A better estimate for the impact of Covid-19 on the UK
Covid-19 has led to significant changes in the UK and has had a devastating human impact. Following the daily death toll has become a new habit for many, and at the time of writing the official UK toll has exceeded 35k deaths. However, the official death toll is not representative of the actual deaths. I used data from the Office for National Statistics (ONS) and exponential smoothing, a statistical technique, ****to estimate an actual death toll. I believe that the actual deaths as a result of Covid-19 are almost double the official death toll.
- NB - this article makes use of statistical techniques and data analysis methods, but I am deliberately not elaborating on them.
What’s wrong with the official death toll?
It’s fairly obvious that the official toll given to us by the government undervalues the actual human impact. The ONS toll counts a Covid-19 death if the cause of death on the death certificate itself was definitely or probably Covid-19. I understand the rationale behind this, but I believe it is too reductive.
Covid-19 has changed the face of the country, and the human impact follows accordingly:
- there are people dying directly from Covid-19;
- there are people who catch Covid-19 but die of other causes;
- people who are ill and die as they’re too afraid to go to hospital;
- people with terminal illnesses who have had treatment stopped;
- there may even be a decrease in deaths from roadside accidents and air pollution.
One way to estimate an actual Covid-19 death toll would be to compare two Spring 2020’s - one with Covid-19 (the current one) and one without Covid-19. We don’t have a 2020 without Covid-19, but I can use statistics to forecast this.
Time Series Analysis
Time series analysis is a form of statistics where historic elements of a time series are analysed to forecast future values.
I started by looking at the yearly deaths in England and Wales, where we see a strong positive trend.
Fig 1. This graph presents the total deaths/year in England and Wales. The solid blue shows the actual number, and the grey dashed shows the trend as time goes on.
Using the trend line from Fig 1. we can forecast an expected total for the number of deaths in 2020.
However this shows data for the entire year: it is not representative of the actual period I want to analyse (a three month one). If I look at quarterly deaths in England and Wales, I can see there are strong seasonal trends. This means I can’t use the yearly forecast.
Fig 2. This graph shows the total deaths per quarter since 2010.
Number crunching and methodology
To analyse a time series, it first needs to be decomposed. This shows some key things about the series - if it is has seasonal cycles, if it has a constant upward or downward trend, and how the individual values vary from theseasonal cycle.
I analysed two datasets - the quarterly deaths from 1960 - 2019, and the monthly deaths from 2001 - 2019. After decomposing these datasets, I used the Holt-Winter exponential smoothing method on some training data for both of these. I used 4 variations of the Holt-Winter exponential (damped/not-damped and additive/multiplicative trends). The predictions made with these models were then compared to test data, which is shown below:
Fig 3. Training the additive Holt Winters model on historic monthly deaths for England and Wales. The model forecasts are a good fit, but do not account for the spike in January 2018.
The root mean squared error and the Akaike information criterion (RMSE and AIC) are both measures of the success of a predictive model. These metrics were used to find the best modelling technique for each dataset. They can be seen here:
| Monthly | Quarterly | |||
|---|---|---|---|---|
| RMSE | AIC | RMSE | AIC | |
| Damped, Additive | 6,436.62 | 2,861.67 | 17,444.10 | 3,377.66 |
| Not Damped, Additive | 6,370.89 | 2,828.04 | 18,846.05 | 3,377.73 |
| Damped, Multiplicative | 6,550.81 | 2,831.91 | 18,951.04 | 3,384.01 |
| Not Damped, Multiplicative | 6,536.21 | 2,827.82 | NA | NA |
Showing the key model metrics for each run. These metrics can be used to find the best and most representative model.
The best monthly approach is not damped, additive. The best quarterly approach is damped, additive. This makes sense - the quarterly data set was from 1960, and damping accommodates for these more distant values. I also expect the additive models to be most successful, as this reflects the linear trend shown at the start of this article.
The above metrics cannot compare quarterly models with monthly models. These metrics only show which is the best quarterly and which is the best monthly. I have chosen to use the monthly model for the rest of this article, as this will allow me to compare on a month by month basis. I will come back to the quarterly forecast in the future, when data for May and June is available.
Comparing values
For the monthly dataset, the most successful model is the not-damped additive model. The predictions made from this model for the 2020 deaths can be seen in the graph below:
Fig 4. Showing historic monthly deaths in the UK alongside the model forecast for 2020.
The actual forecast values are as follows:
| Month | January | February | March | April | May |
|---|---|---|---|---|---|
| Forecast | 63,800 | 53,000 | 54,000 | 51,000 | 49,000 |
If we compare this to the actual deaths, as reported by the governments of England, Wales, Scotland, and Northern Ireland, we can see what the human impact of Covid-19 really is. The most recent mortality figures for the UK are as follows:
| Month | January | February | March | April | May |
|---|---|---|---|---|---|
| Forecast | 63,800 | 53,000 | 54,000 | 51,000 | 49,000 |
| Actual | 63,990 | 49,552 | 56,500 | 106,491 | 16,508 |
Comparing the forecast data with actual UK deaths. The May data is provisional, and only up to the week ending 8th May.
The forecast is relatively similar to the actual for January - March. This was expected and was demonstrated by the model training.
However, we can see a huge difference in April - an excess of 55,000 deaths. According to John Hopkins University, the UK had 26,800 official Covid-19 deaths by the end of April. This means the official death toll was almost half of the real impact, not yet accounting for May.
Conclusion
Using time series analysis, I propose that the actual death toll due to Covid-19 is almost double the official government death toll for the month of April alone. This is just an estimate - there may be other statistical techniques that are more accurate. This will change as more data is released.
The purpose of this analysis is to better quantify the human impact which Covid-19 has had on the UK.