*Last updated on 26th May 2020*

The latest data for deaths due to COVID19 (Coronavirus) in England as of Tuesday 26th May 2020 show that the worse is clearly over but it will be a number of weeks yet before this first wave is over.

I intend to update twice weekly on Tuesday and Saturday. You can follow me on Twitter to be told when I have made updates.

**The 6 time series for COVID19 related deaths in England**

Each time series is denoted with a 4 letter code which I will use throughout. Clicking on the 4 letter code will take you to the source data. I have only extracted data for England from these sources but some also cover Scotland, Wales & Northern Ireland.

**PHEr – Public Health England COVID19 Registrations –**Daily number of deaths by date of registration with COVID19 on the death certificate and confirmed with a positive test in an NHS/PHE laboratory. Published everyday, this is the most common headline figure.**NHSo**–**NHS England COVID19 Occurrences**– Daily number of deaths by date of occurrence with COVID19 on the death certificate. This is also published daily**CQCn**–**Care Quality Commission COVID19 Notifications**– (NEW) All care home are required to notify the CQC of any death in their home within a short period. Since the outbreak, care homes are now able to say if they suspect the death was COVID19 related without a test. The data is passed onto the ONS who published the data weekly.**ONSr**–**ONS COVID19 Registrations**– Daily number of deaths by date of registration with COVID19 on the death certificate from all locations. This is published weekly on a Tuesday but the daily data can be found on the COVID19-ENGLAND tab of the downloaded spreadsheet.**ONSo**–**ONS COVID19 Occurrences**– Daily number of deaths by date of occurrence with COVID19 on the death certificate from all locations. This is published weekly on a Tuesday but the daily data can be found on the COVID19-ENGLAND tab of the downloaded spreadsheet. Note two columns are shown with different cutoff dates and I take the data from the column with the latest cutoff date.**ONSx**–**ONS Excess Death Registrations**– Daily number of deaths by date of registration with COVID19 on the death certificate from all locations. This is published weekly on a Tuesday and can be extracted from the WEEKLY DATA tab of the downloaded spreadsheet. I use the day of week pattern of the ONSr series to convert the ONSx weekly data into ONSx daily data.

I am assuming that the reader understands the terminology used but for an in-depth explanation please read the first half of this post. The reader should note that since that post was published, PHE revised their time series and now include all death registrations with COVID19 on the death certificate which has been confirmed by a test in a PHE or NHS laboratory. Previously PHE/DHSC data only counted deaths in hospitals like the NHSo series.

To summarise, 4 time series (NHSo, ONSo, ONSr, PHEr) are all for deaths where COVID19 is stated somewhere on the death certificate with PHEr requiring a positive COVID19 test in addition. The other two time series (ONSx & CQCn) do not require COVID19 to be mentioned on the death certificate.

I will now show the latest data and trends for each time series in turn using the same chart format for each. The format is explained in the first section PHEr but all charts use the ONS definition of a week running from Saturday to Friday. All charts also begin with the week commencing Saturday 14th March 2020 which is recorded by the ONS as week number 12 which makes the latest week ending 22nd May week number 21. Where necessary, the same week number convention is used throughout this post.

**1 – PHEr – Public Health England COVID19 Registrations**

As of 25th May 2020, a total of 32,979 death registrations in England have been recorded in the PHEr series. The breakdown by day is shown in the chart below as bars.

A solid line showing the 7 day Centred Moving Average (CMA) is also shown. A 7 day moving average is used since a week has 7 days and registrations are affected by weekend & bank holiday working patterns. The moving average is centred which means that an average for day T is the average number of daily deaths recorded between day T-3 and day T+3. CMA’s are the best way of spotting turning points in the data and the chart shows that the CMA for PHEr peaked on 9th April 2020 and turned downwards on 11th April 2020.

A dashed purple line shows a simple extrapolation model I have used to project the 7 day CMA up to the 29th May. A number of steps are needed to get to this point. First, I calculate the **daily growth rate** for each day T as follows:-

**Growth Rate (Geometric) = dcPHEr(T) = Log[ cPHEr (T)/cPHEr(T-1) ]**

where **cPHEr(T)** is the total number of death registrations as of day T. The data is plotted as diamonds on the chart with a scale that looks like a percentage scale. That is because this formulation of the growth rate will give more or less the same answer as the standard arithmetic % growth rate

**Growth Rate (Arithmetic) = %DcPHEr(T) = [ cPHEr (T)/cPHEr(T-1) ] – 1**

when the growth rate is around 10% or less. It starts to diverge above 10% but I use the convention of treating geometric growth as a percentage.

The advantage of geometric growth rates is that they can be properly averaged over time whereas arithmetic growth rates can’t be averaged. For example, if you have a quantity Q that starts at 100, grows by 20% the next day and then falls 20% the day after, the average growth rate is 0% but you don’t end up back at 100 but 96 instead. Geometric rates get around this issue so +20% geometric followed by -20% geometric get you back to where you started i.e. 100.

This is why I can calculate and plot a dashed black line showing the 7 day CMA of the geometric growth rate. From the end of March, this fell fairly rapidly but not in a straight line. Instead the 7 day CMA is curving which is indicative of cumulative growth that gradually slows down. It is this 7 day CMA of the geometric growth rate that I have extrapolated and results in the solid black added to the chart below.

It is then straightforward arithmetic to convert that solid black line into an estimate of the 7 day CMA of the daily number deaths as shown by the dashed purple line.

The extrapolation itself is a straightforward statistical model which is built automatically in my spreadsheet. First I have to identify the time period I want to use to build my model. For this time series I’ve used the period 25th April up to the present day i.e. the days after the number of daily death registrations peaked and Easter which distorted registration timings. I denote the 25th April as day 0, 26th April as day 1, etc and then plot this scatterplot with day number on the horizontal axis. On the vertical axis, I plot the logarithm of the 7 CMA of the growth rate.

If you’ve followed the calculations so far, you will spot the vertical axis is in fact a log of logarithm but it does result in a near straight line fit in the chart. Those who know about these things will spot there is autocorrelation of the residual errors in the chart but I have not bothered to include this in my formula since I just wanted something that was simple to code automatically in a spreadsheet. With this model, it is then straightforward to apply it to day numbers beyond the end of the data set used to build the model and give the black line shown on the chart above. The 95% confidence interval (not prediction interval) for the extrapolated black line is +/-0.2%.

**2 – NHSo – NHS England COVID19 Occurrences**

As of 25th May 2020, a total of 25,867 deaths in English hospitals have been recorded in the NHSo series. The breakdown by day of death is shown in the chart below as bars.

The format of the chart and the extrapolation into the future uses the same format and method as for the PHEr chart in section 1 above. The major difference with the NHSo series is that the historical data is continually updated as deaths registered on dates in the future are allocated back to the date death occurred. On average, death occurrence takes place 5 days before death registration but it can be both quicker and slower than that . Some deaths don’t get registered until a month after occurrence, perhaps because a complicated autopsy or coroner investigation, which then results in data over a month old being revised upwards.

Because of this, the last 5 days of the NHSo series is ignored when calculating trends and extrapolating the 7 day CMA into the future. If you’ve followed my Twitter feed, you will know that from the middle of April, I realised the 7 day CMA in the geometric growth rate stabilised if you did this. The scale of deaths can still change but the trend is stable and at this point in the pandemic, it is the trend that is most important. Certainly the peak in daily number of death occurrences in hospitals is clearly marked on 8th April 2020.

The 95% confidence interval in the extrapolated 7 day CMA of daily deaths is +/-0.2% but this does not take into account future revisions to the historical data. You might notice from the chart that the extrapolated dashed line does not appear to join with the known 7 day CMA. It is because of the anticipated future historical revisions that explains this. My current method of allowing for this is a crude one and I haven’t as yet tested it properly but it seems to be semi-reasonable for now.

**3 – CQCn – Care Quality Commission COVID19 Notifications**

Since 10th April 2020, the Care Quality Commission has been collecting daily notifications of deaths in care homes where COVID19 was suspected to be the cause of death. It has always been a requirement for care homes to notify the CQC as soon as possible, if a death occurs but up to the end of March, doctors were not putting COVID19 on the death certificate. The ONS tracks deaths by location in their excess deaths data (ONSx) and any spike in care homes would be detected there but care home deaths were not prominent in the ONSr & ONSo series to begin with due to the lack of registration. Since April, this has changed but the CQC decided to start tracking notifications where COVID19 was suspected even if the doctor did not put COVID19 on the death certificate. That decision generated the CQCn series shown below which although is daily, it is in fact published weekly every Tuesday by the ONS rather than CQC.

One point to be aware of is that there is the potential for overlap with NHSo when looking at CQC data. Care homes are required to notify the CQC if any of their residents regardless of the location of the death. That means CQC also record deaths outside of care homes but who were residents of care homes. Given the age of care home residents it should be no surprised that some will die in hospital and will be recorded in NHSo if the death is thought to include COVID19. The data shown in the chart is for deaths of care home residents in care homes & unstated locations but not including deaths in hospitals & elsewhere (such as outside) so this potential duplication is avoided.

Since data was not collected before 10th April, we do not know the true cumulative count which means the underlying growth rate cannot be calculated. This explains why you see no diamonds on the chart. The 7 day CMA for daily notifications can be calculated and this shows a peak of 18th April.

**4 – ONSr – Office of National Statistics COVID19 Registrations**

As of 15th May 2020, a total of 39,191 death registrations involving COVID19 from all locations in England have been recorded in the ONSr series. The breakdown by day is shown in the chart below as bars.

Again the chart format and extrapolation is exactly the same as for the PHEr series. Since this a series of death registrations, weekend working patterns have an effect. Compared to PHEr, the weekend and bank holiday effect is far more pronounced for the ONS who appear to work standard office working hours. The 7 day CMA of both the daily deaths and the geometric growth rate is therefore less stable. I have still extrapolated the time series but this time the 95% confidence interval for the extrapolated 7 day CMA of the growth rate is now +/-1.4% which is much higher than that of the PHEr series.

Unlike PHEr which has a peak date of 11th April, ONSr daily deaths peak is 17th April. ONSr includes deaths from all locations and it has become clear that deaths in care homes were on a different timeline to hospitals.

**5 – ONSo – Office of National Statistics COVID19 Occurrences**

As of 15th May 2020, a total of 40,096 death occurrences involving COVID19 from all locations in England have been recorded in the ONSo series. The breakdown by day of death is shown in the chart below as bars.

As for the NHSo time series, the historical data is continually revised upwards due to future registrations. This time, the trend is stabilised if you ignore the last 4 days which are shown by the checkered green bars. Currently the peak for ONSo is 11th April compared to 7th April for NHSo but future historical revisions might move that peak to the 12th instead. As for NHSo, the 7 day CMA does not join up with the actual CMA since future historical revisions are anticipated.

I need to point out one wrinkle if you are reading the ONS spreadsheet itself. They provide two ONSo series. The first one only includes the total number of death registrations recorded in the ONSr series above in section 4. As of 15th May, there were 39,203 registrations which are then reallocated to date of death occurrence. However, the publication date for this time series was 26th May and ONS were already receiving registrations in the week of 16th – 22nd May but had not as yet compiled the full dataset. Many of those registrations end up being allocated to a date of death occurrence for dates up to 8th May and it is this data series that is shown in the chart above.

Until the end of April, it was possible to plot both PHEr and NHSo data on the same chart since both only recorded deaths in hospitals. Now that PHEr coverage has been expanded, this is no longer possible but it can be done with ONSr & ONSo time series as shown in the chart below. This gives a visual feel of the time lags between death occurrence and death registrations. The current gap between the peaks is 7 days but that is probably larger than it appears due to Easter falling in between the peaks which would have made some registrations later than usual and thus widening the time lag between the peaks.

**6 – ONSx – Office of National Statistics Excess Death Registrations**

I have calculated a total of 52,278 excess death registrations from all locations in England between 14th March and 15th May 2020. If you are not familiar with the concept of excess deaths, this article by Anthony Masters, an ambassador of the Royal Statistical Society, gives an excellent explanation. I am using Excess Deaths as a proxy for all direct and indirect effects of COVID19 hence why the chart title still includes the word COVID19.

Unlike the other 5 time series, ONSx can be negative since Excess Deaths is derived from this chart as the difference between total number of death registrations per week and a baseline number of death registrations.

It is published as a weekly time series but since the data is death registrations like ONSr, I have assumed that pattern of registration by day of week is identical to ONSr. That allows me to generate an ONSx daily series.

The 7 day CMA shows a peak on 17th April. However, the simple extrapolation method is not actually appropriate for excess deaths since excess deaths can be zero or negative which is an impossible outcome for the extrapolation model used here. Therefore, very little weight should be placed on the extrapolations in late May. This motivates a search for other methods of estimating ONSx in the future which I describe in this article.

#### Do the time series show similar trends?

The chart below plots the 7 day CMA of the geometric growth rates for the 5 time series presented in this post. Death registration series (PHEr, ONSr & ONSx) are plotted as dashed lines whilst death occurrences series (NHSo & ONSo) are plotted as solid lines.

Up to the end of March, the 3 registration series are all over the place. This is because of the low number of deaths at this point which means differences in timings of death registrations can have a large effect. By the time we get to around 7th April, the 3 trends are closer together. It is apparent though that the two ONS series lag the PHE series by a few days which is probably the result of deaths in locations outside hospitals, such as care homes, following a later trend than hospitals.

The two occurrence series are much closer together and have been almost from the beginning. There is still a lag of a day or two between the two series which might reflect different timings of deaths in and out of hospitals but the trend lines are very similar.

Finally the two series published every day, PHEr & NHSo, seem to be 5 days apart but are otherwise showing the same trends for the most part.

**– More posts about COVID19 –**

- A very useful guidance to interpreting statistics of COVID19 published by the Royal Statistical Society.
- My collection of links to all kinds of material related to the statistics of COVID19, epidemiological modelling and testing.
- How large a sample is needed in order to decide whether COVID19 restrictions can be lifted? A lot, lot less than you think!
- How many excess deaths have there been as of 20th April? This explains all data sources in more depth.
- How many excess deaths will there be as of 1st May? This is an updated estimate of excess deaths.
- How many excess deaths will there be as of 8th May? This is an updated estimate of excess deaths.
- How many excess deaths will there be as of 15th May? This is an updated estimate of excess deaths.