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Re:Meat consumption and risk of 25 conditions: outcome-wide ... by YeGoblynQueenne on Wednesday March 03, 2021 @08:15AM (#26327857)
"Positive association" means "yes, there is an association". I think of it as answering the question "is there an association?" in the positive.

"Positive association" doesn't mean that there was an association with a "positive", as in "beneficial" result.

The study found that this positive association with health risks was "attenuated" (read: reduced across its range) after adjusting for BMI, meaning there is also a positive association with BMI that confounds the effort to draw a firm conclusion from the studied data.

This is clarified further in the rest of the paper:

Role of BMI

In the present study, most of the positive associations between meat consumption and health risks were substantially attenuated after adjusting for BMI, suggesting that BMI was a strong confounder or possible mediator for many of the meat and disease associations. BMI is an important risk factor for many of the diseases examined (e.g. diabetes [7]). BMI was highest in participants who consumed meat most frequently, and some previous studies have found that high meat consumption is associated with weight gain [56, 57], but it is unclear whether this indicates any specific impact of meat or an association in these populations of high meat intakes with high total energy intakes. The associations of meat with disease risk reported here which remain after adjustment for BMI might still be due to higher adiposity, because BMI is not a perfect measure of this characteristic; we observed similar effects when adjusting for waist circumference (results not shown), but, as with BMI, waist circumference is not a perfect measure of adiposity and there could still be residual confounding.

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