Catching a rat in a trap isn't a simple set-and-forget procedure. The right sort of bait has to have correct physical qualities as well as aroma.
Peanut butter is the most popular and effective bait for rats and mice. It's aromatic, tasty and sticks to the trigger of the trap.
Another aromatic option, cheese will certainly attract rats but might not catch them. Cheese tends to separate from the trigger easily, and a rat might steal it without being caught.
In some cases, bits of string might be more of a draw than food. Tying a bit of bacon to the trigger can be a doubly powerful attractant.
Trap hinges and trigger mechanisms need occasional lubrication to work properly. Don't use machine oil; vegetable oil or a little WD-40 will loosen the action without repelling the prey.
Bait choice might not be the problem. A poorly functioning trap teaches animals to stay away. Test the trap and adjust the trigger for a light touch.