Partial engine failures are 3 times more likely than total failures and are potentially more hazardous if not handled correctly.
The Australians have some interesting stats and papers on this topic:-
Between 2000 and 2010, there were nine fatal accidents resulting in 20 people losing their lives as a result of a response to a partial power loss soon after takeoff. Importantly, there were no fatal accidents where the engine initially completely failed.
Pilots warned of partial power loss dangers
More detailed information here:-
Managing partial power loss after takeoff in single-engine aircraft