I think if you have a good mirror and use it, develop riding-in-traffic skills, don't anger drivers, and keep up your vigilance, you should be safe, except from a random act by an idiot. That could happen driving as well.

I pick roads that either have a nice shoulder or little traffic. Fast traffic doesn't bother me as long as there is a wide shoulder. I keep to the right side of the shoulder. If I have to ride on a road with little or no shoulder I keep checking my mirror. If it looks like someone is going to overtake me at the same time as someone is going to go by in the oncoming lane (so there's no room for the passing car to give me a wide berth) I pull over. Some numbskulls will try to pass anyway when there isn't sufficient room. They think a few inches is plenty, and they're so skillful they can pull it off. Sometimes they can, but what if they can't? I'd rather pull over and let them pass. It takes a few moments of my day, but if I stay alive, great.

Some people talk about "taking the lane" when you need to. I agree, when you need to, but I tend to pull over and wait, rather than taking the lane too soon. If a car has to follow me at my speed for very long, the driver will get mad. I don't want to be on the road with a car driven by someone who's mad at me. I'd rather sacrifice some of my time and convenience. If I need to get in the left lane for a turn and it isn't clear, I'll usually wait on the shoulder until it is.

You need to develop skills for riding on a narrow street with parked cars. You don't want to get hit from behind, but you don't want to get "car-doored" either. Again, being patient and willing to sacrifice some of your own time and convenience for staying safe is a prudent attitude.