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From aggressive to conservative early stopping in Bayesian group sequential designs

Zhangyi He, Feng Yu, Suzie Cro, Laurent Billot

TL;DR

The paper addresses the problem that conventional Bayesian group sequential designs with fixed posterior probability thresholds can exhibit overly aggressive early stopping, risking inflated treatment effects and regulatory pushback. It introduces two refinements—a two-phase posterior-threshold scheme and a predictive-probability monitoring rule—calibrated within the BaySeq framework and demonstrated on the HYPRESS case. Both approaches successfully temper early stopping while preserving interpretability and show alpha-spending profiles that align more closely with O'Brien-Fleming boundaries at early looks, with Strategy 2 offering flexible control over stopping behavior. The work provides regulator-friendly, practical tools for aligning Bayesian GSDs with frequentist practice, and recommends visualizing cumulative alpha spending against standard benchmarks to ensure robust, transparent trial design.

Abstract

Group sequential designs (GSDs) are widely used in confirmatory trials to allow interim monitoring while preserving control of the type I error rate. In the frequentist framework, O'Brien-Fleming-type stopping boundaries dominate practice because they impose highly conservative early stopping while allowing more liberal decisions as information accumulates. Bayesian GSDs, in contrast, are most often implemented using fixed posterior probability thresholds applied uniformly at all analyses. While such designs can be calibrated to control the overall type I error rate, they do not penalise early analyses and can therefore lead to substantially more aggressive early stopping. Such behaviour can risk premature conclusions and inflation of treatment effect estimates, raising concerns for confirmatory trials. We introduce two practically implementable refinements that restore conservative early stopping in Bayesian GSDs. The first introduces a two-phase structure for posterior probability thresholds, applying more stringent criteria in the early phase of the trial and relaxing them later to preserve power. The second replaces posterior probability monitoring at interim looks with predictive probability criteria, which naturally account for uncertainty in future data and therefore suppress premature stopping. Both strategies require only one additional tuning parameter and can be efficiently calibrated. In the HYPRESS setting, both approaches achieve higher power than the conventional Bayesian design while producing alpha-spending profiles closely aligned with O'Brien-Fleming-type behaviour at early looks. These refinements provide a principled and tractable way to align Bayesian GSDs with accepted frequentist practice and regulatory expectations, supporting their robust application in confirmatory trials.

From aggressive to conservative early stopping in Bayesian group sequential designs

TL;DR

The paper addresses the problem that conventional Bayesian group sequential designs with fixed posterior probability thresholds can exhibit overly aggressive early stopping, risking inflated treatment effects and regulatory pushback. It introduces two refinements—a two-phase posterior-threshold scheme and a predictive-probability monitoring rule—calibrated within the BaySeq framework and demonstrated on the HYPRESS case. Both approaches successfully temper early stopping while preserving interpretability and show alpha-spending profiles that align more closely with O'Brien-Fleming boundaries at early looks, with Strategy 2 offering flexible control over stopping behavior. The work provides regulator-friendly, practical tools for aligning Bayesian GSDs with frequentist practice, and recommends visualizing cumulative alpha spending against standard benchmarks to ensure robust, transparent trial design.

Abstract

Group sequential designs (GSDs) are widely used in confirmatory trials to allow interim monitoring while preserving control of the type I error rate. In the frequentist framework, O'Brien-Fleming-type stopping boundaries dominate practice because they impose highly conservative early stopping while allowing more liberal decisions as information accumulates. Bayesian GSDs, in contrast, are most often implemented using fixed posterior probability thresholds applied uniformly at all analyses. While such designs can be calibrated to control the overall type I error rate, they do not penalise early analyses and can therefore lead to substantially more aggressive early stopping. Such behaviour can risk premature conclusions and inflation of treatment effect estimates, raising concerns for confirmatory trials. We introduce two practically implementable refinements that restore conservative early stopping in Bayesian GSDs. The first introduces a two-phase structure for posterior probability thresholds, applying more stringent criteria in the early phase of the trial and relaxing them later to preserve power. The second replaces posterior probability monitoring at interim looks with predictive probability criteria, which naturally account for uncertainty in future data and therefore suppress premature stopping. Both strategies require only one additional tuning parameter and can be efficiently calibrated. In the HYPRESS setting, both approaches achieve higher power than the conventional Bayesian design while producing alpha-spending profiles closely aligned with O'Brien-Fleming-type behaviour at early looks. These refinements provide a principled and tractable way to align Bayesian GSDs with accepted frequentist practice and regulatory expectations, supporting their robust application in confirmatory trials.
Paper Structure (9 sections, 5 equations, 18 figures, 3 tables)

This paper contains 9 sections, 5 equations, 18 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Aggressive Bayesian vs conservative frequentist GSDs
  3. The HYPRESS trial
  4. Contrasting early stopping tendencies
  5. Strategies to transition from aggressive to conservative early stopping
  6. Strategy 1: replacing fixed with two-phase probability thresholds
  7. Strategy 2: replacing posterior with predictive probability criteria
  8. Discussion
  9. Supplementary figures and tables

Figures (18)

  • Figure 1: A comparison of common efficacy stopping boundaries in frequentist GSDs incorporating four equally spaced interim looks with a one-sided type I error rate of 0.025. The Pocock- and O'Brien-Fleming-type spending is generated via the Lan-DeMets alpha-spending function. The information rate is the fraction of total information expected at the scheduled end of the trial demets1994.
  • Figure 1: Overall type I error rates for combinations of posterior probability thresholds and total sample sizes in the conventional Bayesian GSD with two equally spaced interims.
  • Figure 2: The cumulative alpha-spending profiles for the conventional Bayesian GSD and widely used frequentist GSDs incorporating two equally spaced interim analyses with a one-sided type I error rate of 2.5%. The Pocock- and O'Brien-Fleming-type spending is generated via the Lan-DeMets alpha-spending function.
  • Figure 2: Powers for combinations of posterior probability thresholds and total sample sizes in the conventional Bayesian GSD with two equally spaced interims.
  • Figure 3: The cumulative alpha-spending profiles for the calibrated Bayesian GSDs under Strategy 1. The Colour gradient reflects the associated power of each calibrated design: warmer (red) shades correspond to higher power, whereas cooler (blue) shades indicate lower power. The Pocock- and O'Brien-Fleming-type spending is generated via the Lan-DeMets alpha-spending function.
  • ...and 13 more figures