Simpson's "paradox" is a well-known phenomenon that can be counter-intuitive for beginners: it is possible, say, for a medical trial to reveal that a certain treatment is beneficial to men as a group and to women as a group, but harmful to humans in the aggregate.
My first question is: what do practitioners do in such cases? Will doctors recommend the above treatment to their patients or not? Or is the Simpson's phenomenon ipso facto indicative of insufficient sample size/significance level, and hence renders the trial inconclusive?
Finally, has anyone studied quantitative versions of Simpson's phenomenon?
For the case in which all patient descriptors are in the correct part of a causal diagram, a necessary but not sufficient condition for which is that the descriptors are assessed at "time zero" or before, Simpson's "paradox" is nothing more than a failure to ask a specific enough question. Stay away from marginal treatment effects and instead condition on all available information that is consistent with causal pathways. In the case of age and sex it is seldom inappropriate to condition on them. Treatment effects should be conditional and respect information flow. Focus on making the best treatment decision for the one patient being treated.
- Solved – Is Simpson’s Paradox always an example of confounding
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- Solved – Examples of Simpson’s Paradox being resolved by choosing the aggregate data
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- Solved – How to resolve Simpson’s paradox