Cutoff Points in Medicine -- Why Use Them?

Andrew J. Vickers, PhD


September 03, 2010

Here's the world as brought to you by fans of cutoff points:

The news. A suspect has been identified in the Brinks case. Police are searching for a man older than 25 years, who weighs more than 200 lbs but is less than 6 feet tall. On Wall Street, the Dow rose on news that the economy gained more jobs that it lost. Tomorrow's weather: sunny, with a temperate above 65°. Winds will be below 20 mph.

Recipes. Add less than 1 teaspoon of salt to more than 1 cup of flour. Mix in more than 1 oz of butter. When the mixture looks like breadcrumbs, moisten with less than 1 pint of milk. Bake for less than 30 minutes at a temperature above 250°.

Sports. In the Yankees-Red Sox game, both sides scored more than 4 runs. Andy Pettitte struck out more than 3 batters.

Medicine. The patient's body mass index was more than 30 kg/m2, prostate-specific antigen level (PSA) was less than 4 ng/mL, blood pressure was more than 140 mm Hg, and glycosylated hemoglobin level was less than 0.9%.

It's odd that only the medicine example seems to make sense: we give a weather forecast of 68° or 92°-- not just "higher than 65°" -- but we describe a patient as obese, hypertensive, but free of diabetes and not suspicious for prostate cancer. Indeed, cutoff points are so ubiquitous in medicine that statisticians have developed special methods to choose them. Many of these methods are, well, rather silly.

For example, one approach to choice of a cutoff point is the "minimum P value" method. In brief, some marker (say, heat shock protein values) is compared with some outcome (such as a cancer recurrence). Different criteria are used to categorize patients into "high" and "low" values of the protein. Then, the "high" and "low" groups are compared. For example, the investigators might say that patients with a value of more than 200 have an "elevated heat shock protein" and then find that these patients have an increased risk for recurrence (P = .003). The researchers might then choose another cutoff point (eg, 220) and recalculate the P value for the difference between high and low levels (eg, P = .008). The investigators then compare their results and say that, because the P value for the cutoff point of 200 is lower, the cutoff point of 200 should be used in clinical practice.

From a mathematical standpoint, this is all very interesting but makes no sense at all. The P value is the strength of evidence against the null hypothesis. Just because "there is stronger evidence that heat shock protein is associated with cancer outcome if you use a cutoff point of 200 rather than 220," it doesn't mean "use 200 to determine how to treat breast cancer."

The larger point, of course, is whether we should use cutoff points at all. This is especially because there is an alternative, which is to use a statistical prediction model to give a probability to a patient. In the case of PSA, for example, we currently tell patients with a PSA of 4 ng/mL or more that "your test was positive, get a biopsy." On the other hand, we tell patients with a PSA below that range that "your test was negative, everything is fine." This creates particular problems for incorporating patient preference in decision making. If a patient was very uncomfortable about having a biopsy and asked us whether we were sure he needed one, we wouldn't have much to go on. Instead, if we gave the patient a risk for cancer, such as 8% or 63%, then it's possible to have a rational conversation that incorporates the patient's attitude about biopsy and his anxiety about cancer.

When you turn on your radio, you're much likely to hear that tomorrow's high will be 88°, not just "it will be hot." So when you go to your clinic, adopt the same approach: tell patients their risk, not just whether they are above or below a cutoff point, especially because that cutoff point probably was chosen badly in the first place.


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