Hello Tanguy,

Thank you for the comments; I’m glad to see folks are getting use from the material. I would be happy to address your questions.

To start, both of your questions are fully explored in the text “What If” by Miguel Hernan and Jamie Robins at Harvard. The textbook is a freely available PDF. A hyperlink is included in the Medium post. This text is an awesome awesome awesome text, I cannot recommend it highly enough. Below I will mention the general chapters that pertain to your questions. But if you have the opportunity, I would suggest reading this text from back to front like a novel. It starts simple, but ends with the most novel state-of-the-art methods for causal inference under time-varying confounding. It’s awesome.

Regarding the use of “stabilized weights” in my coding example, apologies on my part, I don’t think I explicitly mentioned stabilized vs unstabilized weights in the Medium piece itself. I’m going to assume you understand Marginal Structural Modeling with unstabilized weights (which is just the inverse of the Propensity Score weights for the treated, inverse of the (1-Propensity Score) for the untreated). It turns out, it’s also valid to have any functional of the intervention (in this case “A”) in the numerator of these weights when fitting a Marginal Structural Model. Having the probability of the observed treatment in the numerator of these weights are sometimes called “stabilized” weights in the literature. Using stabilized weights over unstabilized weights can (in certain situations) have statistical efficiency benefits and produce sampling estimators with lower sampling variance. Chapter 12 in “What If” covers this question in more detail.

Great question on SWIGs. Your comment that SWIGs seem awful similar to cDAG without adding much value is quite correct, at least for the simple toy problem presented in my post! Where the power of SWIGs over traditional cDAG comes into play is for problems with more complex causal structures. In particular, when you get into sequential longitudinal interventions with time-varying confounding, it can be very difficult to identify if quantities of interest on the graph are d-separated from simply examining the cDAG. Examining the SWIG makes it much more clear. Part III of “What If” (Causal inference from complex longitudinal data) delves into this topic deeply. If you’re interested, another one of my posts (Causal Inference in Data Science: A/B Testing and the need for Marginal Structural Modeling) leverages a toy problem where the usefulness of SWIGs over cDAG is a bit more clear. For more SWIGs info than what is covered in “What If”, please see the following link:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.644.1881&rep=rep1&type=pdf

I hope you find the above useful. Please reach out with any further questions.

Happy reading! 😊

- Andrew