There are several factors involved in deciding when a party is appropriate for children unaccompanied by parents: venue, theme, parent/guardians, child's maturity.
There are friends whom I would trust my youngest child, 4, even when he was younger, to care for my children at a small birthday party. However, there are other bday parties I did not allow a 10 or 11 year old to attend bc I did not feel "good" about the parental guidance (lack thereof) of birthday person.
As far as a party where many children are invited at a home, and I don't know the parents (I'd have to meet them!), I'd say maybe 10 or 11, when they are old enough to be confident in their discernment of appropriate and inappropriate behavior by others.