I'm planning a clinical study, in which my desired primary outcome is time to event. My new treatment is non-inferior to the current one in it's therapeutic abilities, however it makes an impact much faster. The follow-up points the clinician wishes to perform (apart from baseline) are 3, 6 and 12 months. At 12 months, it is expected that both treatments will be the same. However, at 3 and 6 months, it is expected to be different. I was thinking at first about survival analysis (time to event), but my time is not continuous, it is discrete, and with a very small number of time points. How should I analyze such data ? With an answer to this question, I'll try thinking how to dig up the sample size.
If you're ready to assume that survival is constant between discrete times, then you can use 'Nelson-Aalen Estimator' and 'Kaplan-Meier Estimator' to get Estimator for survival.
To compare clinical trials hypothetically, new treatment with current one use Log-Rank Test.(as it is nonparametric test, you can test for time 12 and time (3&6) differently)
After test, choose the better Estimator.