Covid-19 and Antibody Math (for English majors)

I’m taking a break from talking about painful knees today because, well, it’s coronavirus all the time for everyone right now, it seems.

As ordinary people push harder to be allowed to return to work, and for their lives to go back to normal, health experts have been puzzling over how best to accomplish this.

One idea involves widely testing for antibodies, to see who has had the virus (and maybe didn’t even know it). Anyone with antibodies would then get some kind of “free movement” badge, I guess, and could go wherever they want without fear of becoming infected.

But of course it’s not that simple, as we are being told:

... we still know very little about what human immunity to the disease looks like, how long it lasts, whether an immune response prevents reinfection, and whether you might still be contagious even after symptoms have dissipated and you’ve developed antibodies. Immune responses vary greatly between patients, and we still don’t know why.

And so: lots of questions being asked, good questions. But what I found more intriguing was a Twitter thread I stumbled upon recently talking about, let’s say, “antibody math.” It was written in Twitter shorthand, and flung about phrases like “Bayes theorem” and “Pr(are+|test+).”

So yeah: practically unreadable.

But I thought it would be fun to unpack its message about the reliability of antibody tests. After all, if you’re going to get a badge that says, “Hey, I’ve got Covid-19 immunity!” you’ll want to know if it’s worth the paper it’s printed on.

The accuracy of antibody tests, it turns out, is basically measured two ways: by “sensitivity” and “specificity.”

“Sensitivity” is the percent chance that, if you indeed have Covid-19 antibodies, the test will detect that. So if a certain test has a sensitivity of 95%, that means that out of 100 people that actually have the antibodies, it will correctly identify 95 of them (on average).

“Specificity” is the interesting flip side: the percent chance that, if someone doesn’t have the antibodies, the test will get that right as well. So a specificity of 95% means that the test will incorrectly report the presence of antibodies, when they’re not there, only 5% of the time.

Now, it so happens, that if you dial up the sensitivity on a test, the specificity drops, and the other way around. So there’s a tradeoff between the accuracy of the two variables.

Okay, now for the “antibody math,” using an actual FDA-approved test by a company called Cellex. It has a “sensitivity” of 93.8% and a “specificity” of 95.6%. That sounds pretty good! Suppose you were issued a Covid-19 antibody badge based on a Cellex test.

What are the chances that you actually have the antibodies, and the test didn’t make a mistake?

This is where things get really, really interesting.

First, we have to make an assumption: how prevalent is Covid-19 in the population being tested? For this example, let’s say it’s fairly rare, and only 1% of the population has had the disease.

Let’s suppose we’re testing 100,000 people (by using this number, the math works out more easily, and we don’t even have to use decimals!). Let’s take that population and divide it into 100 slices of 1,000 each (so each percentage point is represented by 1,000 people).

We expect that 1% of our population, or 1,000 people, have had the virus. The test will detect 938 of these people because it has a “sensitivity” of 93.8%.

Now for the “specificity.” Let’s take the next 1,000 people in line, all of whom have never had Covid-19. The test mostly gets this right, but mistakenly classifies 44 as having the antibodies. (If you’re unclear how I got there: it correctly identifies 95.6%, or 956 of the 1,000 people, as not having the virus. The remaining 44 thus become “false positives.”)

44 may not seem like much. But remember: this is only one percentile that we’ve looked at here. And 99% of people haven’t had Covid-19. So we have to multiply that 44 times 99. Suddenly – yikes! – we’ve got 4,356 false positives out of our population of 100,000.

Now it’s time to wrap this up. The test identifies 938 people correctly. But it messes up on 4,356 more. That means we’ve got 938 positive antibody test results that are correct out of a total of 938 + 4,356.

Do the division, and that gives you 17.7%, which means a positive result implies a less than one in five chance that you actually had Covid-19! It would be a disaster to release people into the workforce based on this scenario.

The problem is, the number of false positives really distorts the accuracy for a rare disease. But if we tweak the numbers, and assume 10% of the population has had Covid-19, the math becomes more comforting (I’ll spare you the steps, but they’re the same as above).

In this scenario, if you test positive, there’s a 70.3% that you did have the coronavirus. Maybe still not high enough to get comfortable with, but a step in the right direction.

So what can we learn from all this?

* Antibody tests will be more effective in areas where the Covid-19 infection is relatively high, such as New York.

* If we decide to make antibody tests a key part of our “return to normal” plan, it’s important to first do enough random sample testing to get a good handle on what percentage of a given population has actually had Covid-19, because that number is a key input for accuracy.

* We can overcome the inaccuracy problem, to some extent, by testing someone multiple times. For example, in the example above where the test is 70.3% accurate for finding Covid-19 antibodies, testing three times lifts that percentage to more than 97% -- which is pretty good.

Okay, I’m tapped out for now. Hope someone out there finds this edifying (and useful).

Cheers, and keep moving those knees!

How to Move Your Knees in Quarantine

First, an update from last time, and thanks to all those who have expressed concern:

We live on Long Island’s north shore, in Nassau County: a beautiful place, God’s own heaven on earth it sometimes seems.

But Nassau County, as of today, has almost 14,400 cases of Covid-19. That’s more than the vast majority of U.S. states. Per capita, that’s even more than New York City. All this infection has blown up in a county I can drive across in less than half an hour. It’s a bit frightening.

But I don’t feel stress. My family, for now, is healthy. My 6-year-old son, who has pronounced anti-social tendencies and sometimes lives in a box house I helped him build, is flourishing and doesn’t seem to care if he ever sees a school again. :)

My wife is Chinese, and her mother keeps calling and asking if she is okay. She said the Chinese don’t understand why America wasn’t more prepared for this. We saw the images coming out of Wuhan. But that’s a story for another day, and perhaps another blog.

Today I want to briefly address this problem: how do you move your knees enough when you’re inside most of the time?

This is the easiest question for me to answer, because early in my knee recovery, much of my self-administered treatment came in my apartment. When I realized that walking, walking, walking outside was actually making my knees worse, I realized I had to severely cut back.

So I started doing walkarounds around my apartment. I’d just walk back and forth, every 10 minutes, then rest my knees in a comfortable position (e.g., I’d lie on my back with my knees slung over the edge of a couch). I lived in a small apartment, so there wasn’t a lot of room to move. But you really don’t need a lot of room.

The thing is, it’s nice being able to walk outside. You can enjoy the sunshine, the flowering trees, the birdsong. But you can also move in a space as small as a jail cell. It just takes some imagination and persistence to find ways to move your knees.

So how about all of you? How have your activity routines changed during these unsettled times? Drop a comment below; I’d love to hear from you! 

The Only Post I Can Write Right Now

I was thinking about what to write about this week and realized there is only one thing to write about, and that’s what everyone is thinking and talking about.

I live on Long Island, in New York. In my county of some 1.4 million people, there were perhaps a handful of coronavirus cases a little more than a week ago. Today there are almost 2,000.

I have seen the panic: long store shelves completely bare of toilet paper; pasta and rice stocks wiped out. I have also seen the blithe indifference to the danger, in a video of a crowded Florida beach during spring break. College students milled about in close proximity to total strangers.

I have two thoughts, and there is a connection to knee pain, and getting yourself in the right frame of mind to win a long battle against what seems like a formidable foe.

First, this is a time to make decisions based on reason, not emotion:

This virus is only rarely a death sentence. Many mild cases aren’t being counted in the tallies of total cases because of poor testing. That skews the “case fatality rate” misleadingly higher. In South Korea, whose widespread testing has been praised, I recently saw a death rate of 0.7 percent, which means 7 people in 1,000 die. Many of those who don't make it are older or have underlying health problems.

One thing to take some solace in: there are either no, or very few, children under the age of 10 who are dying.

Yet this epidemic remains a very, very serious problem. A lot of people, young and old, are winding up in the hospital and are being put on ventilators to help them breathe. This is not a run-of-the-mill flu, and that cannot be overstated.

The nature of this crisis threatens to overwhelm the health care system in America. We don’t have enough ventilators, enough masks, enough tests. Our government, sadly, wasted a couple of months when it knew the virus was spreading abroad and when it could have been preparing.

Second, a for-profit health care system, like the one in the U.S., is the worst possible one to have at a time like this:

Americans who feel secure knowing they have employer-paid health insurance should pause and think again. What if they lose their job, as so many are now? Or what about the tens of millions of people who don’t have health insurance, who will avoid getting tested and try not to go to the hospital to avoid being saddled with a $34,000 bill they can’t pay?

They may be in the Target where you’re buying your groceries. They may be delivering that Amazon box to your doorstep, even if they’re sick, because they can’t afford to take a day off. They may contribute to the spread of the virus because they are effectively outside the health care system.

This is tragic, insane really (as I’ve said before) for a nation this rich to have health care that only works for part of its population. We really need to fix that. We need to take care of everyone. In addition to that, we can have an extra layer of private insurance, if people really want that.

In the meantime, much like conquering knee pain, it’s to our advantage to take a positive attitude toward beating this virus. Right now life is surreal. We’re living through what feels like a bad movie. But we shouldn’t panic. The road ahead may be tough at times, but we’re tougher.

And Now for Something Different ...

I thought I’d try something different today.

Every day, people who are brand new to the world of knee pain are anxiously sorting through advice and ideas from websites they have frantically skipped through, hoping to find the formula for what works.

So what I’d like to do is invite people to submit questions below, related to knee pain. They can be questions directed toward me, and my book, or can be just questions about knee pain, and any of the problems related to it.

Obviously, this exercise is more suited for first-time visitors, but others feel free to jump in as well.

Then, what I’ll do in successive weeks, is pull out questions and devote blog posts to them. In cases where I don’t have answers, I’ll invite other people here to chime in.

One of the strengths of this blog, I think, is the community of rational, inquisitive, determined knee pain sufferers who regularly drop in.

Let’s see how it goes! What people care most about, I’ve found, are specific answers to specific questions, and in many cases, their questions are shared by many others.

When a Bad Knee Just Gets Worse

I came across this tale recently. It begins with our protagonist limping a little.

A few Tuesdays ago, I noticed Joel limping a bit, dragging his right leg. I asked him what was the matter. “Knee’s a little sore. Don’t know what I did,” was his response.

“Maybe you should rest it,” I suggested. “Do you need some ice?” 

“No, I don’t need ice. Good grief. Geesh. You think I’m a weakling?” he grumped.

Now what happens?

This is an interesting juncture for someone who has just developed knee pain seemingly out of the blue. The sudden, unexplained onset of knee pain can be frightening. It’s one thing if you bang your knee hard against something and then it becomes sore. A simple line can be drawn between cause and effect.

But if you can’t even recall what you did? Yikes. That’s not a good sign.

Well, Joel decides his leg needs more exercise. He chooses to walk downtown to run errands instead of drive. The next morning? Yup, you guessed it:

The knee is swollen. The limping is worse.

So he drags himself around the house for a while. He rests on the couch, an ice pack over the hurting joint. He starts wearing shorts, because his jeans won’t slide up over his swollen knee. His wife (narrating all this) gets exasperated with him.

Finally he breaks down and sees a doctor. An MRI is done. The report comes back with a lot of impressive-sounding jargon like:

“Large joint effusion,” “periarticular fluid signal and edema, greatest in the popliteal fossa and lateral soft tissues,” “subcutaneous edema in the prepatellar region, complex cystic structure along the later [sic?] popliteal fossa, adjacent to the lateral head of gastrocnemius.”

Of course the effusion and edema just mean that Joel has swelling. His doctor tells him the test confirms that his knees are getting old and orders medication for swelling and pain. And that is pretty much where the story ends.

But after reading this, I found myself thinking: Where did things go wrong for Joel, and why?

Things really went wrong when he decided he needed more exercise. So think about this in terms that have become familiar to visitors to this website: Joel’s envelope of function had narrowed. His knee joint hurt. It was less capable of handling stress.

So what does he do? He goes out and stresses it more than he would during a normal day when it wasn’t hurting!

Where the heck is the logic in that? What could have possessed the poor guy?

Here we can only speculate, but:

What’s the message you hear constantly from physical therapists trying to rehab bad joints? You need to strengthen your legs to protect the joint! Build up your leg muscles!

One can just imagine poor Joel Googling around for answers for his condition, landing on this message repeatedly – strong muscles protect weak joints! – and deciding, by God, he was going to strengthen those leg muscles and banish that knee pain!

Building up leg strength is a great idea ... before you have bad knees. Once you do, you need to move much, much more carefully. This is something that Joel has now presumably learned. That, and an MRI often isn’t really very useful. :)

Open Comment Forum: What Discovery Has You the Most Excited?

Okay, I'm going to hand the controls over to all of you.

As I've said a number of times, as I move farther away from my knee pain days, and as I exhaust new subjects to write about, and also -- frankly -- as I find myself increasingly strapped for time, I am writing shorter and also letting all of you talk among yourselves more often.

At this point, turning over the comment section to readers and letting you discuss issues that you're having, with people chiming in to suggest ideas, is probably most valuable.

So here's a question to get everyone started (or feel free to ignore this suggestion, and just talk about whatever you want to!): What's the discovery you've come across, say in the last five or six months, that has you the most excited when it comes to healing your knees?

It could be a scientific discovery. Or if you want to broaden the topic a bit, it could be an article you came across or a personal story you read about a knee pain sufferer who tried something that worked that you think may work for you too.

Anyway, open comment forum, so everyone's welcome to share their thoughts on anything!

Cheers, and I hope everyone is doing well in the new year.

The Villain in the Story: Inflammation

I’ve written about chronic inflammation a number of times. It’s sort of like writing about the hazards of being overweight, a subject that I think deserves multiple posts, even if they do become a bit repetitive.

My thoughts returned to inflammation recently because of an article in the New York Times that I happened to see in a newspaper I scavenged one day on my commuter train into the city.

Near the top is this paragraph, written with plenty of dramatic flair:

Specialists in the biology of aging have identified a rarely recognized yet universal condition that is a major contributor to a wide range of common health-robbing ailments, from heart disease, diabetes and cancer to arthritis, depression and Alzheimer’s disease. That condition is chronic inflammation, a kind of low-grade irritant that can undermine the well-being of virtually every bodily system.

Chronic inflammation is a dangerous beast. It’s hard to understate this. I had it. It started in my knees and, I’m convinced, spread in small, practically undetectable ways throughout my body. I say this because at one point (as readers of my book know), I went in for a blood test, thinking I might have rheumatoid arthritis, after experiencing weird problems with multiple joints.

My blood test was excellent: no signs of systemic inflammation. However, I am still convinced that there was something going on throughout my body that was related to my troubles with my bad knees. A knee doesn’t exist in perfect isolation. It’s not walled off from the rest of the body.

At one point I had bursitis in an elbow. And I had throbbing, constant back pain.

Now, being blissfully free of knee pain for a decade now, I see the inflammatory aspect of the condition as even more alarming than I did back then. To escape knee pain, I think it’s partly a race against time, if you have constant burning, or inflammation. You need to get beyond that, and as soon as you can.

Inflammation of course is a natural reaction by the body to injury, or even to vigorous exercise. What becomes a problem is when the inflammatory response doesn’t die down, when whatever is prompting the reaction continues to fire up the immune system. It becomes a problem as we age, the Times notes, because “immune responses become less regulated.”

So what’s the solution? The Times mentions five recommendations:

* Fix your diet. A diet focused on fruits and vegetables is less inflammatory than one full of foods that are heavily processed, deep-fried, or sugar-sweetened.

* Lose weight.

* Make sure you get enough sleep.

* Minimize mental stress in your life.

* Be careful about overuse of antibiotics, antacids and nonsteroidal anti-inflammatories. They can kill off good bacteria in your stomach and lead to a “leaky gut” that lets bacteria loose in your body that encourage inflammation.

* Exercise regularly.

How do you rank on these five recommendations? Personally, I know I could be better. My diet isn’t great, but I am very fastidious now about maintaining a lean weight. On sleep, I slip behind (like most people) during the workweek. Sometimes I feel stress building up.

Where I can excel now, thank goodness, is in exercising. I work out hard on the weekends.

What about you? What steps are you taking to control out-of-control inflammation?