Category: General

I have had some feedback from readers on mortality rate and why I have paid so little attention to it so far.

Why is the stated mortality rate around the world so different?

UK and Italy are on the high side with mortality rate around 13%.  On the low side, Germany at 3% and Norway at 2.3%.  The US is in between at 5%.  There are various issues with data collection but the biggest factor is how widespread testing is.

In relatively overwhelmed countries e.g. Italy and the UK there has been a limited roll out of testing, with a high proportion of those tested because they have symptoms already.  In the extreme case, if we only tested people for COVID who had already died with COVID symptoms, then it would have a mortality rate of approaching 100%.   In the UK a quarter of people tested test positive, which means we are far from seeing a random sample.

The countries with much high testing rates will give a much better idea of the actual mortality rate.  Norway has only 5% of tests come back positive and their mortality rate is much lower.  It does not necessarily mean that Norwegian people have better outcomes, it is just that they are better at catching the cases where people have COVID but are either asymptomatic or recover by themselves at home.

What is the mortality rate really?

Getting a narrow range on this estimate is not at all easy.  We really need random sampling and tracking of outcomes.  This has recently begun in Germany, but it will be a long time before we get decent results.  While it is known there is some underreporting in the number of deaths e.g. care homes, it is also clear that underreporting of cases from incomplete sampling/too few tests is a far bigger distortion.  This means that the mortality rate will be lower than the reported mortality rates at the moment.

The lowest estimate from a good source that I have come across is from the Diamond Princess cruise ship; adjusting for the average age of the passengers gives an estimate of 0.66%
https://www.eurosurveillance.org/content/10.2807/1560-7917.ES.2020.25.12.2000256

I have used 1% as my base case in my modelling, but 0.5% would also seem very reasonable.

Could the mortality rate be much lower?

There are some scientists arguing that the mortality rate is far lower.  Their argument assumes the virus was spreading earlier than we thought and it must be far more rapidly transmitted.   It follows that lots of us have been infected without knowing it and therefore the mortality rate is extremely low.

A recent highly publicised study in Santa Clara used antibodies tests to find that 50 times as many people were infected than we thought with 50 out of 3300 testing positive for antibodies associated with COVID.  https://www.nature.com/articles/d41586-020-01095-0

I find it very hard to reconcile these theories with the known data.  Countries that have done large scale testing such as Iceland have not found the large numbers of positives that would be consistent.

If the virus had infected 50 times as many people as we thought, then virtually all cases must not show any symptoms.  This is not consistent with other reliable studies.  Studies with a controlled set of patients such as Diamond Princess do show that perhaps half of cases are asymptomatic, which is why the mortality rate of people infected could be below 1%.  There is no evidence that a large majority of infected people are asymptomatic.

False positives

The more likely explanation for the Santa Clara result are false positives which occur in all medical tests.  The test for HIV is also an antibodies test i.e. we do not detect the virus directly but we can detect the antibodies which are associated with our immune response to the virus.  If 3300 people were tested for HIV using a rapid test, we would EXPECT to see 50 positive tests even if NO ONE has HIV.  This is because the test has a 1.5% false positive rate.

Can a treatment breakthrough reduce the mortality rate?

Another argument for a lower mortality rate is that we will develop treatments for the disease.  The stock market soared on “news” that Gilead had developed a treatment https://www.thetimes.co.uk/article/coronavirus-patients-given-us-trial-drug-are-off-ventilators-in-a-day-pb3jnzf3k

I see two problems with this

1. It is overwhelmingly likely that it is not true. I have written before at length about the misuse of statistics and this is a classic example.  Every possible drug is being given to patients with a view to treating Covid, but these are not the controlled trials that would confirm effectiveness.  By random chance, some outcomes will be better than others.  If I dressed all patients in different coloured gowns, I would find that those wearing perhaps pink gowns had better outcomes than those wearing red ones.  Swapping all gowns to be pink would not then lead to lower mortality rates. Until we have some proper testing, I will assume this is a nonsense story.
   
   
2. Even if it turns out to be true, this treatment only works for people on ventilators. It is only relevant for bringing down the mortality rate in a scenario where everyone has access to a ventilator i.e. the number of people infected is small. It does not change at all the need for lockdown or have any major economic implications as the story currently reads.  For a treatment to have an impact on lockdown policy, it would need to have a material impact on patients to stop them requiring hospitalisation.

Could the mortality rate be much higher?

If treatment makes a large difference to the outcomes, here there could be an important skew to the mortality rate higher.  Currently, the countries with the lowest mortality rates have, in common, a low number of cases and excellent access to healthcare.  There is good evidence so far that early treatment and access to oxygen makes a big difference to the outcomes.  If a patient is admitted late to ICU, then the prognosis is very poor.  With Boris Johnson for example, early intervention with oxygen led to a positive outcome.  For many this is not the case and if our health systems are overwhelmed then very few will get this level of treatment and the mortality rate could be far higher. My fear is that if this virus gets out of control, then the mortality rate will be far higher than we have observed so far with total deaths far higher even than the current high estimates.

If it is much lower what difference does this make to lockdown policy?

The reason that I have focused on R0 rather than mortality rate is that it is far more important for policy decisions.  A lower mortality rate is relevant in two cases:

1. We aim for herd immunity.
   This was the initial idea for the UK and requires a lower mortality rate that we have estimated, and thus the number of people already infected to be far higher.  With current estimates, we only get herd immunity after perhaps 500,000 people die in the UK, which dramatically swamps the system.  The other big problem with this is there is only limited evidence on the level of immunity we get after recovering from COVID.  Looking at our response to other respiratory viruses, the current best guess is that it provides a decent level of protection for only a year or two.
   
   
2. We let people die
   The idea here is that “losses” to the virus are acceptably low in comparison to the economic damage we otherwise take.  This is the common argument of the right and, particularly in the US.  I will leave it up to each reader’s own ethics on how they would make that trade-off.  But I will reiterate that we currently have no evidence that the mortality rate would be lower than 0.5% i.e. 1 million US deaths, and good reason to think it would be a multiple of that with this many cases and thus no medical treatment available.

 

 

 

 

 

 

Many countries are starting to move towards relaxing their lockdowns.  Across Europe, some restrictions have been lifted or dates to do so announced for the next few weeks.  In the US, despite starting lockdowns much later, there has been some relaxation already, including Florida beaches and shops in Texas.

This is as I expected, countries reached peak daily death rate around 3 weeks after the imposition of strict lockdowns whilst the clamour to end them builds.  We now see a lot of optimistic headlines and articles about the worst being over now, and how people are impatient to restart their lives.

Unfortunately, my read of the recent data is not so optimistic.

A key metric to look at right now is how rapidly the virus spreads during the lockdown.  We have initial data from the UK whereas Spain, Germany and Italy are 2 weeks further along.  In the last post, I estimated R0 of 0.8 during lockdown but this could be optimistic.  For example, in Italy the ICU cases have dropped from 4,000 to 2,800 in the last 2 weeks which has been hailed as a “dramatic drop” – actually a drop of 30% in 2 weeks implies a lockdown R0 of 0.85.  In the UK we are past the peak in daily deaths, but actual numbers remain close to it.  This may be caused by data issues, for example we know registering covid deaths can have a delay of a few days.  In Germany Merkel stated her estimate of R0 is 0.7 under lockdown, but every country will be different.

I will stick to my estimate of R0 under lockdown as 0.8 and now I want to make some projections based on relaxing lockdown (R0 rises) at different dates.  If we consider the R0 of the period when we were first trying social distancing (hand washing etc) to be 2 and given that it is currently 0.8, then it seems plausible that, upon some return to more normal behaviours, we can easily reach R0 of 1.3.  I will use this figure as post-lockdown R0.

Projection –  if UK ends the current lockdown on May 8^th and R0 rises to 1.3 thereafter

Given the lag between infections and deaths, the initial 3 weeks after 8th May will look like things are under control – we ended lockdown and daily deaths keep falling!
A low of 164 daily deaths is reached on 25^th May – but with the R0 at 1.3 (as discussed it could easily be higher) the deaths quickly rise again and breach the 1,000 level by 29th June.

What if we attempt another lockdown when death rate starts to rise?

Projection –  UK ends the current lockdown on May 3^rd and then restarts in early June

Let’s say we relax lockdown for the month of May and restart it on 11^th June, with R0 returning to 0.8.  We peak again at around 1,000 deaths per day, similar to early April.  This is a theoretical cycle that is sometimes mentioned in the press, we alternate 1 month of lockdown and 1 month in a slightly less severe lockdown. We would never get close to returning to the “hand washing” level of freedom and of course, we should not assume the NHS can keep functioning at this level of crisis indefinitely, given that most routine operations and scans have been put on hold.

What if we delay the end of lockdown until the start of June?

Projection – UK ends the current lockdown in early June

The low point of deaths and infections is pushed out and is much lower, with a low of 54 per day on June 19^th.  However the power of compounding is relentless and we soar back into high infection rates by mid-summer.

What can we do?

This analysis is not very encouraging. I was hoping that R0 under lockdown would be far lower than we have seen, which would mean both that the rate of infections and deaths would fall more quickly, giving more headroom to relax the restrictions while still keeping the R0 close to 1.

This suggests that there is no easy way forward and that we are not on a path to progressively relaxing lockdown restrictions.  If a minor relaxation in lockdown leads to R0 of 1.3, then we merely have a short period until the pressure on health services increases and we return to more severe lockdown.

Are there reasons to be optimistic?

Yes.  This is not hopeless, but the key is to focus on R0.
One reason for optimism is my lack of access to accurate and detailed data.  Smart people, mainly in Germany, are doing high quality scientific work to understand the transmission of COVID-19.  If we better understand the transmission, then we will not need blunt tools such as lockdowns to reduce R0.  The rate of transmission, R0, is an average statistic; some areas will still have very high levels and so can be targeted accordingly.  I am sure we could find many current, restricted activities are less actually risky in terms of spreading and can be allowed to grow. Finding out what is driving the R0 to persist so high during lockdown is critical.

In my first post, I mentioned how sensitive the model is to small changes in R0, this is also reason for optimism.  If I run the model with R0 under lockdown at 0.5, rather than 0.8, and the post-lockdown R0 as 1.2 rather than 1.3 then the outcome is fantastically better.

 

What will actually happen?

From what we have seen so far, we are likely to see wildly different outcomes in different countries.  Singapore and China brought down R0 using testing and contact tracing that many in the West would oppose as an infringement of civil liberties.  Without almost total compliance, the lockdown methods are far less effective, and the UK and US are certainly making only minimal progress in that direction.  In Germany, led by a well-liked, credible, smart leader from a science background, we have seen early imposition of lockdown and investment in scientific research that gives me confidence they will find a balance between personal liberties, economic activity and public health.  The US appears to have the worst possible leadership and political structure which will make containing the R0 extremely difficult.  The UK government has had a very bad start relying on herd immunity, ignoring building testing capacity, refusing to work with the EU and failing to prepare the NHS for the oncoming storm.  But the failures of the government have been offset by the public spirit and compliance to adapt to this awful situation and by the extraordinary response of the NHS workers.  There is always the opportunity for the government to learn from others and adopt better policies and find a path though this crisis.

 

The most common method of modelling the spread of COVID is to consider estimates for how rapidly it is spreading (R0) and how deadly it is (mortality rate).

R0 is the number of new people infected by a given individual.  If R0 is 1 then the number of cases and deaths per day is stable, i.e. total deaths continue to rise but at a constant rate.  An R0 above 1 and the disease is accelerating.  I have found it hard to find a transparent source for this and have therefore built my own simple version which I found to work extremely well and be very instructive.

Parameters 

R0 I estimated R0 initially at 2.7 considering the UK case.
This was observed during the period before we applied measures to change the population’s behaviour.  The speed of the spread changes as we become more aware and change our behaviour.  We would expect the speed of spread of an airborne disease to reduce during various forms of lockdown.

For the pedants amongst you, I am aware that in the scientific literature they tend to say Re (effective) has fallen but this is just semantics and I will just say that R0 changes.

If you recall we went through a stage of around 2 weeks of hand-washing and cancelling football matches and some form of social distancing.   I estimate an R0 of 2.0 from the 3^rd of March

On March 23^rd we started official lockdown.  Here I use an R0 of 0.8, a big reduction resulting from a dramatic change to economic and social behaviours.

Mortality rate I used 1%

I assume that people are infectious for 5 days and death occurs 18 days after infection.  This produces the following results for what we have seen and gives a projection for the next few weeks.

Cumulative and daily deaths in UK – actual v model

We can also consider countries which are further advanced to see if the model works going forward.  Here we see Spain and Italy fit the daily deaths model very well, including the recent period when death rates are declining.

Daily deaths in UK, Spain, Italy (adjusted start date)- actual v model

I then applied the same model to look at the US.  The state level data is messy and dominated by NY and NJ.  To see what is happening outside of those, I totalled all the states excluding New York and New Jersey and compared to the same model as previous.

Daily deaths in USA (excluding New York/New Jersey) – actual v model
Until recently, the model works extremely well but worryingly the actual US daily death rate has continued to rise rather than fall.

 

How sensitive is the model to the assumptions?

R0

The model is very sensitive to changes in R0.
For example, if R0 actually remained at 2.7 in the 2 weeks pre-lockdown rather than 2.0, then the peak death rate would be dramatically higher.

This helps appreciate how hard it is to give accurate forecasts as minor changes in assumptions can give hugely different results.  It further shows how scary this virus it as it could easily be far worse than we are currently experiencing. Given the problems in estimation, it helps explain why the NHS were so concerned that we would exceed capacity and how important it was that the measures we took at least slowed the acceleration of the spread.  The sensitivity of the model to R0 makes forecasting very difficult but conversely makes our confidence much higher on what it has been historically.  We know that R0 cannot have been much higher or lower than the model as otherwise the outcomes would be wildly different.

Mortality rate

The other key assumption is of course mortality rate. I was encouraged that the model is robust to changes in mortality rate, given that this parameter is most controversial.  For lower mortality rates, it would require a higher R0 for the initial period  to match the actual data we are seeing i.e. we have more cases but a lower mortality rate to reach the same number of deaths.   This means we can look separately at the evidence on mortality rate, but it does not materially change the projections for the next few months.

What does this model suggest about the virus and our policy response?

The model is robust across the US, UK, Italy and Spain over different time periods without having to change parameters, apart from considering different start dates, which makes me quite confident in the approach.

Before we had any response to COVID, the R0 was around 2.7 which means that cases and deaths roughly double every 3 days.  The initial period of attempting to slow the spread by washing our hands, stop touching our faces, social distancing etc only seems to have reduced R0 to 2.0 which is still a rapid spread.  But this made enough difference that we did not run out of hospital beds, even if we did run out of PPE.

The number that I think is most important is the R0 ,post lockdown.  This can be seen by how quickly the death rates decline after the peak.  It is clear from the UK, Italy and Spain that the R0 is below 1 as the death rates are declining, and the peak deaths were around 3 weeks after the lockdown.  But I am very concerned that the death rates are coming down so slowly which suggests that the R0 may be 0.8 or perhaps even higher.  The US data is even worse as it implies that the average R0 in 49 of the states may still be over 1.

The reason this is so important is that this is the number that tells us how soon we can end lockdown and how far we can relax.  I will expand on this in my next post.