Most often this refers to “time to progression” (abbreviated TTP), which is simply the time from randomization to progression of the disease. This differs from “progression-free survival” in that it will not include patients who died before their disease progressed. Thus, the FDA generally considers progression-free survival an endpoint that more closely matches overall survival, and you will not see very many drugs approved on the basis of this endpoint.
Cancer clinical trials can also consider time to other events. For example, clinicians may be interested in seeing how a treatment affects the time to progression on the NEXT treatment. This is termed time to second progression, and it can help answer important questions about whether the new drug has some kind of lingering effect that helps or hurts your further treatment options.
Another common time-to-event analysis is time to treatment failure (abbreviated TTF). This measures the time from therapy start to termination, which could be due to toxicity, progression, or death. This can be useful for getting a sense of how much the toxicity is impacting efficacy of a drug.