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Architect Joanna Yeates, 25, has not been seen or heard from since Friday following a night out with work colleagues in Bristol.
Her parents David, 63, and Teresa, 58, from Hampshire, have spoken of their fears during a press conference at a police station in Bristol.
Mr Yeates said: "I think she was abducted after getting home to her flat. I have no idea of the circumstances of the abduction because of what was left behind."
He continued: "I feel sure she would not have gone out by herself leaving all these things behind and she was taken away somewhere. I don't know by whom. She's a sensible girl and professional lady."
Miss Yeates' mother said her daughter was planning to spend the weekend at the flat in Clifton to prepare for a party she and her boyfriend had been planning to hold on Tuesday.
"She had a nice flat and new things and wanted it to be special," said. "She wanted to finish her Christmas shopping and do some cooking and baking for Tuesday."
Police investigating the disappearance are examining new CCTV footage and have also taken a phone and laptop computer from Miss Yeates' boyfriend Greg Reardon.
Known as Jo to friends, Miss Yeates was last seen leaving the Ram pub in Park Street, Bristol, at about 8pm, walking up the street.
She stopped in Waitrose and then carried on to the Tesco Express on Regent Street at about 8.40pm where she bought a pizza.
A receipt from Tesco was found in her flat, along with the cream-coloured coat she had been wearing.
Police said Mr Reardon had already left to go to Sheffield before she returned from the pub and it was not until he came home that he realised there was something wrong.
She has not taken any possessions with her and her family say her disappearance is very unlike her.
Police have appealed for any information that may help their inquiries.