Simple views of the data

The data are the daily deaths from Covid-19 in the UK, announced by DHSC each day, and available at https://coronavirus.data.gov.uk/archive. The data were revised on 29th April to include all deaths certified to be caused by the coronavirus, and not just those in hospital. There was a retrospective revision of all daily figures, and now for each “publication day” there is a whole series of death tallies for each past day. (I previously provided analyses of the pre-29th April data.)

An initial look at the whole archive concludes that

  1. the revisions are insubstantial, so it is reasonable to operate with only the most recent dataset. Of course, this may change in future.

  2. there are strong day-of-the-week effects, but these changed between Fri 17th April and Sat 18th April, for a reason unknown to me. Furthermore, they changed suddenly, with no evidence for change within either half of the dataset. This may also change as new data arrives. The data will be presented here for all days and, for the moment, the statistical analysis will only be applied to Sat 18th April onwards.

This document was prepared using R-markdown and RStudio. To find all the R code used to generate the tables and figures, download the .Rmd file. The only thing you will need to change is the directory to which you have downloaded the data file, in .csv format, for the day to be analysed. The program expects that file to be alphabetically the last file in the directory, as it will be if the only files you keep there are the series of .csv files for death rates from 29th April onwards.

Turning to the data, Table 1 shows the death tallies arranged by day of the week, and Figure 1 plots them by day of the week. Each curve has a much simpler pattern than if we ignored day of the week. The weekly pattern is presumably due to working shifts and administrative arrangements for people involved in different stages of reporting a death.

##            6 Mar- 13 Mar- 20 Mar- 27 Mar- 3 Apr- 10 Apr- 17 Apr- 24 Apr- 1 May- 8 May- 15 May-
## 6Friday       1      1      36     284     714   1152     935    1005     739    626    384   
## 7Saturday     1     18      56     294     760    839    1115     843     621    345    468   
## 1Sunday       0     15      35     214     644    686     498     420     315    269    170   
## 2Monday       1     22      74     374     568    744     559     338     288    210    160   
## 3Tuesday      4     16     149     382    1038   1044    1172     909     693    627    545   
## 4Wednesday    0     34     186     670    1034    842     837     795     649    494          
## 5Thursday     2     43     183     652    1103   1029     727     674     539    428

Table 1. The numbers of deaths arranged by day of the week

Figure 1. The numbers of deaths plotted by day of the week

Next, in Table 2 and Figure 2, we express each figure as a ratio, by dividing it by the figure of exactly one week previously. These ratios are not affected by day of the week effects, and they also incorporate a whole week of change, so are likely to be more reliable indicators. The obvious pattern is that the ratios are high to begin with, and do get gradually lower. The grey line at a ratio of one separates ratios indicating numbers are increasing, from those that indicate a decrease

##            13 Mar- 20 Mar- 27 Mar- 3 Apr- 10 Apr- 17 Apr- 24 Apr- 1 May- 8 May- 15 May-
## 6Friday     1.00   36.00    7.89    2.51   1.61    0.81    1.07    0.74   0.85   0.61  
## 7Saturday  18.00    3.11    5.25    2.59   1.10    1.33    0.76    0.74   0.56   1.36  
## 1Sunday      Inf    2.33    6.11    3.01   1.07    0.73    0.84    0.75   0.85   0.63  
## 2Monday    22.00    3.36    5.05    1.52   1.31    0.75    0.60    0.85   0.73   0.76  
## 3Tuesday    4.00    9.31    2.56    2.72   1.01    1.12    0.78    0.76   0.90   0.87  
## 4Wednesday   Inf    5.47    3.60    1.54   0.81    0.99    0.95    0.82   0.76         
## 5Thursday  21.50    4.26    3.56    1.69   0.93    0.71    0.93    0.80   0.79

Table 2. The ratio of number of deaths to the preceding same day of the week

Figure 2. The ratios plotted against time

How quickly will the death rates fall?

The ratios seem to be currently between 0.7 and 0.9, and we can ask how quickly will the numbers decrease? A transformation of the ratios allows us to see in Table 3 and Figure 3 the number of doublings or halvings per week. In the early days, there were large positive figures, indicating more than two doublings per week, so four times as many people were dying at the end of the week than at the beginning. This was a very steep ascent at the beginning of the epidemic.

Later, the doubling times came down, and did so gradually, and eventually became negative on the 15th April (apart from a couple of rare reversions). Once negative, we can take the signs off, and think of them as the number of halvings in a week. For the figures to drop as fast as they rose, we would need to see the number of halvings per week to rise to more than 2, to match the number of doublings per week of 2. However, the number of halvings hovers around 0.3 to 0.4, suggesting it would take 2.5 to 3 weeks to halve the number of deaths. This clearly indicates a very slow tailing off, certainly compared to the very rapid initial increase.

The slowness of decline must be the result of ineffectiveness in our lockdown. Infectious people are still meeting susceptible people, and passing the infection on. These figures don’t tell us whether these are key workers who use public transport, health workers and hospital patients, care home workers and residents, or people not obeying the lockdown restrictions. Or, indeed, it is possible that non-key workers who are obeying the lockdown restrictions are still not sufficiently protected. I am sure someone connected to SAGE is studying these important questions, with more informative data.

These figures can also be used to note that a delay of one week in imposing the lockdown, at a time when there were two doublings per week, would result in an extension of over four weeks now, to get down to any given level. The sharp rise and slow fall makes those early decisions look very important.

##            13 Mar- 20 Mar- 27 Mar- 3 Apr-  10 Apr- 17 Apr- 24 Apr- 1 May-  8 May-  15 May-
## 6Friday     0.0000  5.1699  2.9798  1.3300  0.6901 -0.3011  0.1042 -0.4435 -0.2394 -0.7051
## 7Saturday   4.1699  1.6374  2.3923  1.3702  0.1427  0.4103 -0.4034 -0.4409 -0.8480  0.4399
## 1Sunday        Inf  1.2224  2.6122  1.5894  0.0911 -0.4621 -0.2458 -0.4150 -0.2277 -0.6621
## 2Monday     4.4594  1.7500  2.3374  0.6029  0.3894 -0.4125 -0.7258 -0.2310 -0.4557 -0.3923
## 3Tuesday    2.0000  3.2192  1.3583  1.4422  0.0083  0.1669 -0.3666 -0.3914 -0.1444 -0.2022
## 4Wednesday     Inf  2.4517  1.8489  0.6260 -0.2963 -0.0086 -0.0743 -0.2927 -0.3937        
## 5Thursday   4.4263  2.0894  1.8330  0.7585 -0.1002 -0.5012 -0.1092 -0.3225 -0.3327

Table 3. The doublings/halvings per week, based on the ratios in Table 2. It is the number of doublings in a week if positive, and the number of halvings in a week if negative.