Age-Specific Risks for Covid-19 to the Individual Year
Age-based risk factors for Covid-19 have been reported in 10–20 year age bands. We can do better than that. It’s easy to estimate age-specific risks to the individual year, which allows people to assess their personal risk levels more accurately.
TL;DR
We now have reasonably good data on risks associated with Covid-19, but it isn’t being presented in ways that make it easy for people to understand or use. The purpose of this series is to help people more clearly assess the risk of Covid-19 to themselves and to the people they care about.
Check out Figure 8 at the bottom of the article to see the risk level for your specific age.
Who Describes Their Own Age in 10-Year Age Bands?
You’ve probably seen numerous graphs like the one shown in Figure 1, which shows how age affects Covid-19 risk.
These graphs are useful for communicating the general concept that risk increases with age. But they aren’t very good at communicating the risk level at any specific age. As Figure 2 highlights, what happens the day I turn 70? Does my risk increase from 0.9% to 2.4% in one day?
Of course your risk doesn’t increase in one day. It’s been increasing throughout your 60s and will continue to increase throughout your 70s. The graphs in Figures 1 and 2 are really crude approximations of a steadily increasing level of risk, as shown in Figure 3.
Each bar on the bar graph is actually showing the average level of risk for each age band. Or, stated differently, it shows the risk for the mid-point of each age band.
Your risk at the lower end of each age band is lower than shown, and your risk at the higher end of each age band is higher than shown. At age 61 your risk is lower than 0.9%. At age 69 your risk is higher than 0.9%. Your risk is exactly 0.9% only when you’re close to the middle of the age band, that is, close to 65 years old.
Estimating Year-of-Age Risk Factors Using Interpolation
To my knowledge, no governmental agencies or researchers have published year-of-age specific risks from Covid-19. However, more specific risk levels are easy to estimate from available data using the mathematical technique of interpolation.
Let’s look at an example. Suppose we want to estimate the fatality rate for someone age 69. We start with what we know. As Figure 4 illustrates, we know that at age 65 the fatality rate is 0.9%, and we know that at age 75 the fatality rate is 2.4%. What we want to know is what the fatality rate is at age 69.
We know one additional fact that might not be so obvious, which is that 69 is 40% of the way from 65 to 75.
Interpolation is the assumption that, if you have two related scales, and if one factor on one of the scales is 40% of the way from one end to the other, then the related factor on the related scale must also be 40% of the way from one end to the other. This assumption is not necessarily 100% true, but unless we believe that a person’s risk factor really does jump abruptly on their birthdays, it’s a reasonable approximation.
As Figure 5 shows, when we do the math, that means that the fatality rate for a person age 69 works out to 1.6%.
One Small Wrinkle
The midpoints used in Figures 3–5 are the straight arithmetic midpoints of the age bands. For example, I showed 65 as the midpoint of the 60–69 age band because it is the midpoint of 60–69.999. (The real age band is not 60–69, it’s 60–69.999.)
The more accurate midpoint of each age band should be calculated using a weighted average of the actual number of people at each age. Up through age 60 the difference between this kind of population-weighted midpoint and the arithmetic mid-point is de minimis, but for the 60–69 age band the difference is a quarter of a year, and for 70–79 it’s two-thirds of a year.
The specific differences for each age band are shown in Figure 6.
Now that we have more accurate age-band midpoints, we should revise the interpolation shown in Figure 5 to use the more accurate midpoints. That revision is shown in Figure 7.
As you can see from Figure 7, in this specific case the risk factor of 1.6% for age 69 remains unchanged. However, risk factors for some of the other ages do change.
True Age-Specific Risk Factors
We can go through the same process we went through in Figure 7 for all the other ages, using the population-weighted midpoints for the age bands, and create a table of age-specific risk factors for every other age. The results of those calculations are shown in Figure 8.
Limitations and Considerations
Interpolating in this way is an exercise in approximation. The numbers in Figure 8 are not based on fatality data per se; they amount to additional precision that can be inferred, approximately, from rough data.
There are a few additional limitations to this approach.
The first limitation is that we can’t interpolate past the midpoints of the youngest and oldest age bands.
On the low age side, we know the midpoint of the age band is 10.15, and we know the risk factor is .0012%. But since we don’t have data on the risk to people younger than 10.15, we have no basis for interpolating risk factors at younger ages. That means that all the factors below age 10.15 are the same. Additional factors for ages 11 and 12 look the same because of rounding.
On the high age side, the fatality data stops at 80+. We know the midpoint of the age band below is 74.35, and we know its risk factor is 2.4%. We know the risk factor of the next age band is 4.4%, but we don’t know its midpoint, because it’s described as “80+”. For that top range I defined the midpoint to age 85. US census data shows 6.1 million people age 80–84, and 6.5 million people age 85+. With those numbers, the true midpoint must be within a year of 85.
As with the young side of the age band, since we don’t have data on fatality rates older than age 85, we can’t interpolate past age 85, and every older age is thus assigned the same risk factor.
Why Do Year-of-Age Specific Risk Factors Matter?
The risk factors in Figure 8 allow a person to more accurately assess their personal risk than 10 year age bands do. If you’re in your late 50s and you’re feeling pretty good because the average risk factor from age 50–59 is only 0.30%, check the table. At age 58 your risk factor is 0.50%, and when you turn 59 it climbs to 0.56%, which is almost double the risk factor at the midpoint of your age band.
At the beginning of the article, I stated that a person who turns 70 does not have their fatality risk increase from 0.9% to 2.4% the day they turn 70. Indeed, as you can see from the table, their risk increases from 1.6% to 1.7%, and of course that doesn’t all occur in one day either.
Although this article has presented Covid-19 risks more precisely than they have been presented elsewhere, there is still one piece missing, which is the presence or absence of comorbidities. I will show how comorbidities affect the personal risk picture in the next article in this series.
This is Part 4 of a 5-part series on the fatality rates of Covid-19:
- Part 1: Establishing an overall base IFR for the US
- Part 2: Age-based IFRs
- Part 3: Variation in IFRs across states and countries based on demographics
- Part 4: IFRs by individual year of age
- Part 5: IFRs with and without co-morbidities
More Details on the Covid-19 Information Website
For more US and state-level data, check out my Covid-19 Information website.
My Background
I have been focused for 20 years on understanding the data analytics of software development, including quality, productivity, and estimation. The techniques I’ve learned from working with noisy data, bad data, uncertainty, and forecasting all apply to COVID-19.
