On 2016 Aug 18, David C. Norris commented:

This JAMA Viewpoint hinges on a categorical claim: “probability is not meaningful in an individual context.” In a subsequent exchange with Van Calster, Steyerberg and Harrell¹ , the authors have backed away slightly from this precipice, stating that it was rather the verifiability (and not meaningfulness) of ‘individual probability’ that was at issue—and indeed that only a frequentist probability notion was targeted by this statement.² The authors also explain that their original citation of Cohen³ in the context of this statement was meant “to direct the reader to the excellent discussion by Cohen of the limitations of the frequentist notion of probability”² . Cohen’s discussion is indeed excellent, and the reader who follows up this citation cannot fail to find a forceful rebuke of this Viewpoint's entire treatment of ‘probability’, delivered no less with particular reference to the very context under consideration—medical decision making:

Nor is it open to a frequency theorist to claim that all important probabilities are indeed general, not singular. It often seems very important to be able to calculate the probability of success for your own child’s appendectomy... ^3(p49)

Cohen proceeds from this observation to advance a Bayesian perspective; why Sniderman, D’Agostino and Pencina don’t do likewise would be a mystery if they did not reveal some peculiar methodological preoccupations in the ensuing development of their argument.

Eschewing a (meaningful|verifiable) notion of ‘individual probability’, the authors substitute the petitio principii of ‘individual risk’—the continuous, probabilistic character of which they conceal through the conceit of “clinically meaningful risk categories” [emphasis mine]. Tellingly, they label these categories “clinically meaningful” because they have forfeited the philosophic basis for making them so. Ultimately, what makes any concept clinically meaningful is its openness to connection with the values and circumstances of individual patients. Classification schemes that prematurely close patients’ decision problems have precisely the opposite character. Without such artificial categories, however, the characteristically incoherent⁴ frequentist approach to decision-making under uncertainty would lack even a semblance of that singular uncertainty which confronts the patient-physician dyad.

The authors conclude by calling on physicians to mop up this shambles. They utter the shibboleth, “models cannot replace the physician,” then incant some vague magic by which physicians should restore the individual patient to a scheme that has excluded the individual from its very epistemology. Mathematically, the requisite magic translates to conditioning on individuals after frequentist methods have already averaged individuals out.^4(pp61,509)

The ‘art of medicine’ has long enough been defined by quixotic attacks upon mathematical impossibilities. Physicians of the future will gladly relinquish the merely computational tasks of medicine to predictive models and other forms of automation. They will rather find a purposive role in the creative, irreplaceably human endeavor of helping patients to formulate their medical decision problems in alignment with their values and circumstances,⁵ and to decide these problems in accordance with appropriate evidence drawn from ever-improving⁶ predictive models.

1] Van Calster B, 2015

2] Sniderman AD, 2015

3] Cohen, L. Jonathan. An Introduction to the Philosophy of Induction and Probability. Oxford : New York: Clarendon Press; Oxford University Press, 1989.

4] Robert, Christian P. The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation. 2nd ed. Springer Texts in Statistics. New York: Springer, 2007.

5] Moroff SV, 1983

6] Mazzola E, 2015

On 2016 Aug 18, David C. Norris commented:

This JAMA Viewpoint hinges on a categorical claim: “probability is not meaningful in an individual context.” In a subsequent exchange with Van Calster, Steyerberg and Harrell¹ , the authors have backed away slightly from this precipice, stating that it was rather the verifiability (and not meaningfulness) of ‘individual probability’ that was at issue—and indeed that only a frequentist probability notion was targeted by this statement.² The authors also explain that their original citation of Cohen³ in the context of this statement was meant “to direct the reader to the excellent discussion by Cohen of the limitations of the frequentist notion of probability”² . Cohen’s discussion is indeed excellent, and the reader who follows up this citation cannot fail to find a forceful rebuke of this Viewpoint's entire treatment of ‘probability’, delivered no less with particular reference to the very context under consideration—medical decision making:

Nor is it open to a frequency theorist to claim that all important probabilities are indeed general, not singular. It often seems very important to be able to calculate the probability of success for your own child’s appendectomy... ^3(p49)

Cohen proceeds from this observation to advance a Bayesian perspective; why Sniderman, D’Agostino and Pencina don’t do likewise would be a mystery if they did not reveal some peculiar methodological preoccupations in the ensuing development of their argument.

Eschewing a (meaningful|verifiable) notion of ‘individual probability’, the authors substitute the petitio principii of ‘individual risk’—the continuous, probabilistic character of which they conceal through the conceit of “clinically meaningful risk categories” [emphasis mine]. Tellingly, they label these categories “clinically meaningful” because they have forfeited the philosophic basis for making them so. Ultimately, what makes any concept clinically meaningful is its openness to connection with the values and circumstances of individual patients. Classification schemes that prematurely close patients’ decision problems have precisely the opposite character. Without such artificial categories, however, the characteristically incoherent⁴ frequentist approach to decision-making under uncertainty would lack even a semblance of that singular uncertainty which confronts the patient-physician dyad.

The authors conclude by calling on physicians to mop up this shambles. They utter the shibboleth, “models cannot replace the physician,” then incant some vague magic by which physicians should restore the individual patient to a scheme that has excluded the individual from its very epistemology. Mathematically, the requisite magic translates to conditioning on individuals after frequentist methods have already averaged individuals out.^4(pp61,509)

The ‘art of medicine’ has long enough been defined by quixotic attacks upon mathematical impossibilities. Physicians of the future will gladly relinquish the merely computational tasks of medicine to predictive models and other forms of automation. They will rather find a purposive role in the creative, irreplaceably human endeavor of helping patients to formulate their medical decision problems in alignment with their values and circumstances,⁵ and to decide these problems in accordance with appropriate evidence drawn from ever-improving⁶ predictive models.

1] Van Calster B, 2015

2] Sniderman AD, 2015

3] Cohen, L. Jonathan. An Introduction to the Philosophy of Induction and Probability. Oxford : New York: Clarendon Press; Oxford University Press, 1989.

4] Robert, Christian P. The Bayesian Choice: From Decision-Theoretic Foundations to Computational Implementation. 2nd ed. Springer Texts in Statistics. New York: Springer, 2007.

5] Moroff SV, 1983

6] Mazzola E, 2015