1. Definition
- The Pocock design is a group sequential test that allows multiple interim analyses while controlling the overall Type I Error (α).
- Unlike O’Brien–Fleming (OBF), Pocock assigns equal significance thresholds to all interim looks and the final test.
In short: Same critical value at each analysis.
2. Why Use It?
- Simpler to implement and explain: every look has the same cutoff.
- More likely than OBF to stop early when there’s a moderate effect.
- Widely used in clinical trials and A/B testing where early stopping is valuable.
3. How It Works
Suppose α = 0.05 (two-sided), with 4 planned analyses (25%, 50%, 75%, 100%).
- Pocock critical z-value (approx): ±2.41
- Corresponding p-value threshold: ~0.0169 at every look.
Compare with O’Brien–Fleming:
- OBF is super strict early (z ≈ 3.47 at 25%) and lenient later (z ≈ 1.98 at final).
- Pocock uses the same moderate threshold throughout.
4. Example – A/B Test
- Testing if new checkout flow improves conversion.
- Total sample size planned: 40,000 (20,000 per group).
- Interim analyses every 10,000 users.
- Pocock cutoff: z ≥ 2.41 at every stage.
- At 10,000 users: observed z = 2.6 → stop early, B wins.
- If z = 2.0 instead → continue to next look.
5. Advantages
- Easier to communicate (“same threshold at every look”).
- More balanced: not too strict early, not too lenient late.
- More efficient for stopping earlier compared to OBF.
6. Disadvantages
- Final test is stricter than traditional α = 0.05.
- Because some α was already “spent” early.
- Less powerful than OBF if you run the trial to completion.
- May require slightly larger total sample size than OBF to maintain power.
7. Comparison: Pocock vs O’Brien–Fleming
| Feature | O’Brien–Fleming | Pocock |
|---|---|---|
| α-spending | Very little early, most at final | Equal at all looks |
| Early stopping | Very unlikely (unless effect huge) | Easier (moderate effects detectable) |
| Final test | Almost same as α = 0.05 | Stricter (~0.017 if 4 looks) |
| Efficiency | Better if trial goes to end | Better if early stopping is likely |
| Typical use | Safety-critical (medicine) | Business/clinical where early stop saves resources |
8. Key Takeaway
- Pocock = equal significance thresholds across all looks.
- More likely than OBF to stop early with moderate effects.
- Simpler but slightly less efficient overall.
In short:
The Pocock method is a group sequential design where all interim analyses and the final test use the same critical value (≈ z = 2.41 for 4 looks at α = 0.05). It makes early stopping easier than OBF, but the final test is stricter than in fixed-horizon testing.