One reason Peter Sellers wasn't in It's a Mad, Mad, Mad, Mad World was that he wanted the same kind of money he'd been receiving for being the sole star of the movie and if they'd paid him that, they would have had to pay the same thing to Milton Berle, Buddy Hackett, Mickey Rooney, etc. So they got Terry-Thomas instead.
Another reason was that Mr. Sellers had another movie to begin shooting…a pretty good comedy which came out fifty years ago tomorrow. It was Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb. According to Eric Schlosser, a lot more of that film was true than some of us might imagine.