My interest in analysing the pandemic began in early April with the initial published data on cases and deaths. It seemed to me that at the time, the deaths per case rate (then around 6%) was higher than the officially published estimates (1 to 4%), and was slowly rising from week to week. Of course I realized that was to be expected since, at any point, the accumulating deaths would lag the accumulating cases by about a week because it would take about seven days for someone to die from the disease after being diagnosed.
Instead, I then looked at the number of deaths and the number of "resolved" cases -- the survivors -- which may be lagging in the opposite way, it taking longer to show that someone is no longer ill than it takes to die. That number has remained around 9% of resolved cases (survivors plus deaths) every week I updated the numbers. Adding to those results the estimated 30% of "asymptomatic" cases -- cases undetected because the person does not feel sick (and does not die) -- and the overall fatality rate drops to something between 4 and 6%, still above the WHO and international estimates.
I started looking into these results and discrepancies, and quickly hit on the age of the person as the principal factor in determining risk of death. The graphs of Ontario deaths by decadal age range, normalized to a population of 100,000 showed a distinct exponential curve shape, so I took their data and plotted it on a logarithmic scale. I was shocked to find how precise the exponential trend was. I redid this analysis every two weeks and in June, got the results shown in the following graph.
Here I have plotted three trends by age group, using an X-Y plot instead of the usual bar chart to allow further analysis. Each age group is therefore one decade of people; e.g. the 30 to 39 year datum is shown as age 35. I plot the number of cases up to June 8 per 100,000 population in that age range for Ontario, by age group, from 0-9 years through 90+ years old (blue squares). More description about that curve later.
The orange diamonds plot the number of deaths per 100,000 population up to the same date. It was this straight line that first intrigued me -- an almost perfect exponential relationship! However, since the number of deaths continue to accumulate over time, I decided to further normalize the data, by dividing the orange diamond data by the average risk of death for the entire population, to get the yellow triangles, which represent the relative risk of death (percentage) by age, which should not change over time.
The yellow triangles are, of course, also a straight line, and I have included the trend line as an exponential equation. The R-squared value indicates how good the fit is over eight orders of magnitude, from 20 to 95 years old. (Below 20 years old, the numbers are estimates since, at that date, there had been no deaths in that age range.) I imagine such close a fit is almost unheard of in medical and disease statistics -- a fascinating discovery!
To better explain the yellow trend line, the average relative risk of death is 1.00 by definition, and that occurs around age 67 years old. Older people are at more risk, as everyone knows, while younger folk are at reduced risk. However, nowhere else have I seen it shown how important this age factor is, and over such a wide range. Indeed, between age 20 and age 95, the risk of death from this disease doubles every 5.77 years older you are! An 85 year old is therefore over 450X as likely to die from COVID-19 as a 35 year old, all other factors being similar!
That is a huge difference, yet rarely talked about. After finding these results, I sent them to the Ontario public health people, my elected member of the provincial parliament (MPP), and the local health authorities. I figured they would want to know these results and perhaps apply them to choose public policy going forward. I heard nothing back, so I wrote a letter with the results to my local community paper. The letter got published and I got a couple of private responses, but again, no public, or broader-media recognition. I guess I am not an "expert" so no one pays me any attention.
There are some further things to note in this data. For the oldest Ontarians, those over 90 years old, the disease has been devastating. Fully 35% -- more than a third -- of those who got this disease died! That is comparable to the fatality rate for the black plague in medieval Europe. This was reflected in the huge number of deaths seen in nursing homes or "long-term care" facilities in the early months of the pandemic, a black mark on Ontario and how we care for our oldest citizens.
If applied, these results could have an important influence on public health policy. Clearly, people over 70 need to be kept safe from contact with infected people, and monitored closely. This is well known but never quantified as shown here. On the other hand, people under 50 years old have a very low risk of death, especially those without underlying health conditions. Perhaps they could get back to work with minimal constraints? Even more, with few cases and almost no deaths for people under 20 years old (read "students"), there is almost negligible risk if they are otherwise healthy, so re-opening schools with few constraints looks feasible.
The true danger lies in mixing the young with the old: elementary teachers nearing retirement, retired folk driving school buses, kids living with their grandparents, young personal-care workers serving in nursing homes, etc. There would have to be some careful policies put in place to avoid contagion in those, relatively few situations. People between 50 and 70 could decide for themselves what risks they are willing to take, based on their own home, work, life, and health situations.
Such an approach would go a long way to re-opening economies, and thereby minimizing the non-health impacts of the pandemic. Governments in various places seem to be headed in this direction, although hesitantly and still with severe constraints on the young about distancing and masks. Despite ongoing hype about increasing "cases", worries about the fall influenza, and comparisons among different countries' and states' experiences, there does not seem to be general recognition of the results I have graphed here.
I continued to track the Ontario COVID-19 numbers to see how the results would change over time. A month after the above plot I redid the analysis and got the following graphs. As you can see, they are very similar. The number of cases and deaths per 100,000 people has gone up slightly as you would expect, but the overall shapes have remained the same. There was one death of a child under ten, which skews the bottom end in a non-statistically relevant way. For the "relative risk of death" curve (green triangles in this graph), between ages 20 and 95, the results are almost identical, fitting the same exponential equation as a month earlier. The doubling time for the death risk is also almost identical at 5.85 years. Since July there have been fewer new cases to add and even fewer deaths in Ontario, so the results are essentially unchanged as of this writing.
One further note about the top curve (blue squares). between 20 and 80 years old, this curve is almost flat, with about 250 cases per 100,000 population. This suggests that COVID-19 is just as easy to catch at any age -- an equal opportunity disease -- and that it is the fatality that varies with age, not the contagiousness. However, both ends of the curve are different. Below age 20, there are fewer cases found per 100,000 people. This probably reflects that fact that young people don't generally get sick from this corona virus, so many infected people would not be tested to become "cases". One could, in principle, look at the difference between the data points and the 250 average to estimate what percentage of people under 20 had the disease without being tested, at least in comparison to the same percentage for older adults (unknown, but estimated around 30%).
The top end of the curve is more troubling. More people per 100,000 over 80 years old got this disease than those under 80, and it is even worse for those over 90. This may have several causes, but surely reflects the rapid spread of the disease through unprepared nursing homes as we saw in April and May. Another possibility is that some of those folk may have actually died from other causes -- they were in nursing homes after all -- and were then found to have COVID-19, and so were counted as having died from it rather than just with it.
I have stopped analysing COVID-19 cases and deaths in Ontario now that they have levelled off, but I wanted to capture all these thoughts and results, if only for posterity. If you are reading this, you can compare the results where you are to see if they mirror Ontario's experiences so far. These results may also help you decide how worried you should be about this virus, depending on your own age and that of your loved ones. If it merely helps some parents feel better about sending their kids back to school, then it has been a useful exercise.
2021 Update
I dug out the Ontario cumulative case and death numbers up to January 25, 2021 and repeated the same analysis. In the following graph, I only include the percent risk of death from COVID. That is, for each age group, the percentage of cases over the past year who died. The exponential trend is still clear, albeit not quite as precise. The risk doubling time is still 5.8 years of age, and people over 90 years old have a 30% chance of dying if they get the disease, slightly lower than reported above. This may reflect better care being taken in long-term care facilities?
The average risk of death has dropped considerably to about 2.5%. That is largely because it is mostly younger people who are getting COVID-19 now, but the risk to young people is still very low, less than the death risk from the flu for people under 40 years old!
With vaccines being widely administered over the next months, one hopes the overall number of cases and deaths will stop increasing everywhere. As the vaccines are first given to the oldest and most at risk populations, one might expect this curve to shift slightly, but I hope there will be many fewer deaths going forward than over the past ten months. If so, then this curve will not change significantly.
