As the data moves to a flatter curve, I have changed the linear regression to loess regression. Each day (apart from one outlier) the reading is less than the day before – black data points. The regression line has an uncertainty which just touches the growth line (grey area).
We have now had a calendar month of a slow decline in daily hospital mortality. The problem with Covid19 mortality rates is the lag time. It takes many weeks for susceptible individuals to become seriously unwell after contracting the infection.
The first peak of the Covid19 pandemic has been a bit difficult to call because it was so bumpy. Certainly by April 15, 2020 there was a suspicion of a peak – the daily reading was 1 i.e. that day’s reading was the same as the day before.
It bounced around for awhile until the 95% confidence upper limit dropped below the growth line on April 23, 2020. I suppose, at least in terms of hospital Covid19 deaths, we could call that the first peak in the UK.
The grey area and ‘line of best fit’ are a non-parametric regression called loess. Once the data got below the growth line (each successive reading was lower than the day before), the rate of decline in deaths slowed considerably. We still have declines day after day (black dots).
This plot has some similarities with the R0 number but it takes several weeks for a patient to contract Covid19 and then become unwell enough to be admitted. So daily hospital death rate is too much of a lag indicator.
Daily hospital Covid19 death rates are quite volatile. This probably represents incomplete reporting at the weekends. The plot continues to make lower lows. We are watching carefully to see if the partial lifting of lockdown restrictions produces a surge.
Lockdown Day 53. The hospital death rates continue to grind downwards. Covid19 patients in hospital need prolonged treatment. The reduction in very sick patients presenting to our hospital takes a long time work through.
Each data point represents the growth or slowing of the hospital death rate. The 7 day moving average is calculated on a daily basis. The daily reading is then divided by the previous day’s reading. If the result is below 1 (death rate is falling) then a black data point is plotted. If the result is 1 or above a red data point is plotted.
The linear regression (black solid line) and confidence interval (grey area) point to an established downward trend.
As we move to a partial lifting of the lockdown in the UK, I looked for evidence to support relaxing measures that restrict activity outdoors.
There are many Covid19 reports being released preprint i.e. they are available online before being published formally. MedRxiv is a reputable preprint server. This paper comes from Qian H et al and features contributors from 4 Chineses universities.
The Covid19 reports of 120 prefectual cities excluding Hubei province were studied. There were 318 reported outbreaks. 1,125 people contracted Covid19 in their homes. Seventy-six were noted to have become infected from a contact on public transport. There was only one incident outdoors; It involved only 2 people. There was no mention in the study of cases in the workplace. This might well be because businesses were all closed down.
With appropriate hand hygiene, social distancing and self-isolation if one develops symptoms, it appears the lifting of restrictions on exercising is justified. We still have to limit meetings with non-household members to one-to-ones with appropriate social distancing. The study acknowledges one individual could be counted in multiple environments. The implication is, at least in China, that public transport is a major source of infection for households.
Indoor transmission of SARS-CoV-2. Qian H et al. April 7 202. MedRxiv preprint.
This model uses linear regression. The data are from the World Health Organisation and European Centres for Disease Control. The data start from March 23, 2020 when the UK lockdown was introduced.
Each data point is the daily 7 day moving average. For each day, the reading is divided by the previous day’s reading: The result is either below, at or above 1. Where the reading is less than yesterday’s the data points are black (growth is reversed); Where the reading is greater than yesterday’s the data points are orange. The grey area is the 95% confidence interval of the regression.
It took 12 days of lockdown to slow the growth and there was not an obvious peak until April 26, 2020. Since then there has been a slow grind downwards with each daily reading being slightly less than the one before.
There is much media attention directed to the Covid19 deaths recorded in hospitals. As the weeks have passed, the headline figures have shown Covid19 deaths in UK hospitals exceeding those of Italy. I hope to show that comparisons of this kind are not possible.
The weakness in the comparison is it is only possible to compare one country with another if the underlying metric is universal. Not every person dying during the pandemic, in either country, has had a nasal swab. This renders comparisons of the Covid19 deaths in separate populations impossible.
However deaths from all causes are recorded with considerable accuracy. It is therefore possible to measure the excess deaths by comparing the mortality rates in each country with a 5 year average for the same period. Covid19 deaths in hospital are recorded so we do have a fairly accurate start point. These data are based on the six weeks following the first recorded Covid death.
The Italian population is approximately 10% smaller than in the UK; The statistics allow for this. Looking at the chart, we can see the pandemic, excess deaths (2020 rates minus the 5 year average) are greater in Italy than the UK. However is this significant? The chi-squared statistic which measures significance is 283.93, degrees of freedom = 1 and the all important p < 0.0001. This means the difference between the Italy and UK results is highly significant. However chi-squared does not gives us the magnitude or the direction. For this we need the odds ratio.
The odds ratio is 1.13 (CI: 1.11 – 1.14) which means the odds of dying from any cause in Italy in the 6 weeks from the first Covid19 death were 1.13 greater than in the UK. This is very different from headline figures and can be explained by swab testing not being universal.
Summary I provide this analysis not to promote international comparisons but to debunk them. We cannot in the midst of the pandemic make any useful comparisons. This can only be done after we have eradicated the global infection. The time for meaningful analysis will come.