Start by defining the two alpha-spending functions and their trade-offs, then compute the critical z-values for two interim looks using standard software or approximations. Emphasize how Pocock uses constant boundaries while O'Brien-Fleming is conservative early and lenient later, and relate this to practical implications for A/B testing at Meta.
Pro tip: Mention that in practice, O'Brien-Fleming is often preferred for its early conservatism, which aligns with Meta's emphasis on minimizing false positives in early experiment stages, but be prepared to discuss scenarios where Pocock's constant boundaries might be advantageous for faster decision-making.
Explain that Pocock's alpha-spending function allocates equal alpha at each look, leading to constant critical boundaries, while O'Brien-Fleming spends very little alpha early and more later, resulting in decreasing critical boundaries.
State that there are two interim looks plus a final analysis (total 3 looks) and assume a two-sided alpha of 0.05 for concreteness, unless otherwise specified.
For Pocock with 3 looks and two-sided alpha 0.05, the critical z-value is approximately 2.289 at each look. For O'Brien-Fleming, the critical z-values are approximately 3.471 at the first look, 2.454 at the second, and 2.004 at the final.
Highlight that Pocock may stop early more easily but has a higher risk of false positive if early data are noisy, while O'Brien-Fleming requires stronger evidence early, preserving overall alpha and is often favored in confirmatory trials.
Connect to Meta's experimentation culture: O'Brien-Fleming is common for its conservative early stopping, but Pocock might be used when rapid iteration is prioritized, though with caution about inflated false positives.
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Start by explaining the multiple testing problem in sequential analysis and why fixed-horizon p-values fail under continuous monitoring. Then introduce mixture-SPRT and e-values as solutions that maintain type I error control regardless of peeking, and discuss their practical implications for A/B testing at Meta.
Pro tip: Emphasize that e-values are not just a technical fix but enable a new paradigm where you can stop experiments early or continue as needed without inflating false positives, which is crucial for rapid experimentation at scale.
Explain that in standard A/B testing, peeking at data repeatedly inflates the false positive rate because each look is a separate test. This is a major issue in tech companies where experiments are monitored continuously.
Describe mixture-SPRT as a sequential test that combines likelihood ratios with a prior over effect sizes, allowing valid inference at any stopping time. It controls type I error even under optional stopping.
Explain that an e-value is a nonnegative random variable with expectation at most 1 under the null hypothesis. It provides evidence against the null, and can be combined across analyses via multiplication, preserving validity under peeking.
Highlight that both methods yield anytime-valid p-values or confidence sequences, meaning error guarantees hold uniformly over time, not just at a fixed sample size.
Relate to Meta's experimentation culture: faster decisions, reduced opportunity cost, and the ability to monitor continuously without sacrificing statistical rigor. Mention trade-offs like wider confidence intervals or need for effect size priors.
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Start by acknowledging the multiple testing problem and the need to control the family-wise error rate (FWER) or false discovery rate (FDR). Then describe specific methods like alpha spending functions, group sequential designs, or error control procedures (e.g., Bonferroni, Holm, Benjamini-Hochberg) and how they apply to sequential monitoring. Finally, discuss practical trade-offs and how to choose the right approach based on the number of metrics, correlation, and business impact.
Pro tip: Emphasize that in practice, you often prioritize a primary metric with strict FWER control while using FDR control for secondary metrics, and mention that sequential testing requires adjusting alpha at each look to maintain overall error rates.
Clarify whether you need to control the family-wise error rate (FWER) or false discovery rate (FDR) across all metrics and interim looks. This depends on the cost of false positives and the number of metrics.
Select a method such as Bonferroni, Holm, or Benjamini-Hochberg to adjust p-values or thresholds for the number of metrics. Consider correlations between metrics and use methods like the Benjamini-Yekutieli for dependent tests if needed.
Use alpha spending functions (e.g., O'Brien-Fleming, Pocock) or group sequential boundaries to control error rates at each interim analysis. Combine with multiple testing corrections by adjusting the overall alpha or using a gatekeeping procedure.
Implement the chosen design with pre-specified stopping rules and adjust thresholds dynamically as data accumulates. Use software or scripts to compute adjusted p-values and confidence intervals at each look.
After the experiment, report adjusted p-values and effect sizes, and explain how error rates were controlled. Conduct sensitivity analyses to ensure robustness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.