Anne Cameron's family firmly believe she passed away in "tragic circumstances" as police search for a crocodile that may have taken the 79-year-old from a Port Douglas creek.
On Facebook, Anne's granddaughter Isabella Eggins thanked those who helped in the extensive search for her nan.
"It is my deep regret to inform you that following an extensive search and the discovery of certain items as a result of that search, we have the firm belief that my nan Anne Cameron has passed away in tragic circumstances," Isabella wrote.
"She will be missed and will always be loved by her family."
Results are expected today from forensic testing on "biological matter" found near clothing and a walking stick after Ms Cameron, a dementia sufferer, went missing from her nursing home.
She was last seen near the OzCare Aged Care facility at Craiglie, Port Douglas, on Tuesday afternoon.
Police fear Ms Cameron, who had only been at the facility for a few weeks, may have been taken by a crocodile after becoming disoriented when she wandered into a dense area of bushland.
A Department of Environment and Heritage Protection spokesman says traps will be set in an attempt to catch the crocodile as police and wildlife officers continue to look for the woman's body.
Clothes and a walking stick with Ms Cameron's name on it were discovered on Thursday at the end of Four Mile Beach.
"We have also located some biological matter which we believe to be human remains and these are being tested in Cairns," Acting Inspector Ed Lukin said on Thursday.
"We continue to search the area in the hope of finding her alive (but) because of the proximity of these items near the creek bank, we cannot rule out the possibility of a crocodile attack.
The results of the forensic tests are likely to be released on Friday.