Apply sequential testing without p-hacking

Q: Apply sequential testing without p-hacking

This question evaluates a candidate's competency in sequential hypothesis testing, alpha‑spending rules (Pocock vs O’Brien–Fleming), always‑valid inference methods such as mixture‑SPRT and e‑values, and strategies for controlling error rates across multiple metrics.

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Question

Sequential Monitoring With Early Stopping

Context: You are planning a two‑sided hypothesis test with continuous monitoring and early stopping for efficacy or futility. Assume two interim analyses plus a final analysis (3 total looks) at equally spaced information times (t = 1/3, 2/3, 1) and overall two‑sided alpha = 0.05.

(a) Contrast Pocock vs. O’Brien–Fleming alpha‑spending for two interim looks and report the corresponding critical z‑values at each look.

(b) Explain how mixture‑SPRT or e‑values yield always‑valid inference under arbitrary peeking (optional stopping), including the key guarantee.

(c) Describe how to integrate sequential monitoring with multiple metrics without inflating error rates.

Apply sequential testing without p-hacking

Sequential Monitoring With Early Stopping

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Apply sequential testing without p-hacking

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Sequential Monitoring With Early Stopping

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