The boy and his grandparents, Kathy and Alvin Liknes, were last seen Sunday night when Nathan's mother left him at their Parkhill home for a sleepover. The O'Brien family had been over helping out with an estate sale and when she arrived to pick Nathan up Monday morning, his mother found the Liknes's home empty.
Police say there are signs the three did not leave the house willingly.
For the past week, investigators have been interviewing neighbours and are looking to speak with everyone who attended the estate sale on Friday, Saturday and Sunday.
They've also been looking at CCTV video from the area and say they are pleased with the progress being made so far in the investigation.
"I would say it's less a mystery to us," said Staff Sgt. Doug Andrus with the Calgary Police Service's homicide unit. "Are we closer than yesterday? I would say we are."
Police hoping for the best
Many questions are still unanswered about what happened to Nathan and his grandparents.
On Thursday, police said they still don't know the motive behind their disappearance and "have no suspects [they] can name."
The Amber Alert first issued for Nathan at 5:15 p.m. MT on Monday is still active and investigators say they are working with the Canada Border Services Agency and partner agencies in the U.S.
Police say they have had a tremendous response from the public, including tips, and are working hard to keep moving the investigation forward.
"We're keeping an open mind, looking at all possibilities, hoping we'll find them alive," said Andrus on Thursday.
Earlier that same day, the chief of the Calgary Police Service said he is convinced someone knows something about the disappearance.
However, investigators say the circumstances are suspicious.
Search for information continues
A website has been set up for people to offer messages of support to the family.
The blog has been created as a dedicated place for those messages after police say support began rolling in from across Canada.
It also contains information on how people can submit tips to Crime Stoppers.
Anyone with information or who attended the Liknes's estate sale is still being asked to come forward to speak with Calgary Police Services, which can be reached at 403-266-1234, or Crime Stoppers, which is at 1-800-222-8477.
Investigators say people may not even realize they know something that could help the investigation and so they are looking to talk with as many people as possible.