Revisiting the Lockdown vs. Non-Lockdown Comparison

At the end of a previous post, I showed a chart comparing COVID mortality per million people, for the U.S. versus two non-lockdown countries, Sweden and Belarus. Here is an updated version with data through November and the addition of a third non-lockdown country, Japan (which barely registers because its mortality is so low):

Studying the new chart, it appears that, after a long period of minimal COVID-19 mortality, Sweden is experiencing a surge in COVID-19 deaths, just as we are in the U.S. Starting in early November, it’s had a steeper ascent than the curve for the U.S., but Sweden’s deaths per population hadn’t yet eclipsed that of the U.S. by the end of the month.

One could argue that, given Sweden’s lower population density, its numbers are worse than those of the U.S.; however, population density is a misleading statistic, given that Sweden has one of the more urban populations in the world. 88% of Sweden’s inhabitants live in cities, making it the 23rd most urbanized country in the world. The analogous figure for the U.S. is less than 83%, making it the 36th most urbanized country.

Another thing to consider is excess mortality, that is, whether more people are dying in Sweden than is normal for this time of year. Here is the latest (as of this writing) “Z-score¹” graph from European Union Mortality Monitoring project (EuroMOMO):

Off-hand, it doesn’t look like a catastrophic increase in mortality given that, at 5.01 for week 49, it’s barely above the “substantial increase” line (the red dash, which appears to have a magnitude of 4).

Wanting to contrast Sweden’s excess mortality with that of the U.S., I found a feature on the Our World in Data website that displays graphs of excess mortality “P-scores²” for the U.S., Canada, and most European countries. Here is the resulting comparison:

From the above, it’s quite clear that at no time in the COVID era has Sweden’s excess mortality been significantly worse than that of the U.S., and for long stretches, it’s been much lower or even negative³. Moreover, for the last two quarters, Sweden has had declines in GDP relative to the same quarters last year (-7.4% for Q2, -2.7% for Q3), but less than the corresponding declines in the U.S. (-9.0% for Q2, – 2.9% for Q3):

Hardly a cautionary tale.

¹ Here is how EuroMOMO’s website describes this statistic:

Z-scores are used to standardize series and enable comparison mortality pattern between different populations or between different time periods. The standard deviation is the unit of measurement of the z-score. It allows comparison of observations from different normal distributions.

In general, Z-score = (x-mean of the population)/Standard deviation of the population, which could be approximated in our context by S-score = (number of deaths – baseline) / Standard deviation of the residuals (variation of the number of deaths around the baseline) on the part of the series used to fit the model, used as the standard unit.

Z-score are computed on the de-trended and de-seasonalized series, after a 2/3 powers transformation according to the method described in Farrington et al. 1996. This enables the computation of Z-scores for series that are originally Poisson distributed.

“What is a z-score?” EuroMOMO, Statens Serum Institut, 2020,
https://www.euromomo.eu/how-it-works/what-is-a-z-score/

At first blush, it seems to me that this method might exaggerate fluctuations in mortality for large countries relative to smaller countries, because it uses the absolute difference between the historical and target period deaths, rather than a percentage. I’m no expert on the matter, however.

² Here is how Our World in Data describes their sourcing of the chart data, including a brief explanation of P-score:

Data from the Human Mortality Database (HMD) Short-term Mortality Fluctuations project for all countries except the UK (HMD has data for England & Wales, Scotland, and N. Ireland but not the UK as a whole). UK data sourced from the UK Office for National Statistics (ONS).

We used the raw weekly death data from HMD to calculate P-scores. The P-score is the percentage difference between the number of weekly deaths in 2020 and the average number of deaths in the same week over the years 2015–2019. For the UK P-scores were calculated by the ONS.

We do not show the most recent weeks of countries’ data series. The decision about how many weeks to exclude is made individually for each country based on when the reported number of deaths in a given week changes by less than ~3% relative to the number previously reported for that week, implying that the reports have reached a high level of completeness. The exclusion of data based on this threshold varies from zero weeks (for countries that quickly reach a high level of reporting completeness) to four weeks. For a detailed list of the data we exclude for each country see this spreadsheet: https://docs.google.com/spreadsheets/d/1Z_mnVOvI9GVLiJRG1_3ond-Vs1GTseHVv1w-pF2o6Bs/edit?usp=sharing.

For a more detailed description of the HMD data, including reporting week date definitions, the coverage (of individuals, locations, and time), whether dates are for death occurrence or registration, the original national source information, and important caveats, see the HMD metadata file at https://www.mortality.org/Public/STMF_DOC/STMFmetadata.pdf.

“Sources: Excess mortality P-scores, all ages” Our World in Data, Dec., 2020,
https://ourworldindata.org/grapher/excess-mortality-p-scores?tab=chart&stackMode=absolute&country=SWE~USA&region=World [select “Sources” tab]

³ It also merits mention that, like any other information shared with the public in the COVID era, this graph is misleading in that it tends to make the pandemic look more dire than it really is. In calculating excess mortality, Our World in Data compares 2020 all-cause deaths with the average of all-cause deaths between 2015-2019. In part because populations tend to grow with time, this methodology works to understate expected all-cause deaths for 2020, and thus overstate any excess mortality (and understate any negative excess mortality). I plotted and trended the U.S. annual all-cause deaths for the years 2014-2019, as follows:

Assuming that the individual weeks’ all-cause mortality would be understated by the same percentage as the annual all-cause mortality, I calculated the percentage difference between the linear trend’s expected all-cause deaths for 2020, and the 2015-2019 average. I then applied this to a few of the weeks in April when excess mortality peaked, and found that instead of being 45%, 44% and 40% above expected all-cause deaths, recorded U.S. all-cause deaths were 39%, 37% and 34% above expected deaths. Not a gigantic difference, but a substantial one.