Mr Hume said the NHS in Scotland was failing to support older people to live independently at thome, after an investigation by The Herald revealed lengthy delays in providing services such as physiotherapy.
He said: "These figures show once again that SNP mismanagement of the NHS is failing older people.
"With an ageing population … living longer lives and for longer in periods of ill health, the delivery of these key services needs to shape up and it needs the support of government to do that."
Some patients in Renfrewshire are waiting up to 36 weeks to get a visit from staff trained to help them look after themselves, according to figures uncovered by The Herald.
Experts have described the delays as unacceptable.
They say that by the time some receive a visit from a rehabilitation professional, such as a physiotherapist, it could be too late to have the best effect.
Health Secretary Alex Neil recently pledged £5 million to upgrade local health services to help patients stay at home.
Scottish Labour's health spokesman Neil Findlay said: "This is further evidence of the delays to treatment which are endemic in the NHS under Alex Neil."