🎰 O'Brien–Fleming (OBF) Method

O’Brien–Fleming (OBF) Method#

A group-sequential boundary that is very strict early and relaxes toward the final analysis.

Important

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What it is#

The O’Brien–Fleming (OBF) method is a group-sequential design that controls the overall Type I error \(\alpha\) across multiple interim analyses with a distinctive spending shape: very strict early, lenient late. Early on you need overwhelming evidence to stop; by the final look the threshold is essentially the usual \(\alpha\).

The spending shape#

For \(\alpha = 0.05\) (two-sided) with 4 looks, the OBF critical z-values are roughly

25% — \(z \approx 3.47\) (\(p \approx 0.0005\))
50% — \(z \approx 2.45\) (\(p \approx 0.014\))
75% — \(z \approx 2.00\) (\(p \approx 0.045\))
100% — \(z \approx 1.98\) (\(p \approx 0.048\))

so the early bar is extreme and the final bar is almost a normal \(\alpha = 0.05\) test. This is the opposite philosophy to Pocock’s flat \(z \approx 2.41\).

Example#

A heart-drug trial with 4 interim looks: at 25% an observed \(p = 0.002\) (\(z \approx 3.1\)) is not below the OBF bound (\(p \approx 0.0005\)), so continue; at 50%, \(p = 0.009\) (\(z \approx 2.6\)) clears the bound (\(\approx 0.014\)) → stop early for efficacy.

Strengths and trade-offs#

OBF gives strong early protection against false positives (random noise can’t stop the trial prematurely) while still permitting an early stop for a genuinely large effect, and its final test barely loses power versus fixed-horizon. The downside: it rarely stops early unless the effect is huge, so you often collect nearly the full sample. That conservatism is exactly why it suits safety-critical domains like medicine, whereas Pocock fits exploratory or business A/B tests where stopping early saves money.

Theme: Sequential Methods & Bandits · All terminology

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Mind map — connected ideas

Pocock Method · Group Sequential Testing · Stopping Rules · Frequentist · Sequential Settings · Traditional A/B Test (Fixed-Horizon A/B Test)

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More in Sequential Methods & Bandits

Bandit Algorithms · Pocock Method · Sequential Probability Ratio Test (SPRT) · Sequential Settings · Thompson Sampling (TS) in Bandits (Multi-Armed Bandit Problem (MAB))