So I've been having the same battery drainage issues with my Note 4 as well. I got mine back in October and still have the original battery. Yesterday my phone died 3, yes three, times yesterday! I even sent a tweet out publicly to samsung and verizon about this and all I've been doing is chatting with samsung mobile support over twitter direct messages.
I've noticed that my battery will also go from 20% and then turn off. And when I check battery usages, Android OS is running at close to 20%. This has significantly become worse since Verizon sent out an update just a couple weeks ago. I'll post up some of my battery usages soon.
What should I do?