History doesn't give us a guide to determine how to make roundabouts safer for cyclists because hard data are lacking. The National Cooperative Highway Research Program, however, did its best and came up with Development of Roundabout Crash Prediction Models and Methods (https://www.nap.edu/catalog/25360/development-of-roundabout-crash-prediction-models-and-methods).
The study looked at more than 350 roundabouts in the United States and examined previous worldwide research on the topic. Studies dating back as far as 2000, indicated that the more lanes entering a a circle and the greater the variation in speed of vehicles entering, the more dangerous for cyclists. An Australian study showed that bicyclists were more likely to get hit when vehicles entered the circle than when in the circle or upon exiting.
Not only have few researchers studied the subject, few crash reporting agencies note that an accident occurred at a roundabout, making examples unavailable to study. Most of the studies of roundabout safety simply don't consider cyclists. But this one says that fortunately, “frequency of vehicle–pedestrian and vehicle–bicycle crashes at roundabouts is typically very small.” Bicycle incidents amounted to only about one percent of accidents found.
But the program's effort found “insufficient vehicle–pedestrian and vehicle–bicycle crashes represented in the assembled database to enable the development of a model for predicting the frequency of these crashes.”
While the database included some injuries to cyclists, it found no fatalities. But with a paucity of data, the project couldn't recommend ways to make roundabouts safer for cyclists.