The Canadian media reminds us daily of the COVID-19 death count. They never fail to mention each time we reach a grim milestone. But I got to thinking, how are COVID-19 deaths really counted? What is the effect size on mortality? In some cases it might be obvious, but I am sure there are many medical cases which are difficult to label, especially since severe illness from COVID-19 strongly tracks the febrile, people with comorbidities, and people of advanced age. Are we under-counting or over-counting COVID-19 deaths? Conspiracy theories abound with wild claims about COVID-19 inflated death counts.
One way we might be able to help calibrate our counting is looking into changes in the Canadian mortality rate. Sure, labelling a COVID-19 death might be difficult, but counting deaths themselves should be much easier. Statistics Canada has several weekly mortality time series for the Canadian population. Using the website https://www.mortality.org/, I download the Statistics Canada mortality data. I have no way of determining the data accuracy, but I will assume that the data are complete enough for my modelling purposes. As always, conclusions are only as good as the data we have.
The first plot shows the raw Statistics Canada mortality rate data. The data are split across cohorts along with the total population. We see some interesting patterns. First, the mortality rate in Canada has been increasing over the last ten years. This increase is not surprising as Canada’s median age is increasing – the effect is probably due to our aging population. Second, the death rate in our oldest cohorts is decreasing. We are probably seeing healthier people reaching these cohorts each year given that smoking rates decreased over the last 30 years and we are probably also seeing the effect of better medicine. That we see declines in the mortality rate of the oldest cohorts but an increasing rate for the entire population is an example of Simpson’s Paradox. The fraction of the Canadian population entering the oldest cohorts is increasing, but we all die at some point!
A casual glance at the plot doesn’t seem to scream a large COVID-19 effect in 2020, but we have to be careful – looks can be deceiving. We have a long term trend superimposed on a noisy periodic time series and we are trying to detect changes at the tail end of the process. A nice way to proceed is to use generalized additive models (GAM). I will be using Simon Wood’s mgcv R package.
The model I have in mind is a GAM with a cyclic cubic spline with a 52 week period, , and a trend spline, ,
It’s a simple model, but it should be able to pull out a signal or trend, if one exists.
Given that COVID-19 has proven more dangerous to the 75-84 year old cohort, I will start there. The second plot shows the results of the model normalized to the downward linear drift in the data. My model does well fitting the data – well enough to understand the broad features – but an examination of the residuals, while normal in their distribution, exhibit some autocorrelation. There is subtle time series structure that my model misses but for the purposes of detecting the long term trend, this model does reasonably well. We see that the cyclic part peaks during the fall/winter, and the spline trend term sharply moves up through 2020, the effect from COVID-19. The trend component also shows the years with a particularly strong flu season.
In the next figure I show the long term trend in the mortality rate for the 75-84 year old cohort relative to the background. We see that COVID-19 has lifted the mortality rate for this group by about 4.5%, about 4 times the effect of a bad flu year. The final figure shows the long term trend with the original data. Repeating this analysis for the entire population, we see that the over all effect of COVID-19 on the Canadian population is to lift the mortality rate by about 5% above background. We can see the effect in the next two figures.
This helps us answer the question about over counting. If the effect is about 5% and if it sustains for all of 2020, given that about 280,000 Canadians died in 2019, the results suggest that the annual total COVID-19 effect is 15,000 excess in Canada. While it looks like the current official number of 21,000 COVID-19 deaths might be a little bit high, we need to caution that conclusion based on substitution effects. People travelled less in 2020, so some types of accidents are probably down with deaths from COVID-19 making up part of the difference. Those types of substitution effects would mask the severity of COVID-19 in the mortality rate data. On the other hand, there are other substitution effects, such as self-harm, that have probably increased over 2020, which push up the overall mortality rate from non-COVID-19 (or at least indirect) causes. A much more detailed analysis of all the substitution effects would be required to really know just how much over or under counting is present in the COVID-19 death totals. The official count broadly concords with my simple GAM analysis on the mortality rate. My guess is that if there is bias in the official tally, it would probably lean a touch in the over counting direction, but nothing like the crazy conspiracy theories.
The shocking part of what the data teach us is in the 0-14 year old cohort. I repeat the same analysis and show the long term trend in the figures below. We see that in 2020, the mortality rate for children under 15 years old is up over 20%! That equates to approximately an extra 10 childhood deaths each week across Canada. We know that COVID-19 has a very low mortality rate with children, lower in fact than the seasonal flu, and yet we see a dramatic rise in childhood mortality in the data. This analysis is not causal, but if COVID-19 is an unlikely culprit, it must be some other environmental factor. We know that child abuse and domestic violence has increased as the result of stay-at-home orders. Teachers and school staff have a difficult time detecting abuse and neglect in online classes. When this pandemic ends, it will be very much worth while combing through the 0-14 year old cohort data and unpacking the effects of COVID-19 mitigation efforts on childhood well-being.