Well, God may not decide whether you live or die, I may be missing something, but does it specifically say that in the bible?
Working off GCSE R.E here, but I could've sworn there was something about how if you commit suicide its a sin because you're going against God's wishes of when you die. Or something.
Also, maybe it's as a pecaution going the hospital? Maybe it's God making sure the medicine works?
Why would he need to make sure the medicine works if he can save you without it? Or indeed, if he chooses when you die? And why would you need precautions if he's going to save you or kill you, and your fate is already decided?