Not having a roof on your car is, of course, very problematic in rollover accidents, as noted by the Insurance Institute for Highway Safety's Highway Loss Data Institute. This suggests that convertibles increase the risks for drivers. While this may be true when the car actually rolls -- a higher proportion of fatalities do happen in these rollover accidents -- that doesn't necessarily mean that a convertible is less safe overall.
This has changed significantly in the last few decades. For instance, in 1990, the driver death rate in hardtop cars was 29.1 per 1 million vehicles, while the rate in softtops came in at 72.8. Just 15 years later, in 2005, the rate for both had fallen dramatically and become virtually the same: 20.6 for hardtops and 19.8 for convertibles.
The reasons for the decline are many. For one thing, other safety features have helped, such as rollbars and stability control systems. These can make accidents and rollovers less common, leading to a decline in these types of fatalities.
One expert also noted that modern convertibles have additional structural reinforcements, with many of these built into the undercarriage. This makes them heavier than hardtop cars and improves their handling on the road. The sides are also reinforced and heavier to protect those inside, meaning convertibles end up being more crashworthy, despite the lack of a roof.
When buying a car, it is important to know the risks it poses and just how safe it can keep you. However, no car will protect you in all accidents. When a negligent driver causes a crash and you're injured, you need to know how to seek compensation.
Source: IIHS, "Death rates aren't higher in convertibles, but a roof still is safer," accessed Feb. 24, 2017