Elmore Leonard's researcher says the novelist and screenwriter remained hospitalized in a Detroit-area hospital Tuesday, a week after he suffered a stroke.

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Gregg Sutter told The Detroit News the 87-year-old scribe is "doing better every day, and the family is guardedly optimistic.

"He's showing great spirit. He's a fighter, and we're glad to see that," Sutter said, adding Leonard has been working on his 46th book.

Leonard's novels have been adapted as the films "Get Shorty" and "Out of Sight," as well as the TV series "Justified."