Anemic ponderings: Implication and Probabilistic Cause

Yesterday I attended a lecture on “iron deficiency anemia” in athletes, particularly female runners. The hypothesis as it stands is that an increased rate of destruction of red blood cells (RBCs) combined with the menstrual cycle and a diet without sufficient iron cause the condition. My interest in this post is not to help me or the reader more completely understand this specific physiological situation. It is rather to describe some interesting causal inference  thoughts that arose during the discussion of my questions.

Here you can see that each possible cause is put forth as a cause of anemia. One could argue that each - mechanistically - could be a cause of anemia. It simply

dagitty-modeldepends on the extent to which they are occurring (the extent of destruction, the extent of blood loss through menstruation and the extent of iron deficiency). The key - clearly - in “iron deficiency anemia” being the iron deficiency as the root cause. It is also clearly the most modifiable of the causes as modeled.

I think a more accurate causal structure is one similar to that posted on the PT workforce - or any supply / demand problem (see here).

dagitty-model (2).png

With this structure we can see that ultimately the supply (gain of, creation of RBCs influences supply in this depiction) and demand (here modeled as loss of RBCs) that results in anemia. But still the iron deficiency remains the most important element for iron deficiency anemia. In fact, the diagnosis of iron deficient anemia is a claim to know both the cause and the effect (as is “angina” a claim to know the cause of the symptom).

What neither proposed model does is identify the connections between  the causes. Clearly the emphasis of the model is how the causes relate to the effect (anemia). For example, if the diet is lacking in iron, is it possible that it is lacking in other nutrients that impact RBC supply (i.e. protein, which is necessary not just for globin, but also for Epo).

When it was my turn to ask a question I asked whether there was a relationship between the female athlete triad (specifically amenorrhea) and anemia. I was told (and I am not familiar with this literature so I am at the mercy of the presentation) that there most likely is a higher prevalence of anemia in females that have amenorrhea (so yes to whether there is an association). So I asked if anyone has considered whether amenorrhea is, in part or at times, a protective response to avoid anemia. To this I was told most likely not because not all female athletes that have iron deficiency anemia have amenorrhea.

By the logical rules of implication this then makes sense to rule out causal association between iron deficiency anemia and amenorrhea . The only time an implication is “False” is when the antecedent is true and the consequent is false:

If iron deficiency anemia , then amenorrhea

With this implication, if there is a case where iron deficiency anemia is true and amenorrhea is false then the implication is false. But, implication is not the same reasoning process as probabilistic cause (see note below). We do not derive our causal associations and structures from single cases and logical implications.

For example:

If cigarette smoke, then lung cancer

With this implication a single case of a smoker without lung cancer would be a false implication. But the probabilistic case for cigarette smoke as a cause of lung cancer overwhelms such single case evidence.

My point is this - while it is easy to see that implication and probabilistic cause are different - we must be cautious of using implication to rule out a possible cause, just as we must be cautious of using a single case to justify a belief in a causal association.

A model that unfolds the hypothesis across time (just one time step) might look like this:

dagitty-model (3).png

Here anemia influences menstruation, which then influences RBC demand, which then influences future states of anemia. Sorting this rather complex situation out experimentally would be equally complicated. But the answer to the question I posed would require such a set of experiments rather than the use of logical implication.

We must use logic to help us identify the definite, the possible and the impossible. But we must be wary of using logic incorrectly to falsely achieve one of these states of knowledge and thus shutting down an area of investigation.

Note: By probabilistic cause I mean this definition given by Wikipedia: “Probabilistic causation designates a group of philosophical theories that aim to characterize the relationship between cause and effect using the tools of probability theory. The central idea behind these theories is that causes raise the probabilities of their effects, all else being equal.”

This is similar - but not identical - to what I have previously presented as possible cause. In a knowledge based practice system, Probabilistic cause is one way of identifying causal associations. Whereas possible cause is about the mechanisms at play in the phenomenon under investigation. Possible cause can be known through probabilistic cause. The probability distributions in such a situation are influenced by the distribution of the possible causal mechanisms AND the inherent error including the unknown and unmeasured (latent) variables of the full causal system. But even many definite causes are known through probabilistic cause. With a definite cause the probability distributions are influenced by the distribution of the inherent error including the unknown and unmeasured (latent) variables of the full causal system, and NOT due to the causal mechanisms themselves. This statement is basically saying that even with determinant mechanistic systems we tend to use probabilistic cause to come to know the causal structure. I believe this is particularly true in the human sciences, and increases in importance with the complexity of the causal structure under inquiry.

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