Stopping rules for clinical trials are primarily intended to control Type I error rates if interim analyses are planned, but less is known about the impact that potential stopping has on estimating treatment benefit. In this paper, we derive analytic expressions for (1) the over‐estimation of benefit in studies that stop early, (2) the under‐estimation of benefit in completed studies, and (3) the overall bias in studies with a stopping rule. We also examine the probability of stopping early and the situation in meta‐analyses.
Numerical evaluations show that the greatest concern is with over‐estimation of benefit in stopped studies, especially if the probability of stopping early is small. The overall bias is usually less than 10% of the true benefit, and under‐estimation in completed studies is also typically small. The probability of stopping depends on the true treatment effect and sample size. The magnitude of these effects depends on the particular rule adopted, but we show that the maximum overall bias is the same for all stopping rules. We also show that an essentially unbiased meta‐analysis estimate of benefit can be recovered, even if some component studies have stopping rules. We illustrate these methods using data from three clinical trials.
The results confirm our earlier empirical work on clinical trials. Investigators may consult our numerical results for guidance on potential mis‐estimation and bias in the treatment effect if a stopping rule is adopted. Particular concern is warranted in studies that actually stop early, where interim results may be quite misleading.