this peak has very large effects on the overall death toll.

Here is the figures plotted from 1st March 2020 to 1st March 2021:

This graph shows the daily in-hospital deaths in England for each individual day. The blue line is the daily deaths. The red line is a seven-day rolling average. The reasons for using that figure is that is smooths out the natural daily variation. The shaded areas show the three national lockdowns. The darker shading is the time from initiation of lockdown to the peak (the ligher shade being the rest of the lockdown).

It is important to note that by using death figures the peak is behind the peak of infections. (I discussed perviously why this is the best measure but it is important to realise this time delay is implicit in the data).

One thing that is very noteworthy here is the timing from lockdown to peak of deaths. The first lockdown was 23rd March; the peak of deaths was 8th April (16 days later). The second lockdown was on 5th November; the peak was 25th November (20 days). Third lockdown, 5th January; peak 19th January - 15 days.

There is a lot of work to do studying these; it is known (although the data is imcomplete) that survival rates have improved in the second wave as we have better treatment protocols from lessons learnt from the first wave. It is also true that the accelaration phase of the waves was slower in the second and third waves than in the first. In the first, the number of deaths per day increased from 159 on the day of lockdown to 900 at the peak in 16 days; that an increase in the death rate of 46/day. In the second lockdown the rise was 5.4/day and in the third 16/day. These differences may be simply a feature of the phase of the exponetial rise when the lockdowns were instituted or may reflect that prior to the 2nd and 3rd lockdowns, various restrictions were still in place. Or there may be a different explanation such as better medical care.

Anyway, the whole point of my previous post was that earlier lockdowns have big effects. One of the implications of this chart is simply that the relaxation of the lockdown from 5th November after only 4 weeks was far too early. But I also want to ask the question, what would have happened if the Autumn lock-down had been two weeks earlier? 

Here's what that looks like:

As I discussed before, the only assumtion I am making here is that the lockdown would cause cases to fall at the same time interval; i.e. if lockdown occurred two weeks earlier, the peak would be two weeks earlier. 

The pink shading is the actual 4 week lockdown that we had. The green shaded area is a lockdown started on 22nd October and running until the death rate was the same as when the spring lockdown was relaxed.

The dotted lines show the expected death rates going forward, if the pandemic follows the same sort of trajectory as it has done previously. I will post in the future, a comparison between these predicted figures as the real ones.

So if a lockdown had been instituted on 22nd October 2020 and it had been as effective as expected what effect would that have of the death rates?

Well: Currently the number of in-hospital deaths in England is around 69,000 (upto 24th January 2021). If the lockdown had been instituted on 22nd October and worked as this graph suggests then that total would be 41,000. That's 40% fewer deaths.

The official UK deathtoll from Covid-19 is currently 106,000. As I discussed before, the excess death figure is the best one to use but if we simply take that figure at reduce it by 40% then we are talking about OVER 42,0000 fewer deaths if we had acted sooner in the Autumn.

In my next post I will discuss a bit more the issues around politics and decision-making and how I think this mistake in the Autumn a gross error of government with the cost being massively high.

AFZ