The Blackstone Ratio and Medicine's “n” problem

There is a trade-off between overdiagnosis or overtreatment and underdiagnosis or undertreatment because of partial information. Furthermore, the information problem creates an equivalence for the physician. If one cannot tell, for example, in which patients the ductal carcinoma in situ (DCIS) will proceed to invasive breast cancer and curtail survival and in which patients it will not, even if fewer patients are harmed by DCIS than are not harmed, if patient’s risk tolerance is constant, the physician must necessarily consider all to be the same.

However, the information problem does not explain the imperative to treat. Imperfect information explains only why physicians must, in the absence of knowing more about the natural history of the disease in the individual with certainty, manage all such patients the same way. The management could just as well be intervening in none as intervening in all.

To understand our default position, it is important to understand why we must choose a default when the information is imperfect. For that, it is important to appreciate burden of proof as an epistemic concept. When information is partial, the burden of proof does not fall symmetrically. This is well recognized in law which not only deals with imperfect information but acknowledges it explicitly . The legal burden of proof is on the plaintiff to prove the guilt of the accused, not on the defendant to prove his or her innocence.

Aside from ethical and common sense reasons for the burden of proof falling on the plaintiff, not accused, there is an important epistemic consideration. It is methodologically easier to show the presence than prove the absence. This was articulated by Bertrand Russell, a philosopher of science, in his allegorical “Russell’s teapot.” Russell explained that were he to assert that there is a teapot orbiting between the Earth and the Mars, then the burden falls on him to prove the presence of the teapot, not on the skeptic to prove the absence of the teapot .

The legal world recognizes, as well, that imperfect information may lead to an error, which is asymmetric and which one must choose, that is, one must choose which of two errors one prefers. There is a chance that an innocent is convicted, and there is a chance that a guilty person is set free. Law accepts the trade-off, best illustrated in the Blackstone Ratio, which is that it is better that 10 guilty men be set free than one innocent man be sent to the gallows .

It is important not to quibble with the value of “n,” which has biblical not computational origins. The important points to appreciate are where the legal world places the burden of proof, its acknowledgment of error and its asymmetry, and its preference for one type of error over the other.

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References

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4. Genesis: 18:23–32
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The Blackstone Ratio and Medicine's “n” problem

References

Further Reading

Adherence to Thresholds

An Overview of Methodologies in Detecting Overdiagnosis

Analysis of Statistical Biases in Studies Used to Formulate Guidelines