There are some things that annoy me as a scientist. When I read a newspaper article about new and exciting research results, and then I read the original paper and "the new and exciting results" are, to put it mildly, exaggerated. Or when my husband is impressed by someone else’s research but not mine, because mine is too complicated. And also when my fellow scientists download a dataset, run several regressions, and then publish without even starting to think why it should be the way it is. The book that I read is exactly about asking why: “The book of why: the new science of cause and effect” by J. Pearl and D. Mackenzie.

I was trained to abstain from causal claims. Let me give you a specific example. Neurons in our brain engage in rhythmic patterns of activity. We call these patterns oscillations. However, it’s not that neurons shake, but rather their membrane potential changes from time to time, which creates a flow of charged particles. When these charged particles move, we can measure them with, for example, electroencephalography (EEG). Because the flow of particles is directed and direction changes from time to time, on the EEG signal we observe oscillations. I am trying to unravel the relation between the number of neurons in the cortex and the power of alpha oscillation. 

Based on the description above, I suppose you can agree that neurons produce alpha rhythm. If there were no neurons, no alpha rhythm could be observed. Alpha rhythm does not produce neurons. However, if I were to measure somehow the number of neurons, correlate them with the power of alpha rhythm, and find that they are correlated, I would say “the number of neurons correlates with alpha power”. So I would say “correlate” and not “cause”, because correlation is not causation. I was trained that way.

Apparently, the uncomfortable discrepancy lies in the fact that I assume causation while I say correlation. Many, if not all, researchers do that. Moreover, the problem is that society needs causal explanations. We, as researchers, should try to deliver causal explanations. 

Not that it’s all hopeless. The gold standard for revealing causation experimentally is a double-blind, placebo-controlled interventional study. If we want to know if a drug cures allergy, we should run a study with three groups: one would receive the drug, the second would receive a placebo, and the third would remain on the waiting list. Given that the groups only differ in the intervention and nothing else, we may afterward claim that a drug caused relief from allergy symptoms. 

However, if I want to claim that 100 neurons cause 1 unit of alpha power, I would have to add or remove some neurons and see if alpha power changes. This is not possible. Does it mean that all that I’m left with are correlational claims? The book suggests that there is a way.

The way is causal graphs and do-calculus. A causal graph is a representation of all experimental (observed or hidden) variables and relations between them. Do-calculus is a set of formulas to apply to causal graphs. This way, firstly, requires us to take on responsibility for hypothesizing a causal model that could operate. Secondly, to try to make a causal model sufficiently accurate and detailed. Thirdly, to find out what data we need to collect or whether the data we have are sufficient to answer a causal question by classifying all variables into the treatment, the outcome, mediators, colliders, and confounders.

Let’s assume we cannot run an interventional study for a drug and seasonal allergy, but we may collect observational data. Then for the case of allergy drug (treatment) and allergy symptoms (outcome), we may have the following additional variables:

1. A confounder is a variable that affects both the drug use and the allergy symptoms. For example, allergy sensitivity (how pronounced the allergy is). Because the person is more sensitive, she will experience more symptoms. Because the person is more sensitive, she will take a larger dosage of a drug. The confounder is the evil one; it should be measured and controlled for. if not, we are risking to attribute causal effect, when in reality, there is none.

2. A collider is a variable that is caused by both the drug and the symptoms. For example, sleep problems. Certain allergy drugs cause sleepiness, so the person may report sleep problems. Some allergy symptoms, like a runny nose, cause difficulties with falling asleep or staying asleep, so the person may report sleep problems. Both drug use and symptoms independently contribute to sleep problems. The collider is the peaceful pal; don’t control for its effects.

3. A mediator is a variable that lies on the causal path between the drug and the symptoms. For example, inflammation. The drug reduces inflammation. Less inflammation leads to fewer allergy symptoms. The mediator is the cool guy. Introducing a mediator in the model may reveal the mechanism of drug action. With a mediator, such as inflammation, we may claim that the drug works by reducing inflammation. However, it all will work only if we can measure the mediator. Otherwise, we may only speculate.

To summarize, the confounder is bad. If we are running a regression, we should control for it, e.g., add it in the regression model. A collider and mediator can be omitted. However, and this is very important, first we have to think in terms of causal relations. We have to build a causal model for our data and decide which variables are confounders, mediators, and colliders. Only after that do we proceed with regression.

The process of controlling for all confounders but not colliders is called the back-door criterion. A back-door path is every non-causal path between treatment and outcome that contained a confounder. We block the back door when we add a confounder to a regression. If a confounder is categorical, like allergy severity (could be light, medium, and bad), stratification on the severity is an option (running regressions within categories).

For cases when a back door cannot be blocked but there is a mediator, the front-door rule exists. However, it’s not an easy fix. For this to work, the causal graph should agree with several other assumptions. For example, the effect should be fully mediated via the mediator (or several mediators). It’s not clear how common it is to use the front-door rule. But in my field of research, it’s not even common to use causal graphs.

TLDR To allow causal inference on observational data, we should have a causal model with treatment, outcome, and all confounders, colliders, and mediators. Then we use back-door and front-door rules to block all the causal paths from treatment to outcome except for one, the one that we are interested in.

I was introduced to causal graphs during a statistics course in my first year of my PhD. However, only now, after reading the book, was I able to appreciate the power of causal graphs. The common argument against using causal graphs could be "but how did you know?" The answer is "we don’t know". The true power of causal graphs is thinking in terms of causal graphs. It clears the relations; it formalizes the operations. The truth is that including too many variables in the regression is just as bad as not including enough. After all, when the causal graph is thought through and published as a part of research, other scientists will estimate how plausible these causal assumptions are and may further suggest an improvement. By not explicitly stating causal assumptions but holding them implicitly and hiding behind the correlation facade, we decrease the ease with which the results could be communicated. I would appreciate scientists openly stating in papers what they believed to be the causal influence with plain words rather than convoluted sentences aimed at avoiding the word "cause".

I’m not sure if I would be able to convince my co-authors to use a bit of causal language in my next paper, but I will certainly allow myself to think in causal terms and use the causal graphs to guide my hypotheses and interpretations.

Favorite quote:

“It is okay to base your claims on assumptions as long as you make your assumptions transparent so that you and others can judge how plausible they are and how sensitive your claims are to their violation.”

June, 2025