Medical Mistakes with Probability, 1

Misapplication of the law of large numbers applied to the maximum heart rate

Max Heart Rate

Lach J. et al. (2021). Hr max prediction based on age, body composition, fitness level, testing modality and sex in physically active population. Frontiers in physiology, 12:695950

When you do a stress test, say the Bruce Protocol, the administering doctor relies on something called the “age predicted maximum heart rate”, usually 220 minus your age, or some formula slightly more complicated but equally unrigorous. Once you reach that point, they stop, depriving you of potent information — at low risk since they are monitoring via live ECG your cardiac strain. In fact, such an estimation based on age, no matter how complicated its computation, appears to explain only 20% of the variation between individuals. I believe that explained variations are even smaller for, clearly, in the graph above, to the right, samples above 55 are sparce and the expected maxima would be considerably higher.

I noticed this myself as I am easily able to reach the 170s without feeling strain, guessing the effective max would be in the 180s (next test, but would require some live ECG for caution).

The Law of Large Numbers is not reversible

This video tutorial explains how an average can apply in a clinical setting if and only if the variations around it are small. Otherwise it is not informational.