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Two sisters say their father would be alive today if he had been given a CT scan when he was admitted to Medway Maritime Hospital.
Tammy Reeder, 25, and Naomi Rose, 21, have rejected a compensation offer of £15,000.
In a letter to the family's solicitor, the NHS Litigation Authority said it was admitted Medway NHS Foundation Trust "breached its duty of care" following 64-year-old Peter Rose's admission to hospital.
The letter added:"It is further admitted that had the Trust not breached its duty, Mr Rose may have survived."
Mr Rose’s daughters, who are both from Rainham, are now suing the Trust for alleged negligence. They are also demanding that an inquest is held and an investigation carried out by the Health Care Commission, the Government's watchdog body.
The family contacted clinical negligence solicitor Sarah Harman to see if they had a case after they read about Jenna Lester - the 16-year-old, from Wainscott, who died in 2007 after Medway Maritime Hospital failed to carry out a CT scan which could have also saved her life.
Mr Rose, from Wigmore, died at the hospital last July
A CT scan was meant to have been carried out on Thursday, July 24, 2008, but it never took place. Instead medical staff relied on a scan taken in 2006, wrongly thinking it was a recent one.
He died from a twsited intestine, which led to other complications, including a heart attack.
Sarah Harman said: “This is a very serious and worrying case."
She said that an up to date scan would have shown that Mr Rose had a bowel obstruction which could have been operated on and his life saved.
No-one at the hospital admitted to Tammy and the family that serious errors had been made and if she had not come to me as a result of other media reports about the hospital the family would never have known the true situation.
A hospital spokesman declined to comment.