Assessing bias in treatment effect estimation for hybrid goldilocks adaptive trials with continuous outcomes

Background The Goldilocks design is a Bayesian adaptive clinical trial design using predictive probabilities (PPs) to guide sample size selection. In practice, the hybrid designs employ PPs to guide interim stopping for efficacy/futility, while the primary endpoint is analyzed using frequentist methods. The objective of this study is to investigate the impact of early stopping on bias in trials with continuous outcomes. Methods We considered a two-arm trial motivated by a previous trial for pulmonary embolism. The primary continuous outcome was generated from a normal distribution under small, moderate, and large treatment effects. Interim analyses were conducted after 100 patients and every additional 50 until 500. Trials stop for efficacy if PP for success at the current sample size exceeds 0.95 or futility if PP at the maximum sample size is below 0.05. Final analysis used a one-sided Wilcoxon–Mann–Whitney–based test. For each scenario, the percentage bias and mean absolute percentage error were evaluated among trials stopping early across 10,000 simulated trials. Results Early accrual stopping for predicted success occurred in >79% of trials. Among early-stopped trials, median percentage bias ranged from 15 to 20%, 10–14%, and 5–7% for small, moderate and large effects, respectively, with greatest bias at early interims. Compared with the fixed design, this hybrid design reduced the sample size required by a median of 51%. Conclusion The hybrid Goldilocks design yields substantial efficiency gains in sample size. However, it also introduces notable bias in the treatment effect, particularly when trials stop very early.