Posts Tagged ‘Corona Virus’

COVID-19: Day 115: About half-way through.

April 25, 2020

Warning: Discussing death is difficult, and if you feel you will be offended by this discussion, please don’t read any further.

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Today is Day 115 of 2020 and as I stare again at the COVID-19 data, two things seem particularly striking.

The first thing is that – as we pass 20,000 deaths – we are only halfway there. My expectation is that another 20,000 people will yet die from from COVID-19 over the next 50 days or so.

And the second thing is that on Monday March 23rd, when the UK ‘locked down’ – the cumulative number of deaths was 280. This is less than 1% of the number of people who would eventually die. And yet at that point, we were in some sense already committed to the astonishing total of deaths we are facing.

Thing#1: Halfway 

I have been look ahead to see what we might expect to happen in the coming days and weeks.

I assumed that:

  • 19% of people diagnosed with COVID-19 using ‘Pillar-1’ testing in hospitals will die after – on average – 6 days. This is 1% less than I assumed previously, but seems to match the recent data better.
  • The number of Pillar-1 confirmed cases is declining linearly. These are mainly patients being admitted to hospital.

Based on these assumptions I have calculated the expected cumulative totals of confirmed cases and consequent deaths.

Slide1

The above graph shows various statistics plotted versus the day of the year.

  • The vertical green lines show the date of the ‘lock down’, the end of ‘phase 1’ of the ‘lock down’, and the upcoming end of ‘phase 2’.
  • The blue curve shows the cumulative number of ‘Pillar 1 tested’ COVID-19 cases.
  • The red curve shows the cumulative total of COVID-19 deaths in hospital.
  • The black dotted line shows the predicted number of deaths based on
    • 19% case mortality after 6 days.
    • A continuation of the current linear decline in Pillar 1 cases.

There is considerable uncertainty in this projection. But I think it represents a fair expectation.

It indicates that in terms of deaths,
we are still only half-way through.

Thing#2: Growth Rate

Slide2

The above graph shows various statistics plotted versus the day of the year.

  • The vertical green lines show the date of the ‘lock down’, the end of ‘phase 1’ of the ‘lock down’, and the upcoming end of ‘phase 2’.
  • The blue curve shows the cumulative number of ‘Pillar 1 tested’ COVID-19 cases.
  • The black dotted line shows the predicted number of cases based on a continuation of the current linear decline in Pillar 1 cases.

There is considerable uncertainty in this projection. But I think it represents a fair expectation.

What also struck me here was that on Day 81, at the start of the original ‘lock down’, there had only been 280 deaths and the daily death rate was about 50 people per day. And yet this relatively small number was a sign of a tsunami of illness about to overwhelm our country.

By acting then we have undoubtedly saved the lives of probably hundreds of thousands of people.

Thing#3: Life after Day 123 (3rd May)

On day 123, the cumulative total of people testing positive for the corona virus as they entered hospital will be approximately 150,000. 

Based on the loose statistic that 20% of people require hospital treatment, we can guess that

  • the cumulative number of true cases in the population is around 750,000.
  • a significant fraction of these people will have had the illness and recovered.

Thus after 3rd May, the number of people who will be unwell will be much less than 1% of the population.

So relying on chance alone, for every 100 people one meets, 99 will be virus free.

It seems to me that even with substantial relaxation of our current social distancing, it will likely be possible to keep the chance of person-to-person virus transmission low.

But given the sensitivity I mentioned in Thing#2 – we will need to remain vigilant.

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Discussing death is difficult, and if you have been offended by this discussion, I apologise. The reason I have written this is that I feel it is important that we all try to understand what is happening.

COVID-19 Hospital Mortality

April 12, 2020

Warning: Discussing death is difficult, and if you feel you will be offended by this discussion, please don’t read any further.

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Yesterday, I concluded that the mortality of UK COVID-19  patients entering hospital i.e. people already seriously ill with COVID-19, was roughly 25%. I was shocked at this large figure.

Sadly, after further investigation it appears to be increasingly plausible.

UK hospital deaths versus age

UK Government data is available in a spreadsheet downloadable from a link on the COVID-19 ‘Dashboard’

The data show the age ranges of people who have died from COVID-19 in hospital. The age ranges are rather broad but I have taken the liberty of drawing a smooth line through the data points.Slide4Based on this data (and also shown on the graph) is my calculation of the average age of people dying in UK hospitals from COVID-19: it is approximately 74 years of age.

However this data does not tell us how many people in these age ranges were admitted to hospital, so we cannot calculate the mortality.

 

US hospital mortality versus age

The Washington Post has an article which includes data on COVID-19 mortality in US hospitals admissions versus age. The data is based on the admission of 6479 patients since 1st March 2020.  I have re-plotted the data below.

Slide5

This mortality is for US hospitals, rather than UK hospitals, but assuming that treatment is similar, then we can look at the expected mortality for patients at the average age of death of UK patients. This is shown below below with a red horizontal line indicating 25% mortality.

Slide6

This data seems self-consistent.

  • The relationship between UK daily cases and UK daily deaths that I discussed yesterday seems to indicate that mortality is around 25%.
  •  US mortality data shows that at the average of UK deaths, mortality for hospital admissions is 25%.

Ideally we would also like to know the ages of UK patients at admission, but I could not find that data.

Discussion

Notice that this only concerns patients who are admitted to hospital i.e. patients who are already poorly and who have generally been suffering at home. Most people recover at home without needing medical care.

But even so, I have again been saddened by this result which makes it less likely that yesterday’s analysis was in error.

This support gives increased confidence to the prediction  that the number of daily deaths for the next 7 days is unlikely to fall significantly, because these deaths correspond to people who have already been admitted to hospital.

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As I mentioned, discussing death is difficult, and if you have been offended by this discussion, I apologise. The reason I have written this is that I feel it is important that we all try to understand what is happening.

COVID-19 Numerology

April 11, 2020

Warning: Discussing death is difficult, and if you feel you will be offended by this discussion, please don’t read any further.

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Life is very pleasant for me and my wife in this ‘stay at home’ world, but I find myself permanently anxious and neurotically focused on ‘the numbers’: trying to understand them and use them to foresee what’s coming next.

I had thought naively that the ‘lock down’, which started on Day 81 of the year, would be completely effective, and that new cases of COVID-19 would begin to decline. But as the data below shows, that doesn’t seem to have happened.

Slide1

The number of new cases has stopped rising – but new cases are still occurring at around 4500 ± 500 cases per day.

As I understand the data, and the way in which testing is done, these are mainly people entering hospital. People who have probably been ill at home for some time, but their symptoms have now become serious enough for them to come to hospital.

But even so, some of those people will have been infected after Day 81.

Relating New Cases to Deaths

Some fraction of the people entering hospital will die a few days later.

I have looked at the UK data to try to understand how many people would die – the fractional mortality – and the delay.

To do this I took the ‘new cases‘ data and:

  • Applied a delay to the data that moves it to the right on the graph
  • Adjusted the fractional mortality to try to match the statistic for daily deaths. This moves it downwards on the graph.

Slide2

I found a reasonable match to the data for a delay of 7 days and a fractional mortality of 25%. i.e. the data seem to imply that 1 in 4 people being admitted to hospital as a new case will die, on average just 7 days later.

Slide3

Is this right?

Well obviously I don’t know if this is right or not.

I had expected a much lower mortality for people entering hospital – perhaps 1 in 10. On the graph above this would push the dotted black curve downwards.

But if that were so, then in order to match the ‘daily deaths’ data, the time to death would have to be very short, and in fact the curve doesn’t match the data well.

I found that reasonable matches could be obtained with:

  • mortality of 30%  and a time until death of around 9 days,
  • mortality of 20%  and a time until death of around 5 days,

But the best match (by eye) seemed to be with a mortality of 25%  and a time until death of around 7 days,

Discussion

I was shocked and saddened by this result. I hope I have missed something out or misinterpreted the data. Perhaps the mortality or time until death have improved throughout the last few weeks.

A mortality rate of 25% has been reported in the ‘worst hit’ hospitals, but I assumed this was exceptional. Also, the time until death seemed much faster than I had expected.

One additional feature of this analysis is that – if correct – it predicts the number of daily deaths for the next 7 days. And the prediction is disappointing.

The analysis indicates that the number of daily deaths in the next 7 days is unlikely to fall because these deaths correspond to people who have already been admitted to hospital.

Link to Excel Spreadsheet: Modelling Death Delay and Mortality

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As I mentioned, discussing death is difficult, and if you have been offended by this discussion, I apologise. The reason I have written this is that I feel it is important that we all try understand what is happening.

 


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