Response types + interaction

Response types + interaction

by Jean Digitale -

Can you help me connect the dots with the following:

  • I am fuzzy on exactly how you can infer that at least one of the 10 interactive types is present when additive interaction is detected (slide 12 of part 5), but the same does not hold for when multiplicative interaction is detected.
  • I believe it is related to the following, but can’t quite make the leap:
  • Per chapter 2 in RGL, page 12, if you dig into their example with table 2-1, you understand that the following is true:
    • The risk difference is the % causal types in the population when one exposure is considered
    • The risk ratio is the (% doomed in the exposed + % causal in the exposed)/% doomed in the unexposed in the population when one exposure is considered
  • Thus, for one exposure, the risk difference is dependent only on the causal type, whereas the risk ratio is dependent on both the causal and doomed response type.
  • I assume this relates to the fact that if additive interaction is detected (risk difference scale), you can detect at least one interaction type is present, but can’t determine that based on multiplicative interaction because it must take into account the other response types as well. But I’m not quite sure if this is correct/don’t quite grasp it. Can you offer any clarity?

Thanks,

Jean


Re: Response types + interaction

by Jean Digitale -

Hi all,

One other question on this - can you help us understand what it means for there to be interaction that is not sufficient-cause interaction? Meaning, it is clear that two causes interact if they are in the same causal pie, but we do not really understand how they interact if they are NOT in the same causal pie. Is this interaction or only effect modification? I have a vague sense this also relates to the proportion who are "doomed", but am unsure about this.

Thanks.

Re: Response types + interaction

by June Chan -

Hi Jean, 

for both your questions, can you please refer to where in the slides or readings you are referencing?


thanks, 

JMC

Re: Response types + interaction

by Jean Digitale -

Hi Dr. Chan,

For my first post, I’m trying to bridge the gap in my understanding between RGL chapter 2 section on strength of effects (page 10-13) (how do frequencies of causal complements change the effects we measure), and how this relates to RGL chapter 5 section on relation of response-type distributions to additivity (page 78-79). You also mentioned this in part 5 slide 12.

For my second post, interaction makes sense more intuitively to me when two exposures are in the same causal pie – VanderWeele says in section 1.9: “We might say that a “sufficient cause interaction” is present, if there are individuals for whom the outcome would occur if both exposures were present but would not occur if just one or the other exposure were present”. I can grasp that. However, we know that sufficient cause interaction is not always present; certain criteria have to be met for that to be true (as he goes on to discuss in section 1.9). It follows that you can have interaction that is NOT due to two exposures sharing the same causal pie. I am hoping we can discuss further what this looks like and why it happens. I do not understand how this happens. 

Thanks!

Re: Response types + interaction

by June Chan -

Hi Jean, 

These are good questions and I welcome comments from anyone in class on this, and we can discuss if we have time tmrw.

I can be around MH2 kitchen ~ 12:30 tmrw, in case you'd like to discuss, or I have office hours Monday.  

One thought/question that comes to mind - why do you state that "you can have interaction that is NOT due to two exposures sharing the same causal pie"?  I'm not sure where you are getting that from. It would seem that two exposures need to be in at least one causal pie to "interact". However, they don't need to be "sufficient" causes, and people can have disease other ways, and their "pies" may not have both those factors.  Not sure if that helps, or if I'm not understanding your question sufficiently (ha! no pun intended). 

probably best to try and discuss in person.  

G'night!

JMC

Re: Response types + interaction

by Maria Glymour -

Jean for an easy example of interaction by causes that don't share the same pie, imagine a world in which there are two causes of Y, and Y occurs in the presence of either or both causes.  In Rothman's pies, the two causes would be in different pies, because either is enough to result in the outcome.  But if cause 1 is present, then cause 2 is irrelevant, and vice versa.