Even though I picked up that the fan patting herself on the back for her self-centred behaviour was the trigger, I didn't actually link it with the later description of the child until quite a long way through the book. Of course, that's partly because Christie cleverly obscured exactly what the illness was. I was sandbagged when I finally made the connection -- and I think that I too would have been tempted...

I hadn't realised until I read one of the other reviews on LibraryThing that the inspiration for the story was almost certainly what happened to Gene Tierney.