# Adjustment sets for non-inductive inferences (part 1: deduction)

As discussed many times on this blog there are three basic forms of inference utilized in clinical practice that make up the dynamic inference we use: inductive, deductive and abductive.

Inductive inferences are utilized to generate knowledge (observe particulars, draw universal conclusions, primarily as causal inductive inferences which can then become part of a larger causal model that is representative of knowledge). The previous post explained how and why we must adjust for variables when attempting to draw unbiased causal inductive inferences and we know which variables to adjust for based on the underlying causal structure (so we how we know to adjust based on prior knowledge). I imagine you see we will eventually confront a “chicken or egg” problem soon and that is intentional and goes all the way back to the philosophical roots of KBP as a critical realist epistemology as opposed to EBP as an empiricist or scientific realist epistemology.

The definition for an adjustment set provided is technically for inductive inferences. I say technically because it is based on the idea that several particulars are observed and the rules for generating the set are based on eliminating alternative explanations for temporal constant conjunction observations of X and Y to make the universal statement that X in fact causes Y.

Let’s take deduction first - does deduction need an adjustment set? If so, what are the rules?

Recall that an adjustment set is a: “set of covariates such that adjustment, stratification, or selection (e.g. by restriction of matching) will minimize bias when estimating the causal effect of the exposure on the outcome (assuming that the causal assumptions encoded in the diagram hold).” (Drawing and Analyzing Causal DAGs with DAGitty, User Manual for Version 2.2, Johannes Textor)

I would propose that deduction does need an adjustment set and that it is (almost) the same adjustment set as induction. By the same I mean that whatever the adjustment set is for the causal inductive inference for the exposure X to be known as a cause of outcome Y is in the adjustment set for deduction for consideration when making a deduction. All I can do now is demonstrate this for one form of deduction (the most prevalent form in clinical practice - modus ponens.

If X, then Y (this is our causal inference a universal, generated from inductive inferences)

Do X

Expect Y

I have written the above deduction in practice terminology. We intervene with X (we Do X) with expectation of whatever effect that intervention will cause (Y). Notice though that the adjustment set for the conditional (If X, then Y) which at it’s base as used in practice deductions is a causal claim, is not necessarily considered here, though it is important. Let’s take the causal network from the previous post as an example.

**If Functional Status (improves), then HRQOL (improves)**

**Do an intervention to improve functional status**

**Expect HRQOL to improve**

However, the relationship between Functional Status and HRQOL had an adjustment set including at least Symptom Status and Social. We therefore must understand how those variables influence HRQOL to know whether premise 1 is true for a particular patient because only if premise 1 is true for this patient can we reasonably expect HRQOL to improve in this patient. Here the adjustment set for deduction is behind the scenes, influencing whether it is a reasonable deduction or not. It is a valid deduction - based on its form, but is it sound (that is true)? That has to do with the truth of the premises and premise 1 might only be true for an individual within a certain range of Social or Symptom Status.

There is another consideration that was not part of the adjustment set for induction based on this particular causal structure - Health Perception. For induction Health Perception was not in need of adjustment. It did not interact with Functional Status, so while it influences HRQOL, it would not bias an observed association between Functional Status and HRQOL. But that is for induction (observation of many particulars to generate a universal). With deduction we are taking that universal and drawing a particular conclusion. Therefore the adjustment set for deduction will have to include any variables that can also cause (influence) the effect. For the example practice deduction presented in this post there is a hidden premise.

**If Functional Status (improves), then HRQOL (improves)** (assuming appropriate Social and Symptom Status based on initial inductive abduction set)

**Not (If Health Perception, then HRQOL)** ((hidden premise that in this case, in this deduction we are assuming that the causal association with Health Perception and HRQOL is not applicable - or at least not applicable enough to interfere with the Expectation of HRQOL to improve with improved functional status))

**Do an intervention to improve functional status**

**Expect HRQOL to improve**

I think it is a general rule that for deductions based on this common form in practice the inductive adjustment set modifies the first premise (the conditional) and that any other causes not considered in the inductive adjustment set are hidden premises that need to be considered (adjusted on). But I am not completely sure yet and am not completely sure how to go about a proof for this rule - perhaps after allergy season and I am off of allergy medicine :)

In the next post I will address the adjustment set for abduction.