Does combustion occur more easily at higher oxygen concentrations or just higher oxygen partial pressure?

I saw a trailer for The Martian and started thinking about space flight. I know that spacecraft and spacesuits often operate at low pressure with high oxygen content (near 100% $\ce{O2}$ at about 20 kPa), which is harmless to humans and keeps the mass of the space vehicle lower. Humans do just fine with an oxygen partial pressure of 20-30 kPa as long as other gases present are in safe amounts.

But an issue I hadn't considered is the effect on combustion. A lot of people mistakenly believe that the Apollo 1 fire was due to using pure oxygen in the test, but that's only part of the issue, and astronauts routinely use nearly pure oxygen at low pressure even today.

So my question is, is flammability affected by the total concentration of oxygen in the atmosphere, just its partial pressure, or some combination of the two?

As a specific example, what affect would a 30 kPa almost pure oxygen atmosphere have on flammability?