"She was a true inspiration, a trail blazer for women in fiction and a creative force. She will live on through her characters but we already miss her beyond words."
The best-selling author, who is the sister of actress Joan Collins, 82, had spoken to her three daughters Tracy, 54, Tiffany, 48, and Rory, 46, about her illness.
She gave an interview from her home in Beverly Hills five days ago, saying she had no regrets.
Collins said she had lived life like Frank Sinatra, and "done it my way".
In the interview with People, she said: "Looking back, I'm not sorry about anything I did.
"I did it my way, as Frank Sinatra would say. I've written five books since the diagnosis, I've lived my life, I've traveled all over the world, I have not turned down book tours and no one has ever known until now when I feel as though I should come out with it."
The novelist, who spent most of her later life in America, wrote 32 books - all of which made it onto the New York Times Bestsellers' List.
