Thank you very much for your response!
I did actually consider applying for a PhD in epi or global health. But like you said many such programs require either an MPH (or similar graduate experience) or at least a biology background which I don't have.
My background is in pure math. And I do really really love math - did an REU, did some other research, took a ton of math classes. But I realized I couldn't do something so divorced from practical applications as a career, hence stats. And I've since worked as a days analyst for a university's global health program, hence the interest in biostats. I really want to do any kind of work that helps people with public health, doesn't need to be epidemiology if that isn't reasonable.
But do biostatistics PhDs end up working for NGOs? I have mainly seen a lot of academia, tech companies, or big pharma - not so much of NGOs. Is that something I could do? If not, then maybe a PhD in stats really isn't for me. I just think that I have a chance at getting into some programs and also that I'd really enjoy the math, but if it wouldn't be possible for me to do the sort of work I'd like to, then I'll think more seriously about an MPH.