This story is told exclusively from the perspective of Maud, who is an eighty year old woman suffering from dementia. It seems that Maud lives in her childhood home with a daytime caregiver and a daughter who check in on her regularly. Unfortunately, their checking in isn't enough to keep Maud out of trouble. Maud makes frequent calls to the police or leaves her house in search of her friend, Elizabeth, who she believes is missing. Maud becomes very irritated that no one seems to be looking for Elizabeth but her. Part of Maud's frustration stems from the memory of her sister, who disappeared when they were young and the girl was never found. There are many flashbacks throughout the story telling events leading up to and after Sukey's disappearance.
Two problems with Elizabeth is Missing and you might have figured out the first based on the beginning of this post. Reading a novel from the perspective of a person who has lost their mind is repetitive and exhausting! Definitely makes you realize you don't want that disease though. The other is related to the first, the story gets bogged down in the redundancy and after a while you don't care, you just want to get out of that head.
If you are interested in the effects of dementia or Alzheimer's a better option would be Still Alice.