Structural Causal Models to Clarify Causality in Neuroscience

Neuroscience is full of causal questions. Is this brain area necessary for a behavior? Does this drug decrease seizure frequency in epileptic patients? Does the firing rate of a neuron influence the firing rate of that other neuron? But while there are many different causal questions there are also slightly different notions of causality. Barack et al. 2022 rightly call for more clarity when asking and answering causal questions. Here I want to makea point that will hopefully help with adding clarity to causal reasoning in neuroscience. My point specifically relates to the power of structural causal models (SCMs). (Judea Pearl has taken note of the paper and that SCMs are not mentioned. Find his tweet here. I recommend anyone to read The Book of Why.)

Specifically I want to make two main points:

  • A structural causal model (SCM) is extremely useful and adds clarity to causal reasoning.
  • I agree that multiple concepts of causality will be useful in neuroscience but all of them become much clearer when explained with a SCM.

I will start by defining what a SCM is and then I will try to make some neuroscience questions more clear.

The Structural Causal Model

A structural causal model (SCM) consists of three sets. The set U contains the error terms that are outside (exogenous) to the model. The set V contains the variables inside (endogenous) to our model and we are interested in the causal relations between them. Finally, the set E contains a functions that describe each variable in V in terms of other variables in V or U. Thereby, E describes the causal relationships in the SCM. The mathematical description is neat but SCMs also have a very clear graphical representation, where each variable V is a circle and arrows between circles show causal relationships. For example, the SCM below proposes causal influences on neuronal activity during optogenetic perturbation.

Fig 1.

This is extremely useful. It tells us that the neuronal activity is determined by multiple variables and an optogenetic construct we might introduce becomes one of those factors. A small disclaimer: you might be missing the errors terms U. If each variable in V is associated with exactly one error term they are by convention omitted in the graphical model. So gaining optogenetic control over neuronal activity would be hard. Cutting all other arrows would probably be impossible. But we could use the non-linearity of the system and try to find optogenetic stimulation strengths where other variables become negligible. But I don’t want to stay with this model for too long because it’s just for illustrative purposes. Instead I want to talk about the different definitions of causality.

The Path Definition of Causality

The causal definition I usually work with goes like this: if there is a directed path from x to y, x has a causal influence on y. Also: if there is no directed path from x to y, x does not have a causal influence on y. Below are some SCMs where in the upper three (A, B, C) x has a causal influence on y, whereas in the lower three (D, E, F), x does not have a causal influence on y.

Fig 2.

In A, there is a directed path but z also acts as a confounder. In B, z is a mediator. In C there are two causal pathways, a direct one and one mediated by z. In D, there is a path but it is not directed (it collides on z). In E, there is a path but it is not directed (this is the SCM that gives you correlations between ice cream sales and violent crime). In F, the path is in the wrong direction. So we can use SCMs to clarify any kind of causal relation. One thing the graphical representation of SCMs does not tell us what the exact form of the causal relationship is. This is not necessarily a bad thing because it means our definition of causality does not depend on linearity. But sometimes we need to know whether y is continuous (neuronal rate) or nominal (mouse going left or right or staying). That is usually easy to clarify in writing. A bigger issue is that causal inference in SCMs works best only if there are no cycles between variables. Cycles however, are pretty normal in neuroscience (I work on the hippocampus where a lot of information flows in a loop).

So what to do about cycles? This is where time comes in. We can define the SCM at a timescale where the cycle is negligible. For example, in Fig 1 I have the variable “Previous Activity” (for an interesting usage of previous activity as instrumental variable see Lepperød et al. 2022). If that doesn’t work for you because you are interested in a time scale where the previous activity is still being influenced by the current activity (a truly unbreakable cycle), then there is probably no way around actually simulating the dynamical system with respect to time.

In summary, I believe that any concept of causality becomes more clear when we draw a SCM. If you can think of a concept that does not work in SCMs let me know. Another concept that does not come up in Barack et al. 2022 is do-calculus which also becomes very clear when shown with a SCM.

do-calculus, interventions and counterfactuals would be interesting to write about at some point but for now I’m out of time.