I agree with other posters that it probably isn't as simple as "epidurals cause interventions."
I'm not denying that lying on your back, being immobile or feeling contractions less do have an effect on your ability to labour and push.
However, it's probably equally as likely that women who are already having a difficult labour for one reason or another are the ones who choose to have an epidural.
I had one after 36 hours of early my arse labour - constant contractions, standing up (only comfortable position), not being able to keep any liquid, let alone food, down (HG returning with a vengeance) and till having barely made it to 4cm. So it was less the pain that made me choose to have an epidural than being absolutely bloody knackered and needing something to give me a bit of a break.
I ended up with an emcs fairly swiftly anyway, but I suspect even if I had dilated quite quickly and given birth soon, I would have been more likely to need some form of intervention as I was probably too exhausted and dehydrated to push effectively.
So there's probably an inbuilt aspect where women who have epidurals have a reason (exhaustion, poorly positioned baby etc) that might see them needing intervention anyway.
No idea how you'd measure that though!