From the Ladder of Causation to the ladder of Modeling and Simulation – an essay

In The Book of Why(Pearl and Mackenzie, 2018) on causal inference, Pearl proposes the ladder of causation going up in three steps from the seeing to doing to imagining. The discussion in the book seems to have been inspired by machine learning and reading the book, I was wondering how the proposed ladder relates to pharmacometrics. I concluded that the relation is very tight, but that for pharmacometrics, one could rename the three steps as Data, Model and Simulations. Here my thoughts.

The Ladder

The Data

At the first step of the Ladder of Causation we have associations. Observing what things come together or after each other. We are not able to say what happens, if we do something. In the context of modeling and simulations, it is more intuitive to refer to this step as the data. We have the data, and we can look at associations in the data. Here at this level, it does not matter whether we get the data from observing what happens around us, or whether we perform an experiment with an intervention that produces some outcomes.

The Model

At the second step of the Ladder of Causation we have the intervention. We are interested in what happens if we do something, or how we can make something happen. Clearly one way to answer the question is to do something and observe what happens. We perform experiments and collect and analyze the resulting data. However, performing the required experiments may not always be possible and is not necessarily required. Having some ideas of causal relationships, these ideas can be refined by observing what Is happening around us, and refine our ideas based on what we observed. We say that we use a causal model to analyze the data to obtain our answer. Even, if we do not need a model to analyze the data, we need it to come up with a causal question and design the experiment in the first place.

In the context of model and simulation, this step of the ladder corresponds to the model. We propose a model which we think answers our question, we design an experiment based on it consisting possibly of observations only, and then fit the model to the data to obtain estimates of the causal effect. For an ideal randomized experiment, there is limited discussion on the model to use. We need to regress the treatment on the outcome. Moving away from randomized experiments, the question of which model to use becomes more difficult, and results that we will obtain will depend on the model. In any case, without a model, we cannot ask the question nor design the appropriate experiment.

The Simulations

At the third level we consider aspects which we have not and possibly cannot be observed, the counterfactuals. In the context of modeling and simulation, this simply corresponds to the simulations that can be used to quantify aspects that have been observed but also aspects that have not been observed.

References

Pearl, J., Mackenzie, D., 2018. The Book of Why: The new science of cause and effect. Basic Books, New York.