Engaging busy professionals, like doctors, is very challenging, especially when your value proposition is unclear. Get clear on what the value of them connecting with you is. If what you're offering isn't compelling, don't be surprised when even friendly connections don't bite. Don't be discouraged, instead learn from it and figure out what you can provide that they find value in.

As others have said, you'd likely have more success leveraging your existing network or attending medical conferences, which may lend themselves more naturally to having these types of conversations (you're right that they're expensive though!).

All things considered, I think a 25% connection rate and a 1% interview rate is great.