"Our anesthesiologists are on strike."
When I create my own cartoons, I generally think of a gag first, and then illustrate it. Although once in a while I'll do it the other way around. For me, the latter is harder than the former, and usually when I see The New Yorker's caption contest drawing I'm stumped as far as a punchline. And when I see the winning entry later, I think, "Of course. How obvious!"
Being a New Yorker cartoonist myself, I've submitted drawings for their caption contest. What I try to go for is something that's visually incongruous, throwing things together that don't usually go together. And since I'm not the one who has to come up with the caption, I can get as crazy as I want. When a cartoon is driven by a good verbal gag, you can have that gag delivered by one person talking to another person at a bar, or whatever. But you can't get away with that in a caption contest. The image needs to be more striking, surprising or evocative, and make the reader wonder what the heck is going on in the picture.
Other than making a caption as concise as possible, I really know of no formula for creating a funny cartoon. After doing it for many years, it's still largley a mysterious process to me.