Just from an optics standpoint, a convertible looks like it would be slightly more dangerous than any other type of vehicle. The driver does not appear to have nearly as much protection. Some people are especially worried about rollover accidents because there is no steel cage to protect the occupants if the car overturns.
However, studies have found that convertibles are typically no more dangerous than any other type of vehicle. There does not appear to be any increased danger, even with the reduced amount of protection. Additionally, many companies that make convertibles have taken additional steps, such as strengthening the A-pillars, to give the car more structural stability, even if the roof is down.
Ejection risks
One thing to consider is that there is an increased chance of a passenger or driver being ejected from the vehicle in the event of a rollover. In theory, wearing a seat belt should help them, so some people who are ejected from their vehicles were not wearing their safety belts to begin with. But it is technically a bit more common for someone to be ejected in a convertible, specifically in a rollover crash.
On the other side of the equation, though, convertibles by their very design are often less likely to roll. A small car tends to have a low center of gravity and is very close to the road. Larger vehicles that are top-heavy, like semi-trucks that undergo a load shift, are more likely to roll over.
Seeking compensation
Even though convertibles are safe, there are some risks to be wary of. If you have been injured in an accident that another driver caused, take the time to carefully look into your options to seek financial compensation.