dynamic89

acceptances seemed to come before rejections in previous years tho

Duke statistics or biostatistics? I only applied to their statistics department.

So Duke has sent out some rejections today, but no acceptances?

No I didn't get accepted anywhere. I wasn't serious about attending last time--I only applied to harvard yale princeton and berkeley. Nevertheless a waitlist decision from Yale means there's a chance without the GRE. Having said that one of my recommendation letters was from a very well known PDE guru. I don't know..you'll probably crack a top 5 school if you take the GRE but maybe only manage top 10 or 15 without.

I applied to a few applied and pure maths programs a couple of years ago without the maths GRE. I was waitlisted at Yale and rejected by others. My area was also PDEs (with irregular coefficients). So I guess there's chance but the GRE will definitely help.

You are pretty much on the right track. I graduated with a maths major and only had very limited stats background, so I was in exactly the same position when I finished my undergraduate. I guess you could either take grad level stats courses or work a stats related research job for a couple of years like myself. In my opinion, grad level coursework definitely looks more attractive if you are aiming for a Masters. I would say don't worry about the GRE maths subject test, and take a course that involves lot of programming, which is crucial for a stats program especially data science... I am no expert but I would think that stats/data science is such a interdisciplinary science so a background in chemical engineering with some stats preparation should serve you pretty well in the application process. You've got plenty of time to work on the stats, you'll be fine.