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Matt and Hailey take a deep dive into Chapter 26 in Modern Epidemiology, 4^{th} Edition, Analysis of Interaction. This episode needs a content warning- it is among the most advanced and conceptually complex topics we have ever covered on SERious Epi. Interaction occurs when the effect of one exposure on outcome depends in some way on the presence or absence of another exposure. Seems like a simple enough concept, right? However, as you’ll see in this episode, there are many different layers of complexity to consider related to terminology, scale, and interpretation of interaction analyses.

A note from Matt and Hailey: since this material is very complex, we reached out to Dr. Jay Kaufman for his perspective on the episode before releasing it. He had some very helpful thoughts, and we would like to share them with you (paraphrasing with his permission):

*Part of what is confusing about this topic is the terminology differences, with Hailey using terminology (“interaction”) that lines up with that used by VanderWeele, ME4, and the Hernán and Robins textbook chapter and Matt using terminology (“interdependence”) from other articles in the literature, such as Greenland and Poole (1988). When there are joint effects that are exactly multiplicative, or supermultiplicative, you know it’s a causal interaction (i.e., synergistic or biologic interaction) because multiplicativity is necessarily super-additive as long as both exposures meet consistency, exchangeability, and positivity assumptions. However, knowing that joint effects are submultiplicative is not informative about additive interaction or synergism. It is also not possible to make a conclusion about additive interaction when a results section tells you only that in a logistic or Cox regression analysis there is “no significant interaction effect (p<0.05)” as that just tells you an effect is not exactly multiplicative. Multiplicativity has some causal implications because it is super additive as long as the causal assumptions listed above are plausibly satisfied. There are several proposed causal mechanisms that would generate multiplicative joint effects especially from the cancer epidemiology literature (e.g., Koopman 1990). In general, considering interaction on the additive scale is more useful for assessing public health relevance (e.g. Panagiotou and Wacholder 2014).*

Some of these concepts are difficult to convey in podcast format, so we’re including some helpful resources for anyone interested in learning more about this topic. Thanks again to Dr. Kaufman for helping us put this list together:

- Greenland S, Poole C. Invariants and noninvariants in the concept of interdependent effects. Scand J Work Environ Health. 1988 Apr;14(2):125-9. doi: 10.5271/sjweh.1945. PMID: 3387960.
- VanderWeele TJ. On the distinction between interaction and effect modification. Epidemiology. 2009 Nov;20(6):863-71. doi: 10.1097/EDE.0b013e3181ba333c.
- VanderWeele TJ. The Interaction Continuum. Epidemiology. 2019 Sep;30(5):648-658. doi: 10.1097/EDE.0000000000001054. PMID: 31205287; PMCID: PMC6677614.
- Greenland S, Poole C. Invariants and noninvariants in the concept of interdependent effects. Scand J Work Environ Health. 1988 Apr;14(2):125-9. doi: 10.5271/sjweh.1945. PMID: 3387960.
- Koopman JS, Weed DL. Epigenesis theory: a mathematical model relating causal concepts of pathogenesis in individuals to disease patterns in populations. Am J Epidemiol. 1990 Aug;132(2):366-90. doi: 10.1093/oxfordjournals.aje.a115666. PMID: 2372013.
- Panagiotou OA, Wacholder S. Invited commentary: How big is that interaction (in my community)–and in which direction? Am J Epidemiol. 2014 Dec 15;180(12):1150-8. PMID: 25395027.