Paper 2: Does Obesity Shorten Life? Or is it the Soda? On Non-manipulable Causes?

The doi for this paper is https://doi.org/10.1515/jci-2018-2001.

What is the paper about?

The paper is a commentary about non-manipulable factors such as race and how they do not play nicely with the experimentalist view of causation.

What do the authors want us to know?

There is a mantra in the potential outcomes literature no causation without manipulation. The author of the paper, Judea Pearl, reviews the problems associated with this perspective. For example, we cannot manipulate race in real life but it is common knowledge that there are strong effects of race on numerous outcomes, from health to education to income. Pearl introduces the structural causal model framework as an alternative perspective where:

1. the concept of interventions do not require a real-life or physical counterpart and
2. the notion of consistency is not an assumption, but a theorem¹ of counterfactual logic.

Instead, variables are causal (or have a causal character) because they respond to changes in other variables

What did they do?

The author challenges Hernan’s position that to talk about the causal effects of obesity is meaningless since a vaguely defined intervention can lead to violations of the consistency assumption.

Pearl first takes umbrage with the way that Hernan presents BMI as the marker for obesity and makes it clear that obesity is should be described with reference to many factors².

Next, Pearl raises what he argues is a limitation in the Rubin model whereby counterfactuals may appear inconsistent when the antecedents³ are conflated with the external intervention devised to enfore the antecedent⁴.

Pearl then explans the do-operator (he developed the idea) and that it was intended to denote the operation of holding a variable constant. He argues that when Hernan claim that \(P(mortality = y | do(obesity = x))\) is undefined because the consequences of obesity depend on how we choose to manipulate it, they missunderstand what the do-operator is intended to represent. Specifically, the do-operator does not depend on any choice of intervention, it is defined relative to a hypothetical, minimal intervention needed to establish \(X = x\), i.e. it is defined independently to how the event came about.

Pearl goes into this in more depth to expand on this point, but I didn’t see that he added much to his original argument other than to iterate some parts.

Next Pearl discusses the idea of scientific versus policy-based causation and does provide some analogies. One that I liked was his reference to the ideal gas law⁵ \(PV = kNT\) that approximation of the behavior of many gases where \(P\) is the absolute pressure of a gas, \(V\) is the volume it occupies, \(N\) is the number of atoms and molecules in the gas, and \(T\) is its absolute temperature. The constant \(k\) is called the Boltzmann constant and has the value \(k = 1.38 × 10−23 J/K\).

You cannot manipulate \(P\) directly, but there is a causal implication of changes in \(P\). That is, in order to induce changes in pressure \(P\), there always has to be changes in \(V\), \(N\) and/or \(T\). However, we would think in terms of the effect of \(P\) rather than \(V\) etc. For example, we would generally think in terms of how a specific tyre pressure would influence the likelihood of a puncture on an unsealed road or the quality of the ride. We would not think in terms of the effect of air volume in our tyres.

Pearl caveats the hard versus soft science perspectives, and stresses the need to avoid locking ourselves into pigeon holes.

What did they conclude?

Primarily that applied science requires both scientific and clinical perspectives to communicate knowledge. His position is that both the effect of interventions and the health consequences of obesity are important and meaningful and are legitimate targets of scientific inference.

What was unclear?

Pearl’s writing can be technical, nuanced and philosophically dense. This paper is no exception and therefore I may have missed some important points or subtleties in this summary. For example, what Pearl meant by causal character is unclear to me.

Some of the critique on consistency as an assumption versus consistency as a theorem was unclear due to my own ignorance with alternative causal inference, specifically Pearl’s approach.

Pearls argument rests primarily on the validity of his conceptualisation of causal inference, which is founded on a large body of work drawing from philosophy, science, mathematics and statistics. I am not sure that it provides a clear way forward and the applied researcher is left to choose which approach to adopt with limited guidance. While providing such guidance wasn’t the point of the paper, it feels like it raises more questions than it resolves.

Footnotes

1. A statement that can be proved mathematically.

2. This seems odd given that obesity does have a definition that is based purely on BMI and that is used routinely by clinicians.

3. A thing logically preceeding another.

4. Admittedly I did not understand where Pearl was going with this. However, in On the consistency rule in causal inference: axiom, definition, assumption, or theorem? Pearl expands on this point.

5. I have updated the symbols to align with what are more commonly used in Physics text books.