Trying to figure this out about myself is the thing that finally pushed me to send off a tube of spit - just to see if I had any problematic alleles.
One thing about APOE4 carriers: it's associated with a blood brain barrier that's less-permeable to EPA/DHA, potentially starving the brain of this, which it appears to need.
There's a workaround though, make sure the fish oil you're taking is phospholipid. There are multiple sources, but the most common is fish roe (so, yes, it's a good excuse to eat caviar).
All that said, it's quite possible that the brain issue with Alzheimer's is not due to a lack of DHA/EPA. The determinant symptoms are tau tangles and amyloid plaques - and possibly relatedly, amylin is secreted from the beta cells in your pancreas, along with insulin (about a hundredth as much). I can't help but wonder if this disease is a long term result of consuming more carbohydrates than that particular person can tolerate, spiking both insulin and amylin.
Once upon a time, I had access to, essentially, all the medical records in Great Britain (in anonymized format, of course) which would have let me try to disprove this. I would have expected long term metabolic syndrome to be correlated with Alzheimer's, and type one diabetics to be inversely so (hey, no beta cells).
If you're someone who does have access, I'm interested enough that I'd be glad to help whip up some SQL queries.