Understanding cumulative risk

The health implications of repeated COVID infections

If you gamble with your health long enough, at some point your luck will run out.

Almost five years into an ongoing pandemic, most people have had COVID at least once. For many people, a bout of COVID can come with symptoms that are not that different from a head cold, and often, people can have COVID without realizing it.

At this point, we have gone back to “living our (pre-pandemic) lives”, which - for most people - means taking no precautions at all. It’s common to hear people use the term “during Covid”, referring to the pandemic in the past tense. The social pressure to stop trying to avoid COVID is intense. It’s endemic now, so we have to learn to live with it, which means that we should accept an annual COVID infection as some sort of “natural booster”. Or so we’ve been told.

Of course, it would be helpful if someone told the virus this as well, because it doesn’t seem to have gotten the memo. Rapid viral evolution, fueled by the unmitigated spread of COVID has created an unpredictable situation, with repeated waves of disease spaced only months apart. We are, in fact, still in an active pandemic, as the WHO has quietly acknowledged.

A couple of years ago, a team led by one of us (A.C.) predicted that people who don’t take precautions to avoid COVID can expect to get it about twice a year (once a year if boosted on an annual schedule. (This number is in broad agreement with the findings from wastewater data). “Expert” predictions that repeated COVID infections were likely to be very rare or present with less severe outcomes over time have not been supported by the data. Because some of the health risks of Covid are irreversible, it's worth digging a little deeper into the practical implications of that annual COVID infection.

The first thing to know is that COVID is not a cold, it's a car accident. It spreads throughout the body, impacting many different organ systems. Some percentage of people who get COVID end up with Long COVID, a debilitating cluster of symptoms that involves fatigue and reduced cognitive ability. A surprisingly large percentage of people who get COVID end up harboring the virus in their bodies persistently (this may or may not overlap with Long COVID). Separate from those two categories of delayed harm, many individuals infected with COVID have delayed health effects (heart attacks, strokes, kidney damage) that are in some cases progressive. It's not unusual to get into a car accident and be just fine, but a lifestyle that involves getting into a car accident once a year comes with a reduced life expectancy.

This makes sense if we think about it from the concept of cumulative risk. Much of the (spurious) argument around COVID benefiting our immunity has centered around the persistence of biomarkers of immune response, neglecting the persistent damage that infection can cause.

What is the cumulative risk of getting Long COVID after more than one COVID infection? According to data gathered by Statistics Canada, the risk of developing symptomatic Long COVID looks like this after each successive infection:

Two questionable claims have been made in the media about the risk of Long COVID after a COVID infection — one, that the per-infection risk declines with each successive infection and two, that risk may be limited to a subset of individuals. Looking at the STAT Canada data, what can we infer about those claims?

The first thing we notice in the STAT Canada graph is that the risk of Long COVID from a single infection is about 15%. Let’s assume for a second that everyone is equally susceptible to getting Long COVID, and that the per-infection risk does not decline after each successive infection. What would the probability of developing Long COVID look like, after the second and third infection?

A simpler way to think of this at first is: “If I flip a coin three times, what is the chance that at least one of them lands heads up?” The probability of NOT getting symptomatic Long COVID from an infection is:

1 -0.15 = 0.85.

The formula to find the chance that something occurs n times is (p)^n, where p is the probability of the event occurring and n is the number of “successes” we are expecting. So, the chance that someone gets infected with COVID three times and hasn't gotten symptomatic Long COVID from any of them is:

(0.85)^3 = 0.61 which is 61.41%

There is a 61.41% chance that someone doesn't get Long COVID after having been infected three times. In order to know the chance of getting Long COVID from at least one of these infections, we want to know the chance that this DOESN'T happen. For that, you simply subtract this from 1:

1 - 0.6141 = 0.3859 = 38.59%

In statistical terms, this coin-flip sequence is known as a Bernoulli process, and its properties have been studied for centuries. Importantly, a Bernoulli process has a constant probability of outcome each time, even though the apparent likelihood of the outcome declines with an increasing number of coin tosses.

Now, let’s superimpose the risk of Long COVID from this simple ‘coin toss’ mathematical model on top of the STAT Canada survey data. The overlap is uncannily tight. (Note that the purple dots are the STAT Canada data, and the predicted risk is shown in the red curve). Importantly, the red curve is the Bernoulli process — a constant per-infection risk provides an apparently declining marginal risk with each additional infection.

So, if you assume that everyone is at equal risk of getting Long COVID after a single infection, and the risk of Long COVID per infection is constant, the prediction that you can make for the risk of Long COVID after a second and third infection lines up perfectly with the Stat CANADA data.

If you want to get a hands-on feel for our model, we have built an interactive widget that you can play with here. You can adjust the slider to set the risk of Long COVID from a single infection and see what happens to the risk after multiple infections, under the assumptions that everyone’s per infection risk of Long COVID is the same and constant with each successive infection.

With this STAT Canada dataset, it’s important to note that the apparent decline in risk is a simple consequence of the numerical properties of the Bernoulli process, and is consistent with a constant per-infection risk of Long COVID, and not with a declining per-infection risk. Studies looking at associations of Long COVID risk with age, gender, race and comorbidities have found mostly weak to nonexistent associations. Anyone can get Long COVID.

There are some pretty profound implications of this little analysis. Given enough time, it’s highly plausible that everyone — or a very large chunk of the population — will get Long COVID. That’s what happens when the vulnerability is not limited to a subset of the population, and when the per-infection risk doesn’t decline.

“Experts” who specialize in rosy predictions of the trajectory of the pandemic have repeatedly assailed the societal risks of Long COVID as “fear mongering”. But claiming, in an evidence-free manner, that such a risk is not plausible can well be called “calm mongering”. It is the irresponsible dissemination of propaganda that is aimed at managing people’s feelings about the pandemic. Dismissing plausible risks in an evidence-free manner is the very antithesis of effective risk management. Magical thinking alone will not get us out of this situation.

Two years ago, one of us (A.C.) made a prediction in Fortune Magazine that a few years of ‘learning to live with’ COVID (i.e., pretending it doesn’t exist) would lead to a billion cases of Long COVID. A recent estimate pegs the total incidence so far at 400 million cases of Long COVID. Long COVID is well on its way to becoming the world’s most common disease.

It's important to note that the common perception of Long COVID corresponds only to a subset of the long-term and delayed harms of COVID. For example, here is the definition used by the CDC’s household pulse survey: “Tiredness or fatigue, difficulty thinking, concentrating, forgetfulness, or memory problems (sometimes referred to as “brain fog”), difficulty breathing or shortness of breath, joint or muscle pain, fast-beating or pounding heart (also known as heart palpitations), chest pain, dizziness on standing, menstrual changes, changes to taste/smell, or inability to exercise.” Note that this is significantly narrower than that used in the National Academy of Science Consensus definition: “an infection-associated chronic condition (IACC) that occurs after SARS-CoV-2 infection and is present for at least 3 months as a continuous, relapsing and remitting, or progressive disease state that affects one or more organ systems”, which includes “single or multiple diagnosable conditions, such as interstitial lung disease and hypoxemia, cardiovascular disease and arrhythmias, cognitive impairment, mood disorders, anxiety, migraine, stroke, blood clots, chronic kidney disease, postural orthostatic tachycardia syndrome (POTS) and other forms of dysautonomia, myalgic encephalomyelitis/chronic fatigue syndrome (ME/CFS), mast cell activation syndrome (MCAS), fibromyalgia, connective tissue disorders, hyperlipidemia, diabetes, and autoimmune disorders such as lupus, rheumatoid arthritis, and Sjogren’s syndrome”. Also note that neither definition of Long COVID includes other delayed health effects of COVID (immune depletion, heart attacks, new-onset diabetes), which have been demonstrated to occur at a significantly increased risk following an infection.

Some percentage of COVID infections end up being persistent. While some of these persistent infections are associated with Long COVID, not all Long COVID cases have been shown to be associated with persistent infections. At the same time, it’s been shown that even “mild” cases of COVID can cause persistent infections, at least some of which are associated with cryptic organ damage. While some individuals with Long COVID recover, for others, the disease is progressive and can be fatal.

We should thus think of the prevalence of Long COVID in the population as a sort of lower bound biomarker of COVID-associated health risks, indicating that the amount of chronic health harm caused by COVID is at least this high.

Getting COVID repeatedly is not a game we can win in the long-term. The good news is that you don't have to sign up for getting COVID once a year. There are things you can do to avoid that. And if you do get COVID, there are concrete steps you can take to reduce the risk of long-term health outcomes. (For example, try to get vaccinated as often as is feasible!)

But the notion that we can continue to live our lives as if it were 2019 flies in the face of the accumulating facts. Long COVID, and the delayed consequences of COVID infections, are everyone’s problem, and the house will always win in the end if you gamble for long enough.

“Learning to live with COVID” should mean learning to live our lives while rationally mitigating the ever-present risks of an airborne disease with debilitating consequences. Not learning to live while harboring the virus, or the scars it leaves, in our bodies.

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