God doesn't cause the problems, but He does allow them, because He is God and He is in charge. That is comforting to me, because it assures me that nothing is beyond His control. But He doesn't allow bad stuff just to be mean. When He does, it's for a good reason, but we may not understand the reasons at the time. But many times He allows us to go through things so that we can relate to and encourage others with the same problems, like the doctor that WG mentioned.
In TWI we were taught that martyrs died for their faith because they didn't or couldn't believe for deliverance. That contradicts Hebrews 11:39, though, which says, "And these all, having obtained a good report through faith, received not the promise." They didn't receive the promise in their lifetimes, but were confident that God would keep His promises, even if it meant raising them from the dead. They held fast to the same promise of blessings that were given to Abraham, who also did not receive it in his lifetime. When we see the "big picture" - that this life is just preparation for what's to come - even the worst of life's problems are nothing in light of resurrection and eternal life.