It has very little to do with maths actually. The maths of meta-analysis is really quite simple, it's just a weighted average, if the included studies all make the same errors in terms of confounding than by definition the weighted average will also have this error
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Replying to @GidMK @K_Sheldrick
"if the included studies all make the same errors in terms of confounding than by definition the weighted average will also have this error" That assumes there is a confounder that is global in bias. Otherwise, it's random. It's a coinflip embedded in a coinflip that...
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...that may or may not change the outcome depending on whether it's larger than the observed effect size. In this case, that would have to be enormous, so it's extremely unlikely you wouldn't be able to name it since you've read the majority of the studies.
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Such global confounders have been found, historically, but are fewer and fewer in modern medical science because it's harder to find anything with a large effect that wasn't thought of after these many decades. Most that remain are likely tiny.
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Replying to @EduEngineer @GidMK
Sorry I know I said I wouldn't respond anymore but I can't not bite at that. Are you serious? Is that actually a serious comment?
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Replying to @K_Sheldrick @GidMK
My last argument is "OMG, you just wrong, man." May I invite *you* to a recorded discussion of the mathematics?
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Replying to @EduEngineer @GidMK
Pre-Recorded? Absolutely not. Live and unedited? I'm interested. What topic, what rules?
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Replying to @K_Sheldrick @GidMK
The topic: Do confounders specific to individual studies with no assumed relationship (correlation) have an expected (binomially normalized) effect on a p-value computed from a set of more than 1 study. Recorded live.
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Replying to @EduEngineer @GidMK
Nope. That's actually not a meaningful topic and makes a number of assumptions that are invalid. Confounders specific to individual studies? Almost all confounders I can think of would be consistent across most studies of a fixed type. 1/
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Replying to @K_Sheldrick @GidMK
But that was the point we were debating. Otherwise, it's up to you two to either identify this globally correlated confounder, or show it exists in the data. Otherwise, it's a complaint that applies to any meta-analysis all the time.
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I mean, either that or you could try an argument that isn't just a weird straw man lol. For a start, consider how confounding might cause similar effects across different studies even if the specific confounders are not identical
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