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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.

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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.

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