Skip to main content

Avoiding a Nightmare by Using Math

The answer lies in trigonometry. -Sherlock Holmes

Don't worry if you never learned trigonometry--the answers here lie in arithmetic.

Medical test results often come back positive or negative, as if the result were a certainty. Of course, there is the accuracy, but if the accuracy is 99% or so, what does that really mean? That you should get your affairs in order? Before you call your probate attorney, let's take an example from the book Calculated Risks by Gerd Gigerenzer.

Let's say you're a 40-something year old woman with no symptoms of breast cancer. You have a positive mammogram. What are the odds you have breast cancer?

Using some assumptions about test accuracy and rates of disease based on real data, the odds that you'd have breast cancer are one in eleven according to Gigerenzer. (If you were way off, don't feel bad--most of the physicians Gigerenzer tested were way off, too--and they had the data in front of them. Not that that's comforting in every way.)

A different example: what if you have no risk factors, but have a positive test for HIV? Your odds of actually having HIV are about 50%. But, if the experience of one of Gigerenzer's students who shopped around for good medical advice in Berlin is any indication, you're not likely to hear that from an AIDS counselor. In fact, one counselor--a physician--said, "With certainty, [false positives] do not occur; if there are false results, then only false negatives, occurring when the antibodies have not yet formed." Several of the counselors searched for information on false positives but couldn't find any.

Those with a positive test for a disease have reason to be cautiously optimistic. With a little data and some arithmetic, using a book on probability like Calculated Risks can help you decide how to proceed.
Labels:

Comments

Post a Comment

Popular posts from this blog

My Long-Term Experience Eating Safe (and Other) Starches

Years ago, before the Perfect Health Diet came out, I followed a program that involved eating quite a bit "safe starch." It was called Body for Life. It involved eating six small servings of carbohydrate along with six small servings of protein, plus two servings of fibrous vegetables per day. (A serving was the size of your fist or the palm of your hand.) There were six workouts a week (three weightlifting, three cardio) and one free day every week where you ate whatever you wanted and didn't exercise. In all fairness, these two programs are different: BFL allows certain grains, legumes and low-fat dairy and discourages fat. It doesn't call for a wheelbarrow full of vegetation. Nevertheless, my experience eating lots of fruit and lots of starch is relevant to the PHD because the amount and type of digestible carbohydrates are similar, and for the first few years, I didn't eat wheat except on free days. At first on BFL, I felt great. Before, I was continually...
17 comments
Read more

Blog Lineup Change

Bye-bye, Fathead. I've enjoyed the blog, but can't endorse the high-fat, high-carb Perfect Health Diet that somehow makes so much sense to some otherwise bright people. An astrophysicist makes some rookie mistakes on a LC diet, misdiagnoses them, makes up "glucose deficiency," and creates a diet that's been shown in intervention studies to increase small LDL, which can lead to heart disease. A computer programmer believes in the diet and doesn't seem eager to refute it because, perhaps, scientists are freakin' liars and while he's good at spotting logical inconsistencies, lacks some intermediate knowledge of human biology. To Tom's credit, he says it's not the right diet for everyone, but given the truckload of food that has to be prepared and eaten, impracticality of following it while traveling (or even not traveling), and unsuitability for FODMAPs sufferers, diabetics and anyone prone to heart disease (i.e., much of the population), I'm...
24 comments
Read more

Carrageenan: A Sickening Thickener. Is it a Migraine Menace?

Let me tell you about my ride in an ambulance last night. I woke up at six o'clock from a nap with a mild headache. I ate dinner and took my vitamins, along with a couple of extra magnesium pills. Since magnesium helps my TMJ flare-ups, I thought it might help my headache. Then I went to see my mother. A few hours later, I had a severe headache, sinus pain and nausea. During a brief respite from the pain, I left for home, but less than a mile later, I got out of my car and threw up. A cop, Officer Fisher, pulled up behind me and asked if I was okay. He believed me when he said I hadn't been drinking, but he said I seemed lethargic and he wanted the paramedics to see me. (Later he mentioned that a man he'd recently stopped was having a stroke.) Thinking I had a migraine headache, the paramedics wanted to take me to the hospital. But since I knew that doctors don't know what causes migraine headaches, and I didn't know what effect their medicine would have on m...
15 comments
Read more