Being knocked off my bicycle by a car door finally convinced me, after too many uncomfortably close encounters, that I was somehow invisible to drivers. Today I believe that for my well-being the risks of biking far outweigh any potential benefits.
1. You, the cyclist, need to be driving very defensively. Read the road and always assume you have not been seen and take action to do fix that.
Here in the tiny streets of Cambridge, UK, I sometimes feel cycling in the middle of the street is the best option. BTW, an equally big risk to cyclists is pedestrians who, by sheer stupidity or collectively having death wishes, start crossing the road without looking. It's worse when it's a group.
2. Get some high visibility gear and get a helmet and pads. I also use two sets of lights: the reds at the back are placed one high (my back or helmet) and one low, and the front lights are angled differently to give me full coverage for a good distance.
The cheapest and lightest way for visibility gear is the "jacket" type that you wear over your clothes.
I used to commute by bicycle about 20 miles a day (total) from the East side of Edinburgh, through the middle of town and out to the West (to the Riccarton Campus) - I worked late a lot so I was often returning in the dark.
Best thing I ever did was get an extremely powerful set of lights (Vistalite I think) - they were very expensive but I'm sure they saved my life on multiple occasions. I used to have one light angled so that it illuminated the road with the other pretty much shining into the faces of car drivers - probably not legal but at least I knew I could wiggle the handlebars to shine a light into a drivers face if they were about to do something that would cause a problem.
Unfortunately, bright lights can't protect you from other road hazzards - kids throwing a brick at me being an example of what cyclists have to put up with.
I never really got why would people cycle/jog on busy roads.