Sequential Monitoring of Randomization Tests
Seminar Room 1, Newton Institute
The U. S. Food and Drug Administration often requires a randomization-based analysis of the primary outcome in a clinical trial, which they sometimes refer to as "re-randomization tests" (we prefer "randomization tests"). Conditional inference is inherently difficult when using a Monte Carlo approach to "re-randomize", and is impossible using standard techniques for some randomization procedures. We describe a new approach by deriving the exact conditional distribution of the randomization procedure and then using Monte Carlo to generate sequences directly from the conditional reference set. We then extend this technique to sequential monitoring, by computing the exact joint distribution of sequentially-computed conditional randomization tests. This allows for a spending-function approach using randomization tests instead of population-based tests. Defining information under a randomization model is tricky, and we describe various ways to & quot;estimate" information using the exact conditional variance of the randomization test statistics.