The effects seen in the various sub-groups and endpoints are all non-significant at the p = 0.05 level. The lowest I can see is p = 0.07 (cardiac death prevention, as reported in their Table 3).
The multiple-hypothesis correction they apply is reasonably appropriate in the case of simply looking at all results, which is what they do.
Furthermore, because the outcomes are disjoint (cardiac survival vs stroke vs sudden death vs all-cause mortality, etc) there is no simple way to combine the results.
To take a silly example, studying the effect of seatbelts on cancer and cardiac death might well show a bit of an effect on both (because people who wear seatbelts are generally healthier, say) but it would be illegitimate to combine those two studies because the endpoints are (so far as we know) unrelated to each other. Without some kind of causal account the issues become very deep and difficult to say anything very definitive about.
So I'd say their statistical treatment is fair and appropriate. If fish-oil is supposed to have such a large effect as to be worth taking the risk that it increases the risk of prostate cancer, its effect should be unequivocally measureable in population studies. That is not the case.
For what it's worth, I think the prostate cancer studies are at least as flawed, at least the one I've seen, which is a case-control study that shows an extremely modest increase in relative risk of the kind it is very easy to produce from statistically identical populations: http://www.tjradcliffe.com/?p=1745
The multiple-hypothesis correction they apply is reasonably appropriate in the case of simply looking at all results, which is what they do.
Furthermore, because the outcomes are disjoint (cardiac survival vs stroke vs sudden death vs all-cause mortality, etc) there is no simple way to combine the results.
To take a silly example, studying the effect of seatbelts on cancer and cardiac death might well show a bit of an effect on both (because people who wear seatbelts are generally healthier, say) but it would be illegitimate to combine those two studies because the endpoints are (so far as we know) unrelated to each other. Without some kind of causal account the issues become very deep and difficult to say anything very definitive about.
So I'd say their statistical treatment is fair and appropriate. If fish-oil is supposed to have such a large effect as to be worth taking the risk that it increases the risk of prostate cancer, its effect should be unequivocally measureable in population studies. That is not the case.
For what it's worth, I think the prostate cancer studies are at least as flawed, at least the one I've seen, which is a case-control study that shows an extremely modest increase in relative risk of the kind it is very easy to produce from statistically identical populations: http://www.tjradcliffe.com/?p=1745