Is it possible to compare stats from this to what is required to be
able to do this hike?
VO2 max is the best indicator of fitness.
Running will increase your VO2 max. VO2 max is the amount of Oxygen your blood can hold per Kg per minute. This is an important factor in all endurance exercise, especially exercise at altitude.
The higher your VO2 max is, the better you will cope with climbing/walking. So running is an excellent training mechanism for walking/climbing.
You can get this tested though it is not straight forward.
One thing to bear in mind is that as you climb the amount of Oxygen in your blood will decrease. The rate of this decrease is complicated and reliant on lots of philological factors. Two seemingly identical people will have varying decreases in this depending on many, many factors.
When you do not have enough Oxygen in your blood you enter an Anaerobic state. Climbing and walking are slow twitch excercises. These work best in an aerobic capacity. So the more oxygen in your blood the longer you will be in an aerobic state and the better you will perform.
That said anaerobic exercise is good at increasing your VO2 max capacity.
Say like running 15 miles in a certain time?
Running 15 miles in a certain time (or whatever) is not a good scientific measurement of fitness. Did you go up hill? How much do you weigh? etc. etc. So no I would say there is no measurement (like running x miles) that is a good indicator of your performance in a climb.
Running is a great exercise but a bad indicator of climbing endurance. Mountain climbing is very different for many reason from running. The best test for mountain climbing ability is to climb mountains. From a practical point of view, try steadily, increasingly, difficult climbs. This will allow you to gauge at what point you start to struggle.