If you have had prostate cancer (PC), or are at high risk of the disease, it would be prudent to stop eating eggs more than occasionally, especially if you live in North America.
Interest in this topic began in 2004, but the thinking at that time was that eggs were innocuous. But this was followed by a “bombshell” study from the Harvard School of Public Health, Boston, showing that “greater consumption of eggs…was associated with [a] 2-fold increases in risk” of a diagnosis of fatal PC compared to men who consumed the fewest number of eggs. A 2011 follow-up study from the same group found that “men who consumed 2.5 or more eggs per week had an 81 percent increased risk of lethal prostate cancer compared with men who consumed less than 0.5 eggs per week.” This led to considerable publicity in the United States.
A follow-up 2015 study found a 47 percent increased risk of life-threatening prostate cancer. A 2016 study from the same group similarly found that high intake of eggs was associated with a doubled risk of advanced PC. 
These are observational studies, of the kind that can find correlations, but do not provide proof that eggs themselves cause PC. That idea is simplistic, in any case. (The Chinese have the highest rate of egg consumption in the world and also one of the lowest rates of fatal PCs.) But there is a biochemical mechanism by which eggs could plausibly promote PC: yolks contain an abundance of choline, a B-vitamin like substance that is found abundantly in prostate cancer. The Harvard authors also found that men with the highest intake of choline had a 70 percent increased risk of being diagnosed with lethal prostate cancer. (Choline is even the basis of an FDA-approved PET scan for prostate cancer.)
The studies in question did not take into account the quality of the eggs consumed. Could it be that American or Canadian commercial eggs are harmful, but that eggs from organic free-ranging chickens are not? Eggs are the basis of a huge mass production business in the United States. To quote the American Egg Board:

“In the major egg producing states, flocks of 100,000 laying hens are not unusual and some flocks number more than 1 million. Each of the roughly 280 million laying birds in the U.S. produces from 250 to 300 eggs a year. In total, the U.S. produces about 75 billion eggs a year, about 10 percent of the world supply.”

These hens are often kept in so-called ‘battery cages” the size of a piece of letter paper! Hens may be starved to increase their egg production. 
Could this production method, or other factors in the production, distribution and consumption of eggs, contribute to the production of unhealthy eggs in the US? We don’t know, but there is a measurable chemical differences in eggs from hens that are raised in cages vs. those that are free-ranged or are enriched with n-3 polyunsaturated fatty acids (PUFA).
There is another important insight contained in the CapSURE study:

“When associations were analyzed separately by geographical region (North America vs. other continents), positive associations between…egg intake…and advanced…and fatal cancers were limited to North American studies….Observed differences in associations by geographical region warrant further investigation” (emphasis added).

Since these effects were limited to North America, it raises the question of whether there is something in the way American eggs are raised or prepared that could account for their particular harmfulness. According to Business Insider:
“In the US, large-scale laying houses are preferred over the free-range systems commonly used in the UK [and many other countries, ed.]. The factory farm environment means more eggs can be produced on a smaller amount of land, but it also makes eggs more susceptible to contamination….”
Could the increased diagnosis of fatal prostate cancers be limited to factory farm-produced eggs in the United States and Canada?  Definitely. But, in the meantime, I recommend erring on the side of caution: I would suggest that all PC patients, or others at high risk, cut back or eliminate their consumption of all eggs, especially the yolks. It is the prudent thing to do.
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Acknowledgement: Thanks to Dr. Geo Espinosa for bringing this topic to my attention through his blog at
Keum N, Lee DH, Marchand N, et alL. Egg intake and cancers of the breast, ovary and prostate: a dose-response meta-analysis of prospective observational studies. Br J Nutr. 2015 Oct 14;114(7):1099-107.
Wilson KM, Mucci LA, Drake BF, et al. Meat, Fish, Poultry, and Egg Intake at Diagnosis and Risk of Prostate CancerProgression. Cancer Prev Res (Phila). 2016 Dec;9(12):933-941
Richman EL, Kenfield SA, Stampfer MJ, et al. Egg, red meat, and poultry intake and risk of lethal prostate cancer in the prostate-specific antigen-era: incidence and survival. Cancer Prev Res (Phila). 2011 Dec;4(12):2110-21