Q:

Do fish oil or omega-3 fatty acids increase the risk of cancer?

A retrospective study came out that found a correlation between increased blood levels of omega-3 fatty acids and increased incidence of prostate cancer.
The skeptical responses I've seen come from those who tend to promote dietary supplements.
Could the correlation really be due to prostate cancer patients taking omega-3 supplements or replacing red meat with fish?

A:

Your question asked whether the association between levels of long chain omega-3 polyunsaturaed fatty acids (LCω-3PUFA) and prostate cancer could be caused by the prostate cancer patients taking LCω-3PUFA supplements. 
The study Plasma Phospholipid Fatty Acids and Prostate Cancer Risk
in the SELECT Trial [1] was a 427 centre trial which enrolled 35,533 patients without known prostate cancer from 2001-2004 and followed them for a number of years.  Those that developed prostate cancer were matched by age-race to controls in the study without prostate cancer.  They studied 834 subjects who developed cancer in the first 6 years of the study.  They then added other subjects who developed cancer in subsequent years. The blood samples examined were those taken from entry into the study, ie. before the diagnosis of prostate cancer.  So, to your question was to whether subjects who developed prostate cancer then took fish oils or ate fish in response to the diagnosis, then the answer to this is no.  The difference between the high risk group and low risk was equivalent to eating salmon twice a week.
The next question of interest is to whether there are any health benefits at all from swallowing marine sourced LCω-3PUFA but all we can say is regarding cardiovascular health, and here the answer is again no.  NICE no longer recommend the consumption of either oily fish, or fish oil supplements to prevent cardiovascular disease based on studies such as this one [2], and a more recent study looking to see if there were cardiovascular benefits with people with already existing peripheral vascular disease also found none. [3]
So, it would seem best at present to source your omega-3s from plants such as flaxseeds. And as the message seems to be again, eat whole foods and not supplements.

[1] Brasky TM, Darke AK, Song X, [..], Kristal AR. Plasma phospholipid fatty acids and prostate cancer risk in the SELECT trial. J. Natl. Cancer Inst. 2013 Aug 7;105(15):1132-41. doi: 10.1093/jnci/djt174. PubMed PMID: 23843441. 
[2] Rizos EC, Ntzani EE, Bika E, [..], Elisaf MS. Association between omega-3 fatty acid supplementation and risk of major cardiovascular disease events: a systematic review and meta-analysis. JAMA. 2012 Sep 12;308(10):1024-33. doi: 10.1001/2012.jama.11374. PubMed PMID: 22968891. 
3] Enns JE, Yeganeh A, Zarychanski R, [..], Taylor CG. The impact of omega-3 polyunsaturated fatty acid supplementation on the incidence of cardiovascular events and complications in peripheral arterial disease: a systematic review and meta-analysis. BMC Cardiovasc Disord. 2014 May 31;14(1):70. doi: 10.1186/1471-2261-14-70. PubMed PMID: 24885361. 

