A proper metric space quasi-isometric to a finitely generated group and a horoball space over such a group must be quasi-isometric to a rank-one symmetric space or the real line.
Metric L ie groups--- C arnot- C arath\'eodory spaces from the homogeneous viewpoint , volume 306 of Graduate Texts in Mathematics
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Hyperbolic spaces with geometric and geometrically finite quasi-actions are symmetric
A proper metric space quasi-isometric to a finitely generated group and a horoball space over such a group must be quasi-isometric to a rank-one symmetric space or the real line.