Dmytry comments on How to avoid dying in a car crash - Less Wrong
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There are studies that were controlled for this, as much as possible.
The double blind trials found no statistically significant effect of medication on attempted suicide rate due to too small sample sizes:
http://www.ncbi.nlm.nih.gov/pubmed/21450154
(see the wide 95% ci). Such findings were reported by media - thanks the advertisment money from manufacturers - as the connection having been disproved. It's a multi billion dollar subject. Mankind is bad at processing multi billion dollar subjects.
[insert standard peeve against frequentists' ridiculous usage of significant here]