You don't often see a cross-over design used in a time-to-event trial. If the event is death, the patient would not be able to cross-over to a second treatment. Even when the event is treatment failure, this often implies that patients must be watched closely and perhaps rescued with other medicines when event failure occurs.

When it is implemented, a time-to-event outcome within the context of a 2 × 2 crossover trial actually can reduce to a binary outcome score of preference. Suppose that in a clinical trial, time to treatment failure is determined for each patient when receiving treatment A and treatment B.

• If the time to treatment failure on A equals that on B, then the patient is assigned a (0,0) score and displays no preference.
• If the time to treatment failure on A is less than that on B, then the patient is assigned a (0,1) score and prefers B.
• If the time to treatment failure on B is less than that on A, then the patient is assigned a (1,0) score and prefers A.
• If the patient does not experience treatment failure on either treatment, then the patient is assigned a (1,1) score and displays no preference.

Hence, we can use the procedures which we implemented with binary outcomes.