# Differential Diagnosis: the abductive challenge

In a previous post we discussed the two ways to consider differential diagnosis (here). There is no problem in considering them separately (screening on one hand, diagnosis on the other). Yet there is a benefit from considering their common core - abduction.

Abduction was covered long ago as a mode of inference making up the dynamic inferential process of clinical practice and is depicted on the “practice” side (right) of the knowledge based practice graphic first presented in the post on graphical causal models.

In summary, abduction is an inference to cause from the observation of an effect. C.S. Peirce introduced the term after having experimented with the terminology “hypothesis” and “retroduction.” I point out his previous attempts to name abduction because they are rather explanatory of his thinking. In science, abduction is the way in which we generate hypotheses. Peirce, a science and philosopher, was troubled by the fact that there are so many possible hypotheses to test and only a limited time to test them. Keep in mind that he was writing (turn of the 20th century) when statistical inference was just starting to mature into the testing of the null hypothesis and either accepting it or rejecting it. Peirce witnessed that scientists did not haphazardly choose which hypotheses to test. They observed effects, and used their existing (a priori) knowledge to put together the best explanation of those observed effects. That best explanation is a causal mechanism (possibly including a complex causal structure). Retroduction is not a bad term either. It seems to refer to what is happening with the process, attempting to explain observed effects by considering possible prior events (causes) that could give rise to the effects.

When we consider the challenges of differential diagnosis we are considering the challenges of abduction. The challenge of abduction is that there is only one form that is “valid” in the sense that we can construct valid deductive inferences. Recall that a valid deductive inferential form means that the truth of premises guarantees the truth of the conclusion.

Deduction:

Premise 1: If X, then Y

Premise 2: X

Conclusion: Therefore Y

As long as as premise 1 and 2 are true; the conclusion is guaranteed, it “follows from”, it is “logically entailed”.

The only form that exists for abduction relies on a particular form of the premise (if and only if (iff)):

Premise 1: Y iff X (meaning Y if and only if X - the only time there is the effect Y is when it was caused by X)

Premise 2: Y

Conclusion: Therefore X

The problem with this form pragmatically is that “Y iff X” is much more difficult to prove by observations of the natural world. With the process of induction it is already difficult to prove the less specific claim that “If X, then Y.” Recall, induction is the process used to generate such general conclusions (universals) about the state of reality. But since the difficulty of generating the conditional “If X, then Y” does not hamper our consideration of valid deductive forms that use this conditional, I do not believe it should hamper our use for abduction. Keep in mind that Aristotle came up with forms for deduction millennia in advance of the problem of induction (ala David Hume), or the explicit formulation of abduction. The “probability logic” of Adams limits the conclusion of deduction by the probability of the premises, and this is really in response to the fact that most claims of “If X, then Y” are only accepted to be true probabilistically. And by most claims, I mean the really interesting ones that keep us up at night. While bothered by the problem of people falling, it is not that we question the mechanisms of gravity that that “If I am dropped, then I will fall.” The problems of people falling that keep us up are those related to “If X, then Y” conditionals where X is some continuous variable, or set of continuous and interacting variables, that don’t seem to always result in falling……

Let me relate back to differential diagnosis before closing for today and giving a preview of my plans for upcoming posts.

Let’s live - for a moment - in a world where the **only cause** of “sub sternal chest pain” (SSCP) was myocardial ischemia. And from years of observation this to be the case (true) we believe:

SSCP iff myocardial ischemia (SSCP if and only if myocardial ischemia)

Then, whenever we observe SSCP we are justified in believing that the person has (or is having or has had) myocardial ischemia. Justified in believing does not mean they actually have it (see belief and truth post) - their report on SSCP might be wrong of course (basic reliability of sensory perception is one of the cores of the critical realist foundations of the clinical epistemology of a knowledge based practice, after all).

The challenge for differential diagnosis would be to determine, through examination / questioning) whether the patient was truly having SSCP (questions about the quality and location of the pain, for example). But once it is believed that the patient is having SSCP, the inference to myocardial ischemia would be justified (if we accept that form of abduction as being justified).

Keep in mind that “iff” premises are rare in physical therapy. Which is why abduction is a challenge, which is why differential diagnosis is a challenge.

In upcoming posts I will continue to consider the challenges of differential diagnosis due to the challenges of abduction and attempt to offer how to move forward though posts that:

reintroduce the idea of an adjustment set for abduction

identify some classifications based on causal structure for abduction (based on adjustment sets)

introduce Bayes theorem and how you are using it even if you do not realize it

demonstrate how Bayes theorem is related to our measures of diagnostic accuracy (sensitivity / specificity; likelihood ratios)

5. extend the understanding of Bayes theorem by introducing “Bayesian Networks” as another name for / form of graphical causal models (at this point we will have come full circle)

Those posts have the potential to be pretty dense. Therefore I will interject commentary posts throughout on such topics such as why teaching differential diagnosis as currently done in curricula makes it more challenging (with a proposal on how to do it better); the connection between differential diagnosis and the issues of coming up with a system for “PT diagnosis”; how a book on differential diagnosis should be organized; and always keep in mind that I am willing to review papers if people want to send them in to start a dialogue.