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The interesting part:

For people without cardiovascular disease, hazard ratios were 1.13 (95% confidence interval 1.10 to 1.17) for the transition from healthy status to atrial fibrillation and 1.05 (1.00 to 1.11) from healthy status to stroke. For participants with a diagnosis of a known cardiovascular disease, regular use of fish oil supplements was beneficial for transitions from atrial fibrillation to major adverse cardiovascular events (hazard ratio 0.92, 0.87 to 0.98), atrial fibrillation to myocardial infarction (0.85, 0.76 to 0.96), and heart failure to death (0.91, 0.84 to 0.99).

I'd love to know what possible mechanism could cause this?

I wonder if it's just a case of reverse causation though? "Healthy" people who have family histories of heart disease, subsyndromal health issues, etc being more likely to take fish oil.

For participants with a diagnosis of a known cardiovascular disease, regular use of fish oil supplements was beneficial for transitions from atrial fibrillation to major adverse cardiovascular events (hazard ratio 0.92, 0.87 to 0.98), atrial fibrillation to myocardial infarction (0.85, 0.76 to 0.96), and heart failure to death (0.91, 0.84 to 0.99).

These people were already sick with cardiovascular disease. I'd be interested in a peer review