Oh, right misunderstood. Yes absolutely true, but I thought we were arguing about whether vegetarians were at an increased risk of depression, not whether carnivores were
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Also, the method of cohort selection can bias a study enormously. You'll be picking only those for whom the diet has worked perfectly, which means that you miss out on the (potentially much larger) cohort for whom it either worked modestly or not at all
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So if you select your intervention group from, say, an online forum, immediately your result is almost certainly going to overestimate the benefit of the diet. Then, there's a good chance your comparison group will also introduce further bias
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Why do you need a control group? Any diet a person says they do is the answer. Couldn't we study many different diets? Maybe ask how 'hard' people do their diets to measure commitment? Get macro averages and food sources. Not CICO but Keto, veg, vegan, carnivore, pkd, etc.
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That's a pretty fundamental issue in research. As a spectacular epidemiologist I know says, "the biggest problem for any study is regression to the mean" Without a comparison group, impossible to know if your treatment did anything or if it was going to change anyway
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