Sunday, October 21, 2012

Yet More Proof Your Doctor Isn’t Infallible

One of the first criticisms I got about Saving My Knees went like this:

“This is a lousy book. All he does is complain about how all his doctors and physical therapists are wrong and I can’t tell if he got better anyway.”

(By the way, if anyone else is similarly puzzled on that last point, I can unequivocally state that yes, I got a whole lot better. My knees are fine today.)

Read between the lines, and the reviewer appears to be annoyed that I have the temerity to suggest there’s something wrong with the expert advice I was given on treating knee pain.

Why such a harsh reaction?

I think among certain people there is a reflexive, total deference to the opinions of “experts,” even though what is accepted as truth by one generation of experts may be soundly rejected by the next. (History is full of examples; in Saving My Knees I mention the once widespread medical practice of bloodletting to cure a host of ailments, which has been debunked as nonsense.)

Today I’m going to show you that your doctor is very much human -- and not an infallible expert at all -- with a bit of math. It’s taken from Fooled by Randomness by Nassim Taleb, who himself has borrowed the anecdote from Randomness by Deborah Bennett.

Medical doctors were given this problem to solve:
A test of a disease presents a rate of 5% false positives. The disease strikes 1/1,000 of the population. People are tested at random, regardless of whether they have the disease. A patient’s test is positive. What is the probability of the patient being stricken with the disease.
(If you want to try to figure it out yourself, go ahead. I start to disclose the solution immediately below.)

Most doctors -- more than four out of five -- got this wrong. They answered 95% because they focused solely on the accuracy rate. But the question being asked isn’t, “How accurate is the test?” The question, stated more fully, is “What’s the probability the patient has a somewhat rare disease if a test that’s wrong 5% of the time says he does?” And the answer to that question is very different: less than 2%.

Taleb explains how he arrives at that figure:
Assume no false negatives. Consider that out of 1,000 patients who are administered the test, one will be expected to be afflicted with the disease. Out of a population of the remaining 999 healthy patients, the test will identify about 50 with the disease (it is 95% accurate). The correct answer should be that the probability of being afflicted with the disease for someone selected at random who presented a positive test is the following ratio: number of afflicted persons/number of true and false positives. Here, 1 in 51.
Got that? The difference between the right answer and the most commonly mistaken one is very significant. It’s the difference between “you almost surely have the disease” and “you almost surely don’t have the disease.”


There are a few points worth making here. The less interesting one, to me, is that doctors often can be mistaken.

The point that I find more interesting (and empowering) is that you don’t have to be a medical school graduate and a practicing physician to analyze information about medical conditions (claims, studies, empirical evidence) and come to conclusions that, in some cases, may be superior to those held by so-called experts.

What’s more, when it comes to your bad knees, you do know more than your doctor on one very important subject: how your knees behave (what they like and don’t like, what causes pain, etc.)

So if a doctor says, “Ah, your knees will never get better” (which is what I was wrongly told), remember: doctors can be wrong -- very wrong.

After all, four out of five missed the correct answer to a basic statistics problem. :)

Extra credit: Did you notice Taleb's approach to solving the problem? Out of a population of 1,000, he removed the person who has the disease (remember, it strikes 1 out of 1,000 people), then calculated that 5% of the remaining 999 were false positives (49.95). So the chance of having the disease is 1/50.95 or 1.9627%.

Alternatively, you could apply the 5% rate of false positives to the population of 1,000, resulting in 50 people who wrongly test positive for the disease, then add the one person who actually has it. So the chance of having the disease this way is exactly 1/51 or 1.9608% -- a bit different.

So, given the information as laid out in the problem, which answer is correct, and why?

Note: The difference in the results from the two approaches is trivial, so you may think it hardly matters which one is correct. While that's true for this example, it wouldn't be for another, say where 30% of the population has some disease and the test has a rate of say 20% false positives.


  1. Hi Richard
    But what is if I certainly have the disease as MRI scan proves it, does it mean I will never fully recover? MRI showed flattened cartilage in my knees. Do you think there I no hope for me? I am 35..

    1. I'm not sure what "flattened" cartilage means. Probably thinning cartilage? I would think there's definitely hope for you. I would look for a way to get active -- gently, gently, gently. Swimming? Easy cycling? Walking? Start out slowly (and work with a physical therapist if you know a good one). Recovery is a long-term process (many months or years).

    2. Depending on where your knee pain is at, swimming could be too much strain on a knee. If so, I will put in a plug for gentle knee water therapy which seemed to help me significantly. Not "water aerobics" or even walking in water. But, even gentler stuff like slow movements in the deep end while suspended from a floatation belt. Good luck!

    3. Yes, good point about the swimming. As I described in Saving My Knees, I used armbands on my ankles to keep them afloat in the pool so I didn't have to move my knees much while swimming, so as not to irritate them. Slow movements in the deep end while using a flotation belt sounds like a pretty good activity.

  2. Lana: Look for my post under the name "Pat" in July or thereabouts. I described how doing what Richard suggested--small resistance, high reps--improved the pain in my knee very dramatically. I just walked barefoot in my apartment for 60 steps every hour or two--still do it from time to time; my knee always will feel better! I am 66 and was at the point of scheduling knee replacement surgery because the pain just kept getting worse, even with PT, Synvisc shot, etc. I was told my cartilage was of "poor quality" by four different surgeons and that knee replacement was the only solution, since the other stuff hadn't helped.

    Then I chanced on Richard's book on Amazon and about a week later, somebody told me about a great trainer nearby who had fixed her knee. He is very creative and has me work (gently) all the different parts of my body--sort of a combo of dance moves/strength training/and PT--I use a stability ball, a Bosu ball, etc., no machines. I was very lucky to find him when I did, just after I read Richard's book. My condition has improved incredibly and stabilized to slight pain (esp after exercise), which I treat with icing and various stretching exercises and just keeping up the twice a week training and some walking for cardio. I almost never even have to take a pain pill! I've gotten much better coordinated, have better posture, better balance, etc.--gradual improvement over the last 6 months, and I'll continue with the trainer. At this point the only thing I don't do that I used to is play tennis--I probably could go out and hit tennis balls but I'm afraid of running on hard courts (we don't have clay courts near me). I can now walk 30 minutes on sidewalk, go on an elliptical or upright bike for 30-40 minutes (actually elliptical always makes my knee feel better even if it's been hurting). Don't give up! Good luck.

  3. Dear Richard, Knee Pain and Pat, thank you for supporting me and I am so sorry that I didn't reply sooner. I was in very bad mood because of the knee pain. Any physical activity, even just swinging my legs very very gently from the side of the sofa makes pain worse. MRI shows this: there is medial patellar facet chondral irregularity with a chondral flap. Features are suggestive of chondromalacia patella. I damaged my knees at the hot yoga, when I came out of the squat too quickly and twisted my knees with a lot of pressure on them. This was last December. I continued going to yoga every day for about 2 months as the yoga instructor said this yoga would heal my knee. Then I was doing yoga for another 6 months, 3-4 times a week, I just can't believe how stupid I was. My right knee eventually became much worse about 10 days ago and my left knee clicks more often and a bit sore (it started clicking after one of yoga postures, it clicks when I go upstairs or get up from a sitting position). I have been putting lots of pressure on my left knee, overcompensating for my right knee. I am concerned about a flap in cartilage in my right knee, the pain is on the edge of the top of patella and movement makes it worse, I think it might be because of the flap. I think I will probably have to have the flap removed. I will only see the doctor on the 22nd November. Sorry for the long rant..

  4. Hi Lana, sorry you have been in so much pain. Let us know how you are doing.