Apply sequential testing without p-hacking

You need continuous monitoring with early stopping for either efficacy or futility. a) Compare Pocock and O’Brien–Fleming alpha-spending at two interim looks, and state the corresponding critical z-values. b) Explain how mixture-SPRT or e-values give always-valid inference under arbitrary peeking. c) Describe how you would integrate sequential monitoring across multiple metrics without inflating error rates. Overview: This question assesses a candidate's proficiency 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.