{"id":16,"date":"2021-07-31T17:48:10","date_gmt":"2021-07-31T21:48:10","guid":{"rendered":"https:\/\/health.uconn.edu\/causality\/?page_id=16"},"modified":"2026-03-14T21:38:39","modified_gmt":"2026-03-15T01:38:39","slug":"firststeps","status":"publish","type":"page","link":"https:\/\/health.uconn.edu\/causality\/firststeps\/","title":{"rendered":"Causality and causal modeling"},"content":{"rendered":"

General definitional and notational setup<\/strong><\/p>\n

*** Causality is not directly detectable<\/em> or observable, much like forces[i]<\/span><\/a> or energy aren\u2019t either: it needs to be discovered\/uncovered – \u2018detected\u2019 through observational consequences[ii]<\/span><\/a>; on the other hand, it\u2019s a pretty natural intuitive human notion[iii]<\/span><\/a>, yet is considered a worthy \u2018problem\u2019[iv]<\/span><\/a>.<\/p>\n

*** Causality is hardly a statistical matter, and it shows up at the very roots of scientific inquiries: the basic notions of substance and time, e.g. are defined in excessive proximity to \u00a0causal relations: e.g. abstract entities (like \u2018number 7\u2019) are those that cannot cause anything[v]<\/span><\/a>, unlike \u2018concrete substances\u2019, and time itself has definitions overlapping with causality [2-6].<\/p>\n

*** Causal language[vi]<\/span><\/a> differs drastically by scientific field[vii]<\/span><\/a>, and some are more shy than others in using the \u201cC\u201d word. In statistics it has been kept at bay for many decades, and epidemiologists have been to first advocates among statisticians at large (Tyler VanderWeele<\/a>, e.g., but also Jay Kaufman [8] and [9] in health disparities, and many other nowadays).<\/p>\n

+++ This follows my \u2018let\u2019s talk (just talk!, no math!) about causality\u2019 recent philosophy. The old adagio \u201ccorrelation does not imply causation\u201d is a structural misunderstanding of constructs: while each are a 2-objects relation, causation is not symmetric, as correlation is, and \u2018proceeding from one to the other\u2019 requires more than the 2 objects of interest. The simple solution was offered >100 years ago by Sewall Wright, and I rephrase to modern language: \u201ca correlation can come from: either variable causing the other one, or another variable causing both\u201d. This makes clear the \u2018logical tension\u2019 and the proper solution: we need to step above the 2 ingredients to make causal statements (otherwise we might just reply: \u201ccorrelation implies causation, but only sometimes\u201d, when there is a causal component of the relation in there).<\/p>\n

To rephrase still: causal inference involves decomposing correlations into their causal and non-causal components. Simple, right? Incidentally, a parallel view uses a similar decomposition maneuver. [0]<\/p>\n

*** Even \u2018simple\u2019 questions like \u2018What causes the universe to expand?\u2019 rely on deeply unobservable constructs, like dark energy.[viii]<\/span><\/a><\/p>\n

*** In medicine, causal questions are broadly aimed at \u2018changing the current course of events\u2019[ix]<\/span><\/a> in the future, whereas in astronomy e.g. mere deep descriptive understanding of \u2018how things work\u2019 is a goal in itself: finding the laws governing the Universe.[x]<\/span><\/a><\/p>\n

*** The task then is to discover<\/em> \u201cwhich variable \u2018listens to\u2019 which others\u201c (\u2018Book of Why\u2019 BoW<\/a> p. 7), e.g. whether blood glucose (say measured by hemoglobin A1c) \u2018listens to\u2019 one\u2019s body weight (say measured by body mass index, BMI), and responds to it: this metaphor invites deeper delving into how the \u2018listening\u2019 works[xi]<\/span><\/a>: is an asteroid \u2018listening\u2019 to the Earth\u2019s gravity when heading to it? Does it have a choice<\/em> not to listen, like biological bodies do? Since biological entities are the first ones to collect information and use it in choosing to respond differently, to benefit themselves, the \u2018listening\u2019 appears to make less sense before the first living organisms appeared: all natural bodies and substances before that blindly (and strictly, without choice) followed the tight grip of the natural laws, gravity among them being the central one.[xii]<\/span><\/a><\/p>\n

*** Note that the way BMI relates to A1c is not merely direct and linear, e.g. [48]:<\/p>\n

FIGURE 1 Dynamic phase of obesity development in the carbohydrate-insulin model<\/em><\/a>[xiii]<\/strong><\/em><\/span><\/a>.<\/p>\n

\"\"<\/a><\/p>\n

*** Intuitively grasping how causal effects are \u2018extracted\u2019 from correlational-kind data, a bit of notational setup will be decisive: for the A1c(BMI) relation of interest, or BMI -> A1c, or probability(A1c | BMI), where \u201c|\u201d stands for \u2018given\u2019, we want to find out whether lowering BMI would cause a A1c drop, and then by how much. To answer the \u2018cause-effect\u2019 research question (RQ), we simply need to compare for each patient i <\/em>his\/her A1c\u2019s under the current (present state) CurrentBMI<\/sub><\/em><\/strong> vs. a \u2018what if\u2019 potential state If.LowerBMI<\/sup><\/strong>:<\/p>\n

A1c i<\/sub><\/em><\/strong> <\/sup>CurrentBMI<\/sub><\/em><\/strong> vs. A1c <\/sub>i<\/sub><\/em><\/strong> If.LowerBMI<\/sup><\/strong><\/p>\n

or with classic \u2018treatment\u2019 (Tx) as the cause: A1c <\/sub>i<\/sub><\/em><\/strong> If.Treated<\/sup><\/strong> vs. A1c i<\/sub><\/em><\/strong> If.NotTreated<\/sup><\/strong><\/p>\n

where superscripts mean \u2018it could happen up there\u2019 [xiv]<\/span><\/a> A1c <\/sub>i<\/sub><\/em><\/strong> If.LowerBMI<\/sup><\/strong> , vs. what actually happened \u2018here on the ground\u2019, in this reality A1c <\/sub>i<\/sub><\/em><\/strong> <\/sup>CurrentBMI<\/sub><\/em><\/strong>. More details in the footnote, suffice to say that there is a causal effect of BMI on A1c for patient i<\/em> if: A1c <\/sub>i<\/sub><\/em><\/strong> If.LowerBMI<\/sup><\/strong> \u2260 A1c <\/sub>i<\/sub><\/em><\/strong> <\/sup>CurrentBMI<\/sub><\/em><\/strong>! One of these two quantities however can never be \u2018seen\u2019, once reality kicks in: either one has his\/her current BMI, or a lower BMI!<\/p>\n

Note though that when realized<\/em>, potential values come \u2018down here on the ground\u2019 (become visible):<\/p>\n

A1c i<\/sub><\/em> <\/sup>*If.NotTreated<\/sup> NotTreated<\/sub><\/em><\/strong> \u00a0= A1c i<\/sub><\/em> <\/sup>NotTreated<\/sub><\/em><\/strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 and<\/p>\n

A1c i<\/sub><\/em> <\/sup>*If.Treated<\/sup> Treated<\/sub><\/em><\/strong> \u00a0= A1c i<\/sub><\/em> <\/sup>Treated<\/sub><\/em><\/strong> <\/sub><\/p>\n

in which I added the *<\/strong>, for \u2018never visible\u2019: what would have happened to these folks, but\u2026 didn\u2019t (couldn\u2019t)!<\/strong> The fundamental causal inference problem is that one of these 2 in each condition is \u2018missing\u2019:<\/p>\n

A1c i<\/sub><\/em> <\/sup>*If.Treated<\/sup><\/strong> NotTreated<\/sub><\/em><\/strong> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 &\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 A1c i<\/sub><\/em> <\/sup>*If.NotTreated<\/sup><\/strong> Treated <\/sub><\/em><\/strong><\/p>\n

***The statistical trickery to still derive a causal effect from such \u2018observational\u2019 data (i.e. not from a randomized controlled research design) is to \u2018identify\u2019 the average causal effect among those who say lowered their BMI, Average(A1c <\/sub>i<\/sub><\/em><\/strong> If.LowerBMI<\/sup><\/strong> LoweredBMI<\/sub><\/strong> – A1c <\/sub>i<\/sub><\/em><\/strong> *<\/strong>If.SameBMI<\/sup><\/em> LoweredBMI<\/sub><\/strong>), in which we added the *<\/strong>, for \u2018never visible\u2019: what would have happened to these folks, but\u2026 didn\u2019t!<\/strong><\/p>\n

We do this by \u2018wiping off\u2019 a bias quantity, the \u2018selection bias\u2019[xv]<\/span><\/a>. All this math is drastically simplified if one uses Judea Pearl\u2019s notation for \u2018setting\u2019 the predictor to a value, so Average(A1c <\/sub>i<\/sub><\/em><\/strong> If.LowerBMI<\/sup><\/strong>) becomes simply Average(A1c <\/sub>i<\/sub><\/em><\/strong> | (set<\/strong> (BMI=Lower))[xvi]<\/span><\/a>, [55, 56], where \u201cset\u201d symbolizes an actual intervention that sets to BMI to a lower value, and E means \u2018expected (average) value of\u2019: the challenge of \u2018causal inference\u2019 then is \u2018simply\u2019 deriving the causal quantity Average(A1c | (set<\/strong> (BMI=Lower)) from the observational one Average(A1c | \u2018seeing\u2019 BMI=Lower). Observing BMI=Low is NOT the same as \u2018setting\u2019 it to \u2018Low\u2019, or \u2018intervening\u2019 to \u2018do\u2019 that:<\/p>\n

Average(A1c <\/sub>i<\/sub><\/em><\/strong> | \u2018see<\/u><\/strong>\u2019 BMI=Lower) \u2260 Average(A1c <\/sub>i<\/sub><\/em><\/strong> | \u2018set<\/u><\/strong>\u2019 BMI=Lower)<\/p>\n

or Average(A1c <\/sub>i<\/sub><\/em><\/strong> | \u2018see\u2019 BMI=Lower) \u2260 Average(A1c <\/sub>i<\/sub><\/em><\/strong> | \u2018do\u2019 BMI=Lower)<\/p>\n

***Again, statistics can \u2018recover\u2019 the causal effects from observational (non-interventional) data when it can turn all \u2018set\u2019 (or \u2018do\u2019) into \u2018see\u2019 in the formulas: then, the math (or software, or AI) can directly yield the actual causal effect: even a simple t-test or a chi-squared test would thus become a \u2018causal analysis\u2019.<\/p>\n

\u00a0<\/strong>*** <\/strong>I start with an illustration of the simplest \u2018data\u2019, the yes\/no, presence\/absence, or 1\/0, like diabetic\/not (which can carry some error in it too[xvii]<\/span><\/a>). This is a quick overview of several topics that all rely on this simplest possible data setup: a 2by2 binary fields\/variables, all using the simple 4-cell setup (0,0), (1,0), (0,1), and (1,1). They make use of the information derived from such a setup completely differently:<\/p>\n

***.1. <\/strong>Finding \u2018it\u2019 vs. missing \u2018it\u2019: the medical sensitivity vs. specificity (& ROC curve \u2013 to be added)<\/p>\n

The setup here is slightly different than most 2by2 tables(as chi-squared test examples, e.g.), and it has Test(for a disease), on the left, and Disease, on top, and inside:\u00a0 (1,1) (1,0), first row, then (0,1), (0,0), or the a,b,c, and d, as they are better known (an image is shown). They mean sequentially:<\/p>\n

a (1,1)<\/strong> Test is positive, Disease present, so we have (+,+) = Good! <\/strong><\/p>\n

b (1,0)<\/em>,Test is positive, Disease not there, so (+,-) = Bad!<\/em> first row, then<\/p>\n

c (0,1)<\/em>, Test is negative, Disease present, so (-,+) = Bad!<\/em><\/p>\n

d (0,0)<\/strong>, Test is negative, Disease not there, so (-,-) = Good!<\/strong><\/p>\n

Sensitivity reads the 1st<\/sup> column downwards<\/strong>: n(1,1)<\/strong> \/ [n(1,1) + <\/strong>n(0,1)<\/em>] or <\/strong>with | meaning \u2018given\u2019<\/p>\n

P(Test + | Disease +) \u2013 this has a more intuitive write-up: percent of all disease+ patients with test+<\/p>\n

Specificity reads the 2nd<\/sup> column upwards<\/strong>: n(0,0)<\/strong> \/ [n(0,0) + <\/strong>n(1,0)<\/em>] or <\/strong><\/p>\n

P(Test – | Disease -) : percent of all disease- patients with test-<\/p>\n

*** Note that it is different to talk about P(Disease + | Test +), than about P(Test + | Disease +), which has a more natural direction; the \u2018direction\u2019 differs: we \u2018condition on\u2018 (know) one, or the other.<\/p>\n

*** Note that this 2×2 setup is not<\/em> direction-less[xviii]<\/span><\/a>, yet here the 1st<\/sup> # talks about the LEFT label (test), second about the TOP label (disease, so (1, 0) means (Test + , Disease -); 2by2 tables read more naturally from left->right and top-down. However, sensitivity and specificity read P(Test | Disease), so the \u2018given\u2019 (or \u2018knowing\u2019) is the Disease, which \u2018happens first. This setup becomes more meaningful when time is incorporated, as in RQ.2. in part 2, which has the before & after of a binary category: here P(Post | Pre) makes sense, but P(Pre | Post) does not.<\/p>\n

*** A similar setup is the by-product of a logistic regression analysis, when the predictors of a binary outcome are more\/less useful in \u2018correctly\u2019 assigning 1\u2019s and 0\u2019s to their category; the \u2018classification table\u2019 shows the correct assignments (1,1) &<\/strong> (0,0)<\/strong>, and the incorrect ones (1,0)<\/em>, (0,1)<\/em>, and provide an average of percent cases incorrectly classified.<\/p>\n

***2. <\/strong>In formal logic \u201cIf Premise – Then Conclusion\u201d or simply \u201cPremise -> Conclusion\u201d follows formal rules, which simply say that the entire statement \u201cPremise -> Conclusion\u201d is false in relation to the 2 ingredients truth value only in 1 circumstance: When \u201cTrue -> False\u201d: truth cannot lead to falsehood! A\u00a0 peculiar one however is \u201cFalse -> True\u201d, this whole statement is \u2018True\u2019, (along with the other 2 possibilities \u201cTrue -> True\u201d and \u201cFalse -> False\u201d), because, as Claude.ai says \u201cSince the condition is never met, the implication can’t be falsified.\u201d, meaning because we start in an \u2018impossible world\u2019, we cannot test its truth value\u2026 \u201cIf pigs could fly, then anything goes\u201d pretty much\u2026<\/p>\n

If we follow the four-cell setup known in the sensitivity\/specificity context below (1,1) (1,0), (0,1), (0,0), the \u2018first\u2019 is logically the \u2018If\u2019 (vertical, from up to down, column), the second the \u2018Then\u2019 (horizontal, left to right, row) follow<\/p>\n

a (1,1), IF is True, THEN is True too, so we have (+,+) or<\/p>\n

b (1,0), IF is True, THEN is False, so (+,-) : this argument only of the 4 is FALSE<\/p>\n

c (0,1), IF is False, THEN is True, so (-,+)<\/p>\n

d (0,0), IF is False, THEN is False too, so (-,-)<\/p>\n

***.3. <\/strong>H0 (null hypothesis) vs. H1 and what statistics says: rejecting H0 – seeing \u2018the effect\u2019 vs. not; unfortunately, the Null Hypothesis language leads to double (and more) negations (fail to reject H0\u2026 meaning \u201cwe see no effect), so the following emphasizes the \u2018Effect seeing\u2019 (or not)<\/em> phrasing.<\/p>\n

If we follow the same<\/em><\/strong> four-cell setup known in the sensitivity\/specificity context below (1,1) (1,0), (0,1), (0,0), the \u2018first\u2019 category is logically \u2018there is\/not<\/em><\/strong> an Effect\u2019<\/strong> (= \u2018H0 (null hypothesis) if true\/false\u2019, vertical, from up to down, column), the second the \u2018Statistics finds\/not <\/em><\/strong>an effect\u2019 (= \u2018we reject\/fail to reject<\/strong> H0 t, horizontal, left to right, row) follow<\/p>\n

a: (1,1) or (+ | <\/strong>+): There is an Effect (H0=False), and Statistics finds it<\/em><\/strong> (rejects H0 true too); we correctly say \u2018There IS an Effect\u2019! This is (1-\u03b2<\/strong>) = \u2018statistical power\u2019 that we often we need estimated before<\/em><\/strong> a study is started: we want some solid\/large value here, a good likelihood we will FIND and Effect when it\u2019s there! This is ~= (akin to) the SENSITIVITY<\/em><\/strong> of a test, from above!<\/p>\n

b: (1,0) or (+ | <\/strong>-): There is NO Effect (H0=True), and Statistics finds it<\/em><\/strong> (rejects H0 true); = we<\/strong> make a Type I error: \u201cTrue null hypothesis is incorrectly rejected\u201d; Type I because<\/em> it is most serious, we \u2018find something that doesn\u2019t exist\u2019 (i.e. \u2018make up stuff\u2019)! This is \u03b1<\/strong>, the customary .05 (5%) threshold value: we set this upfront, to as small<\/em><\/strong> an uncertainty value as we are willing to tolerate<\/em><\/strong>.<\/p>\n

c: (0,1) or (- | <\/strong>+): There is an Effect (H0=False), BUT Statistics does NOT find it<\/em><\/strong> (\u2018we<\/strong> fail to reject<\/em>\u2019 H0); we make a make a Type II error: \u201ctrue null hypothesis is incorrectly rejected\u201d This is \u03b2<\/strong>.<\/p>\n

d: (0,0) or (- | <\/strong>-): There is NO Effect (H0=True), and Statistics does NOT find it <\/em><\/strong>either: we correctly say \u2018There if NO effect\u2019! This is(1-\u03b1)<\/strong>.<\/p>\n

***It is advisable to set up expectations based on prior knowledge in the form of a Hypothesis: Overweight -> Diabetes, (a causal statement), or a RQ: \u201cOverweight -> Diabetes?\u201d. The hypothesis testing procedure is a flexibly \u2018sharp\u2019 decision process, can be e.g. 2-sigma\u2019, rejecting H0 based on the \u20182 standard errors away\u2019 criterion (\u2018p < .05\u2019), common in medicine and health research, or more conservatively based on the 5-sigma rule<\/a> in physics (\u2018p < .00006\u2019): the\u00a0 = .05 rule is a \u2018rule of thumb\u2019, but thumbs differ widely in size\u2026<\/p>\n

***I will demonstrate in part 2 several statistical tests and analyses, with an emphasis on the mechanics of each, the \u2018how to\u2019, all of them done \u2018by hand\u2019 and in Excel alone (no \u2018sophisticated\u2019 statistical software needed).<\/p>\n

FOOTnotes:<\/strong><\/span><\/p>\n

<\/span><\/a>[0]<\/a><\/p>\n

Judea Pearl said in his \u2018Book of Why\u2019 (ch.1 here<\/a>; books seems to be online here<\/a>): “Flip two coins simultaneously one hundred times and write down the results only when at least one of them comes up heads. Looking at your table, which will probably contain roughly seventy-five entries, you will see that the outcomes of the two simultaneous coin flips are not independent. Every time Coin 1 landed tails, Coin 2 landed heads. How is this possible? Did the coins somehow communicate with each other at light speed? Of course not. In reality you conditioned on a collider by censoring all the tails-tails outcomes. “Why:202)<\/p>\n

The format of the book does not allow \u2018spelling out\u2019 of every detail\u2026 (some readers<\/a> reported this too), so I will try. This becomes \u2018visible\u2019 when one \u2018does\u2019 it (! a \u2018do\u2019 operation\u2026), say in Excel\/GSheets directly. I will explain it \u2018verbally\u2019 (a separate post will walk through the Excel exercise). So:<\/p>\n

If one generates a series or random yes\/no (1\/0) events, say flipping a coin 100 times: we list the results in a 1st column; repeat this process, list results in a 2nd column: the 2 cannot be correlated: they are both random occurrences. A third column can be built off the first two, by coding 0 when both ingredients were 0, and 1 otherwise (which is: 3rd = 1st+2nd\u22121st\u2219<\/strong>2nd): this 3rd is \u2018determined\u2019 causally (or \u2018caused deterministically\u2019\u2026) by the first 2. What one can verify directly is:<\/span><\/a><\/p>\n

    \n
  1. <\/strong> Regressing 2nd on 1st will yield a null (near-zero, statistically) relation always (nearly so); BUT, controlling for the 3rd will always yield a non-null (conditional) relation: this is the artificial \u2018creation\u2019 of a correlation between two predictors of the same outcome, when conditioning on that outcome: THIS is the collider problem!<\/li>\n
  2. <\/strong> Following the example as phrased in the book, but now giving extra-meaning to the 1st and the 2nd: say 1st is head injuries and 2nd is heart \u2018problems\u2019 (as a symptom, palpitations of a more serious nature, e.g., that would make one go to the hospital): these 2 should not relate for any natural reason, but if we restrict our data collection to those who had either, by selecting data from a hospital database, all of a sudden we will see a correlation between them. Granted, this particular one will be negative, patients in the hospital either have one, and not the other one (and vice versa). This is pretty much almost any medical study\u2026 which excludes healthy folks, because\u2026 there is \u2018nothing to see there\u2019.<\/li>\n<\/ol>\n

    – There are other implications to be aware of: depending on the sign of the two effects between 1st and 2nd, and the 3rd, this \u2018artifact\u2019 can be >0 or <0: this has the consequence of \u2018shifting\u2019 the \u2018Null\u2019 point of our hypothesis testing process, technically. We start off \u2018crooked\u2019, and we should correct for this!<\/p>\n

    +++ \u201cwe can decompose the observed outcome of a treatment into two effects:<\/p>\n

    Outcome for treated \u2212Outcome for untreated<\/p>\n

    = (Outcome for treated \u2212Outcome for treated if not treated) +<\/p>\n

    + (Outcome for treated if not treated\u2212 Outcome for untreated) =<\/p>\n

    = Impact of treatment on treated + selection bias.\u201d {Varian, 2016 #15819} \u00a0p. 7311<\/p>\n

    [i]<\/span><\/a> \u201cWhat are the merits of these fictitious variables called causes that make them worthy of such relentless human pursuit, and what makes causal explanations so pleasing and comforting once they are found? We take the position that human obsession with causation, like many other psychological compulsions, is computationally motivated. Causal models are attractive mainly because they provide effective data structures for representing empirical knowledge-they can be queried and updated at\u00a0 high speed with minimal external supervision. The effectiveness of causal models stems from their modular architecture, i.e., an architecture in which dependencies among variables are mediated by a\u00a0 few central mechanisms. \u201c p. 383 \u2018 8. Learning Structure from Data\\ 8.1. Causality, Modularity, and Tree Structures\u2019; \u201cthe construct of causality is merely a\u00a0 tentative, expedient device for encoding complex structures of dependencies in the closed world of a predefined set of variables. It serves to highlight useful independencies at a given level of abstraction, but causal relationships undergo drastic change upon the introduction of new variables.\u201d P. 397<\/p>\n

    \u201cWith its dual role, summarizing and decomposing, a causal variable is analogous to an orchestra conductor: It achieves coordinated behavior through central communication and thereby relieves the players of having to communicate directly with one another. In the physical sciences, a\u00a0 classic example of such coordination is afield (e.g., gravitational, electric, or magnetic). Although there is a one-to-one mathematical correspondence between the electric field and the electric charges in terms of which it is defined, nearly every physicist takes the next step and ascribes physical reality to the electric field, imagining that in every point of space there is some real physical phenomenon taking place which determines both the magnitude and direction assigned to that point. This psychological construct had a huge impact on the historical development of electrical science. It decomposed the complex phenomena associated with interacting electrical charges into two independent processes: The creation of the field at a given point by the surrounding charges and the conversion of the field into a physical force once another charge passes near that point.\u201d {Pearl, 1988 #5884} P. 384<\/p>\n

    [ii]<\/span><\/a> \u201cAn interesting philosophical question is whether any method based on probabilities can identify causal directionality among observable variables.\u201d {Pearl, 1988 #5884} p. 396, Learning Structure from Data \u201cFormally speaking, probabilistic analysis is indeed sensitive only to covariations, so it can never distinguish genuine causal dependencies from spurious correlations, i.e., variations coordinated by some common, often unknown causal mechanism. But what is\u00a0 the operational meaning of a\u00a0 genuine causal influence? How do humans distinguish it from spurious correlation? Our instinct is to invoke the notion of control; e.g.,\u00a0 we can cause the ice to melt by lighting a fire but we cannot cause fire by melting the ice. Yet the element of control is\u00a0 often missing from causal schemas. For example, we say that the rain caused the\u00a0 grass to become wet despite our being unable to control the rain. The only way to tell that wet grass does not cause rain is to find some other means of getting the grass wet, clearly\u00a0 distinct from rain, and to verify that when the other means is activated, the ground surely gets wet while the rain refuses to fall. Thus, the perception of voluntary control is in itself merely a by-product of covariation observed on a\u00a0 larger set of variables [Simon 1980], including, for example, the mechanism of turning one’s sprinkler on. In other words, whether X causes Y or Y causes X is not something that can be determined by running experiments on the pair (X, Y), in isolation from the rest of the world. The test for causal directionality must involve at least one additional variable, say Z, to test if by activating Z we can create variations in Y and\u00a0 none in X, or alternatively, if variations in Z are accompanied by variations in X while Y remains unaltered. This is exactly the meaning of causality that the polytree recovery algorithm attributes to the arrows on the branches. The meaning relates not to a\u00a0 single branch in isolation but to an assembly of branches heading toward a\u00a0 single node. An arrow is drawn from X to Y and not the other way around when a variable Z is found that correlates with Y but not with X<\/strong> (see Figure 8.2a). The discovery of the third variable Z, however, does not necessarily mean that X and Z are the ultimate causes of Y. The relationship among the three could change entirely upon the discovery of new variables.\u201d p. 396-7<\/p>\n

    [iii]<\/span><\/a> \u201cAfter all, if you and I share the same understanding of physics, you should be able to figure out for yourself which mechanism it is that must be perturbed in order to realize the specified new event, and this should enable you to predict the rest of the scenario.<\/p>\n

    This linguistic abbreviation defines a new relation among events, a relation we normally call “causation”: Event A causes B, if the perturbation needed for realizing A entails the realization of B.2<\/sup><\/strong> (2<\/sup><\/strong> The word “needed” connotes minimality and can be translated to: ” .. .if every minimal perturbation realizing A, entails B”.) \u201d {Pearl, 1997 #15498} p. 55<\/p>\n

    [iv]<\/span><\/a> \u201cWhen we ask, for example, what causes this fire, it is not its being this but its being fire that we are seeking to account for.\u201d {Anderson, 1938 #15495} p. 128<\/p>\n

    [v]<\/span><\/a> \u201cI shall understand by a \u2018substance\u2019 a particular thing, capable of causing or being caused, such as Richard Swinburne, or a particular table, or a particular electron, or the planet Venus.\u201d [1] Drive<\/a><\/p>\n

    [vi]<\/span><\/a> \u201cDespite heroic efforts by the geneticist Sewall Wright (1889\u20131988), causal vocabulary was virtually prohibited for more than half a century. And when you prohibit speech, you prohibit thought and stifle principles, methods, and tools\u201d Pearl\u2019s BoW<\/a> p. 5.<\/p>\n

    [vii]<\/span><\/a> What \u2018scientific research\u2019 is requires a long detour; a simpler approach is to delineate from \u2018non-scientific\u2019 research, which some deem to be the \u2018farthest away\u2019, e.g. theology, philosophy or knowledge through art [7] (it is rather paradoxical to consider philosophy non-scientific, as long as it provides all sciences the main argumentation tool, formal logic).<\/p>\n

    [viii]<\/span><\/a> And this only talks about the \u2018observable\u2019 Universe, which is to the entire Universe like an atom is to the observable Universe\u2026<\/p>\n

    [ix]<\/span><\/a> \u201cThis chapter deals with the problem of con-structing a network automatically from direct empirical observations, thus bypassing the human link in the process known as knowledge acquisition. [\u2026] it is more convenient to execute the learning process in two separate phases: structure learning and parameter learning. [ \u2026] Our focus in this chapter will be on learning structures rather than parameters. [\u2026] e shall focus on causal structures and in particular on causal trees and polytrees, where the computational role of causality as a modularizer of knowledge achieves its fullest realization. \u201c & \u201cCausal labeling creates modularity not only by separating the past from the future, but also by decoupling events occurring at the same time. Knowing the set of immediate causes \u041fB <\/sub><\/strong>renders X independent of all other variables except X’s descendant; many of these variables may occur at the same time as X, or even later. In fact, this sort of independence is causality’s most universal and distinctive characteristic. In medical diagnosis, for example, a group of co-occurring symptoms often become independent of each other once we identify the disease that caused them. When some of the symptoms directly influence each other, the medical profession invents a name for that interaction (e.g., syndrome, complication, or clinical state) and treats it as a\u00a0 new auxiliary variable, which again assumes the modularization role characteristic of causal agents-knowing the state of the auxiliary variable renders the interacting symptoms independent of each other.\u201d {Pearl, 1988 #5884} p. 385 \u20188. Learning Structure from Data\\ 8.1. Causality, Modularity, and Tree Structures\u2019;<\/p>\n

    [x]<\/span><\/a> The graphical causal models in medicine are gaining ground: [10] [11]\u00a0\u00a0 [12] [12-33] [11, 27, 34-45]<\/p>\n

    [xi]<\/span><\/a> \u201cThe calculus of causation consists of two languages: causal diagrams, to express what we know, and a symbolic language, resembling algebra, to express what we want to know. The causal diagrams are simply dot-and-arrow pictures that summarize our existing scientific knowledge. The dots represent quantities of interest, called \u201cvariables,\u201d and the arrows represent known or suspected causal relationships between those variables\u2014namely, which variable \u201clistens<\/strong>\u201d to which others. \u201c BoW<\/a> [46], p. 7<\/p>\n

    [xii]<\/span><\/a> Listening from a communication (science) standpoint is also an active and deliberate process, not a mere \u2018reception of data\u2019, but a meaning-seeking activity (\u2018sensemaking\u2019 is another such label, see e.g. in the AI context [47]). Note that a large part of the causality thinking in the 1980\u2019s happened on what was then labeled AI research, or \u2018device behavior\u2019 {Iwasaki, 1986 #15488}, and in \u2018decision science\u2019, see e.g. {G\u00e4rdenfors, 2003 #15502} or {Georgeff, 1988 #15503}.<\/p>\n

    [xiii]<\/span><\/a> \u201cThe relation of energy intake and expenditure to obesity is congruent with the conventional model. However, these components of energy balance are proximate, not root, causes of weight gain. In the compensatory phase (not depicted), insulin resistance increases, and weight gain slows, as circulating fuel concentration rises. (Circulating fuels, as measured in blood, are a proxy for fuel sensing and substrate oxidation in key organs.) Other hormones with effects on adipocytes include sex steroids and cortisol. Fructose may promote hepatic de novo lipogenesis and affect intestinal function, among other actions, through mechanisms independent of, and synergistic with, glucose. Solid red arrows indicate sequential steps in the central causal pathway; associated numbers indicate testable hypotheses as considered in the text. Interrupted red arrows and associated numbers indicate testable hypotheses comprising multiple causal steps. Black arrows indicate other relations. ANS, autonomic nervous\u00a0 system; GIP, glucose-dependent insulinotropic peptide.\u201d Medical diagnosing has been the focus or early \u2018decision science\u2019 works, see the \u2018Causal Understanding\u2019 [49] figure e.g.<\/p>\n

    [xiv]<\/span><\/a> This notation was also used by [50] and by [51] p. 244, and by Lok [52]; Reichenbach also used a close-by symbol : \u201cwhere the events that show a slight variation [from E] are designated by E*:\u201d p.137 [53].<\/p>\n

    [xv]<\/span><\/a> The process is more detailed: we subtract and add one same term to the causal effect, and then \u2018take expectations\u2019, i.e. averages the quantities across patients:<\/p>\n

    E(CausalEffecti<\/sub><\/em><\/strong>) = E (A1ci<\/sub><\/em><\/strong>If.LowerBMI<\/strong><\/sup> <\/sub>LoweredBMI<\/sub><\/strong> – A1ci<\/sub><\/em><\/strong>If.CurrentBMI<\/em><\/sup> Current.BMI<\/sub><\/em>) =<\/p>\n

    E (A1ci<\/sub><\/em><\/strong>If.LowerBMI<\/strong><\/sup> <\/sub>LoweredBMI<\/sub><\/strong> – A1c*i<\/sub><\/em><\/strong>If.CurrentBMI<\/em><\/sup> <\/sub>LoweredBMI<\/sub><\/strong> ) + E (A1c*i<\/sub><\/em><\/strong>If.CurrentBMI<\/em><\/sup> <\/sub>LoweredBMI<\/sub><\/strong> – A1ci<\/sub><\/em><\/strong>If.CurrentBMI<\/em><\/sup> Current.BMI<\/sub><\/em>) =<\/p>\n

    ATT \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 + \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Selection.Bias<\/p>\n

    Where ATT\u00a0 = the average treatment effect on the treated<\/u><\/em>: how much the A1c would \u2026 not drop among those who did lower their BMI, if\u2026 they didn\u2019t! Note, Eric Brunner from UConn stated it using econometric language and labels (\ud835\udc37 is Treatment) : \u201cWe suspect we won\u2019t be able to learn about the causal effect of college education simply by comparing the average levels of earnings by education status because of selection bias:<\/p>\n

    \ud835\udc38[\ud835\udc4c\ud835\udc56<\/sub><\/strong>|\ud835\udc37\ud835\udc56<\/sub><\/strong>=1]\u2212\ud835\udc38[\ud835\udc4c\ud835\udc56<\/sub><\/strong>|\ud835\udc37\ud835\udc56<\/sub><\/strong>=0]= \ud835\udc38[\ud835\udc4c1<\/sub><\/strong>\ud835\udc56<\/sub><\/strong>|\ud835\udc37\ud835\udc56<\/sub><\/strong>=1]\u2212\ud835\udc38[\ud835\udc4c0<\/sub><\/strong>\ud835\udc56<\/sub><\/strong>|\ud835\udc37\ud835\udc56<\/sub><\/strong>=1] (ATT)<\/p>\n

    +\ud835\udc38[\ud835\udc4c0<\/sub><\/strong>\ud835\udc56<\/sub><\/strong>|\ud835\udc37\ud835\udc56<\/sub><\/strong>=1]\u2212\ud835\udc38[\ud835\udc4c0<\/sub><\/strong>\ud835\udc56<\/sub><\/strong>|\ud835\udc37\ud835\udc56<\/sub><\/strong>=0] (Selection bias). We suspect that potential outcomes under non-college status are better for those that went to college than for those that did not; i.e. there is positive selection bias\u201d\u00a0 in his \u2018Causal Evaluation\u2019 graduate course handout]; an alternative notation brings both real&potential worlds in one formula, see Jordi Vallverd\u00fa’s<\/a> book (but common among causality writers) \u2018Causality for Artificial Intelligence. From a Philosophical Perspective\u2019: \u201cLet Y(T) represent the potential outcome for a patient with treatment assignment Y (where T is either 0 or 1). We can express the observed outcome Y as follows:<\/p>\n

    Y = T \u00d7 Y(1) + (1 – T) \u00d7 Y(0)\u201d or with my \u2018re-labeling\u2019, similar to David A. Freedman<\/a>‘s in fact (Yi<\/sub> = Xi<\/sub>Yi<\/sub>T<\/sup> + (1 \u2212 Xi<\/sub>)Yi<\/sub>C<\/sup>\u00a0:<\/p>\n

    YRealized<\/sub><\/strong> = T \u00d7 YIf.(T=1) <\/sup><\/strong>+ (1 – T) \u00d7 YIf(T=0)<\/sup><\/strong><\/p>\n

    [xvi]<\/span><\/a> We use Average for better intuition; mathematically inclined analysts use instead E(A1c), for \u2018expectation\u2019, which is the proper way to define a \u2018typical patient\u2019s value\u2019, or the mean of a variable. For a variable X with discrete values, the mean is \u03bcX <\/sub>= E(X) = \u03a3i<\/sub><\/strong> [xi<\/sub><\/strong>\u00b7p(xi<\/sub><\/strong>)], while for one with continuous values \u03bcX <\/sub>= E(X) =\u00a0 \u00a0([54], p. 152).<\/p>\n

    [xvii]<\/span><\/a> Even presence vs. absence can be sometimes difficult to separate: \u201cWhoever studied newspapers in the last decades came across the difficulties of defining when a person is dead, allowing the organs to be transplanted. Our hair and nails still grow long after our hearts stop beating;\u201d [57] p. 2. This topic of measurement error of binary measures is rarely talked about, in psychometric sense.<\/p>\n

    [xviii]<\/span><\/a> The confounding of \u2018causality\u2019 and \u2018time\u2019 is a known definitional problem: e.g. VanFraasen cites Reichenbach defining time in terms of causality ([58], p, 190), and many define time on the basis of the time construct.<\/p>\n

    *** Reichenbach himself said e.g. \u201cwe must now make sure that our definition of “later than” does not involve circular reasoning. Can we actually recognize what is a cause and what is an effect without knowing their temporal order?<\/p>\n

    Should we not argue, rather, that of two causally connected events the effect is the later one?<\/p>\n

    This objection proceeds from the assumption that causality indicates a connection between two events, but does not assign a direction to them. This assumption, however, is erroneous. Causality establishes not a symmetrical but an asymmetrical relation between two events.<\/p>\n

    If we represent the cause-effect relation by the symbol C, the two cases C(E1, E2) and C(E2, E1) can be distinguished; experience tells us which of the two cases actually occurs. We can state this distinction as follows:<\/p>\n

    If E1 is the cause of E2. then a small variation (a mark)” in E1 is associated with a small variation in E2. whereas small variations in E2 are not associated with variations in E1.\u201d [53] P. 136<\/p>\n

    <\/a>\"\"<\/a>\u00a0<\/a><\/p>\n

    References<\/em><\/p>\n

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       <\/p>\n","protected":false},"excerpt":{"rendered":"

      General definitional and notational setup *** Causality is not directly detectable or observable, much like forces[i] or energy aren\u2019t either: it needs to be discovered\/uncovered – \u2018detected\u2019 through observational consequences[ii]; on the other hand, it\u2019s a pretty natural intuitive human notion[iii], yet is considered a worthy \u2018problem\u2019[iv]. *** Causality is hardly a statistical matter, and […]<\/p>\n","protected":false},"author":2514,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"acf":[],"publishpress_future_action":{"enabled":false,"date":"2026-04-12 14:15:05","action":"change-status","newStatus":"draft","terms":[],"taxonomy":""},"_links":{"self":[{"href":"https:\/\/health.uconn.edu\/causality\/wp-json\/wp\/v2\/pages\/16"}],"collection":[{"href":"https:\/\/health.uconn.edu\/causality\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/health.uconn.edu\/causality\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/health.uconn.edu\/causality\/wp-json\/wp\/v2\/users\/2514"}],"replies":[{"embeddable":true,"href":"https:\/\/health.uconn.edu\/causality\/wp-json\/wp\/v2\/comments?post=16"}],"version-history":[{"count":31,"href":"https:\/\/health.uconn.edu\/causality\/wp-json\/wp\/v2\/pages\/16\/revisions"}],"predecessor-version":[{"id":134,"href":"https:\/\/health.uconn.edu\/causality\/wp-json\/wp\/v2\/pages\/16\/revisions\/134"}],"wp:attachment":[{"href":"https:\/\/health.uconn.edu\/causality\/wp-json\/wp\/v2\/media?parent=16"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}