# Your doctor isn’t as smart as you think. Here’s proof…

**From Dr. David Eifrig, MD, MBA, editor, Retirement Millionaire:**

Your doctor isn’t as smart as you think.

Harvard Medical School researchers found doctors aren’t much better at math than the average Joe. This might not seem important… until you realize this means doctors struggle to interpret the results of screening tests designed to show the likelihood you have a disease.

The researchers asked this question: “If a test to detect a disease whose prevalence is one out of 1,000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease?”

The most popular answer was 95%. The real answer is about 2%. Just 20% of medical students knew the answer, and only 24% of attending physicians got it right. The results were similar for other hospital staff.

While this study was small, it confirms what previous studies have shown. And it points to something I’ve told people for years: Your doctor could be killing you.

In 2012, I wrote about my friend Pat. She was having severe abdominal pain. Her doctors diagnosed her with cancer and pleaded with her immediately to undergo dangerous chemotherapy treatments. But Pat sensed something wasn’t right. She delayed treatment until she had more answers. The decision likely saved her life… The eventual diagnosis was a benign condition easily corrected with minor surgery.

I’ve talked to people who are afraid to question or second-guess their doctor. If you get a test result you’re uncomfortable with or want to know exactly why you need a certain test or medication, ask more people than just your doctor.

**Update from Doc: **

We received lots of feedback about this issue…

We wrote about a study that showed how doctors’ struggling with math can result in high rates of errors in interpreting test results. Without missing a beat… many doctors (and related defenders) wrote in to call me an idiot. Here are some of the more polite messages we got…

*I’m not a doctor, but I think the researchers you cite used a trick question (with incomplete information) in order to skew the results. The supposedly ‘correct’ answer of 2% would only apply if the test were used as a screening tool by giving it to everyone or to a random sampling of people, as opposed to testing only those people with symptoms of the disease. Applied in the way a doctor often uses a test (i.e., to confirm a suspected diagnosis), the chances of a positive test actually being correct would be closer to 95% than 2%.*

*I do get your point, though, and I’m a big fan of your work.* – E.B.

Here’s another…

*The researchers asked this question: “If a test to detect a disease whose prevalence is one out of 1,000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease?” The most popular answer was 95%. The real answer is about 2%. Just 20% of medical students knew the answer, and only 24% of attending physicians got it right. The results were similar for other hospital staff.*

*As I understand this, prevalence is irrelevant as the question pertained to positive results. If 5% of positive results are false then 95% of positive results are true. Please show/explain the math as to how this becomes about 2%.* – T.D.

Let me repeat slowly for all you doctors who didn’t understand…

Research shows that doctors commit a lot of errors when interpreting a particular math problem. The danger is that they encounter this kind of problem daily… and routinely screw it up.

Researchers asked this question: “If a test to detect a disease whose prevalence is one out of 1,000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease?”

The most popular answer is 95%. That’s because people and doctors naturally focus on the test’s accuracy.

According to a variety of studies – not just our own conjecture – a lot of doctors miss this. The first study that showed doctors bungling this calculation was called “Interpretation by Physicians of Clinical Laboratory Results” by W. Casscells, A. Schoenberger, and T.B. Graboys in 1978. Many other studies have shown it since.

The correct answer is the patient has just a 2% chance of having the disease. The truth is, the math is not tricky, although it might be a bit counterintuitive…

The test is wrong only 5% of the time – a 5% false positive rate. If you test positive it’s got to mean that you’re likely to have the disease, doesn’t it?

Here’s the key for doctors and patients… you have to focus on both the disease prevalence and the test’s ability to diagnose the disease. Look at it this way… Only one person in 1,000 has the disease. If you test 1,000 people, you’ll find the one true positive result plus 50 false positives (the 5% of the 1,000).

So out of 51 positive results, there’s only one true positive. That makes the likelihood 1.96%.

For a more mathematically rigorous method, you can even use Bayes’ Theorem to combine the effects of the two probabilities.

**This isn’t a trivial matter. **False positives lead to unnecessary, expensive, or invasive treatments. In the best-case scenario, it results in just worry and anguish for a healthy patient. In the worst hands, it can lead to disfiguring surgeries, dangerous drugs, and unnecessary radiation.

One reader wrote in, “The supposedly ‘correct’ answer of 2% would only apply if the test were used as a screening tool by giving it to everyone or to a random sampling of people, as opposed to testing only those people with symptoms of the disease.”

Yup, that’s exactly the point…

Using tests, even highly accurate tests, without considering the full story of a patient’s symptoms gives a skewed diagnosis. And without a basic understanding of probability, your doctor could easily do harm and still believe he was right in ordering the test and recommending treatment.

And as far as medical science has come, there’s still no such thing as a perfect test. The key is considering the pretest probability and the post-test probability of the disease and combining that with the statistical characteristics of the test before thinking about sending patients to get any sort of lab work.

You should check if your doctor truly understands the math. Ask the question we posed. If he misses it, get out of there. Find a doctor who knows the answer.

** Crux note:** If you want to protect your health, you need to see Doc Eifrig’s latest report. It may make you uncomfortable, but Doc says it could be a “wake up call” for millions of Americans who are completely unprepared for one of the biggest risks we all face today. Fortunately, there are some simple, inexpensive steps you can take right now to protect yourself and your family. Click here to get all the details.

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