This is one of the Peanuts specials where Linus' security blanket is not seen or even mentioned.
Originally planned as a 5-minute educational video to be shown to young cancer patients, Charles M. Schulz suggested that the project be expanded to a full half-hour special. CBS and producer Bill Melendez initially balked at the idea, but ultimately went ahead with it due to Schulz's enthusiasm of the project. Schulz was touched by the idea as his mother Dena succumbed to cancer on the night he was drafted for WWII. Schulz himself would later succumb to cancer on February 12, 2000, mere hours before his final strip appeared in newspapers worldwide.
When Charlie Brown and Linus go into Janice's hospital room the loudspeaker announcement calls for a Dr. Melendez, a reference to producer Bill Melendez. Some time later the same loudspeaker calls for a Dr. Jaimes, in reference to director Sam Jaimes.