Her physical decline has been in stages, a tragic reverse of the triumphs of a growing child. At four she could scramble up the nursery climbing-frame; at six she was in a wheelchair; at eight she had lost her power of speech. Now she is fed through a tube into her stomach. There's no name for her illness, but doctors liken it to a neurological condition called progressive cerebellar ataxia.
"We never thought of Anne-Marie as having a disability. She was just our sister," says Agnes who, dressed in a crop-top and hipsters, is the picture of a carefree 18-year-old. But her directness and quiet confidence tell a different story.
"She was always a favourite with everybody. It wasn't until she got her first wheelchair when she was five, that you realised she was different." That difference, and people's reactions to it, have caused Agnes considerable heartache. "I had a few friends who weren't able to cope with Anne-Marie as she is.
"They used to get fed up because I had to phone up and cancel trips and sleepovers, but they have to accept Anne-Marie as well as me." Now, says Agnes, she has more disabled than able-bodied friends.
The Cochranes live in a neat little cul-de-sac tacked onto the bleak streets of Bridgeton in Glasgow. Name-calling, stone-throwing, threats - other children's reactions to the family have been difficult enough to cope with, but the adult responses have been more hurtful, says Agnes. "They would stop and stare and just say nothing. And mothers used to tell their children not to play with us. It's not like you can catch a disability."
Teachers, too, have shown little understanding. When Agnes was in her fifth year at secondary school, her mother had to tell her that Anne-Marie would never get better and was going to die, probably quite soon.
"The first time I found out about it, my grades went right down. I couldn't concentrate on homework and in school I was just trying to get through the day. I didn't want to learn anything. I couldn't see the point.
"My teachers gave me a hard time about homework being late. Some of them were aware of what was happening, but they thought it was just an excuse."
She is grateful to the teacher who always asked about Anne-Marie's progress and suggested her homework could wait until her sister came home from hospital. It was Agnes's own determination and astonishing maturity that got her out of the darkness.
"I realised that no matter what I do, Anne-Marie's death is going to happen anyway. It made me determined to get to university. It's for Anne-Marie. I want to do something to help disabled people."
So Agnes now has five good Highers under her belt and an unconditional place at Glasgow Caledonian University to study nursing, specialising in learning difficulties.
Agnes's 16-year-old sister Annette wants to become a paediatric nurse and her older sister Catherine is an occupational therapist. "Anne-Marie has had an awfully big impact on our lives," says Agnes. "That's why I wouldn't change anything. I wouldn't swap her for the world."
Anne-Marie's condition has taken a heavy toll on her family. Mrs Cochrane,after years of lifting, caring and worrying, suffers from arthritis and Crohn's disease, and her husband has had to give up work to help her.
"My mum has always tried to give us as normal a life as possible," says Agnes. "That's what's helped a lot. Mum's kept it sane."
The only time Agnes's voice breaks a little is when she talks about Anne-Marie's death. "You can't think ahead too much," she says, "but you have to think ahead a bit." Then she laughs. "That sounds like a contradiction, but you have to be prepared, but not dwell on it. It's like my mum said, you don't cope with it, you just get on with it."
Back in the sitting-room, I say goodbye to Anne-Marie.
"She's still the same cheeky wee person inside," says Agnes. "You just look at her and you know what's she's thinking. Anne-Marie's coped with this better than any of us," she adds. "She's the real star."