My understanding is that even a difference in altitude of a few hundred feet may make the difference for someone with altitude sickness, hence the urgent need to get them to a lower altitude as soon as symptoms appear. It would appear that, above 10,000 feet, a difference of air pressure of less than 1 psi would equate to an altitude change of over 1000 feet.

From 9000 feet to 10000 feet: 10.5 - 10.1 = .4 psi
From 10000 feet to 15000 feet: 10.1 - 8.29 = 1.81 psi

(http://www.sablesys.com/baro-altitude.html)

However, there is probably more to it than simply putting someone in an inflatable cylinder and pumping up the volume.