Waikato DHB interim chief executive Derek Wright said Yang was a long-standing oncology nurse.
"Her colleagues are supporting the family and we hope for a safe return."
Detective Sergeant Jason Earl earlier described her disappearance as being "out of character" and said police and her family had serious concerns for Yang's welfare.
Multiple searches of the Waikato river by the Police National Dive Squad over the weekend and on Monday morning found nothing.
Neighbours of the family have also been helping search for her by the river near Pukete and Flagstaff.
Yang is Korean and was wearing a black puffer jacket, black jeans and round black glasses.
Yang's family, through police, declined requests to speak to media, asking for privacy at this time.
Anyone who may have seen Annie since Thursday evening are urged to contact the Hamilton Police on 07 858 6200.