Mae West in "It Ain't No Sin" - 1934

Doesn't this dress just suit her so well? "It Ain't No Sin" was the working title for the movie that became "Belle of the Nineties", due to censor problems. (Check the link to find out about the parrots!)

Radio Stars Magazine -1931 - Mae West and the Radio Jinx

The article inside the magazine refers to the jinx...the idea is that other movie stars hadn't done well in Radio, but they expect that Mae would do fine so long as she passed the censors. She did work in radio, a few sketches in 1937, (Edgar Bergen's radio show), but there were issues with censors and she ended up being banned from Radio.
But Ms. West did OK without radio, she had a fabulous career.