title: Sample size adjustment based on promising interim results and its application in confirmatory clinical trials.
abstract: BACKGROUND
  For a carefully planned and well-designed Phase 3 confirmatory trial, there is still a potential risk of failing to meet the study objective due to possible differences between Phase 2 and Phase 3 studies. As illustrated by the ENGAGE trial, potential sample size increase at an interim analysis can mitigate the risk for an otherwise underpowered study. Many approaches for sample size adjustment (SSA) require certain modifications to the conventional statistical method, such as changing critical values or using a weighted Z-statistic for final hypothesis testing. Without modification, the type I error rate can be inflated, primarily caused by sample size increase for nonpromising interim observation that is close to null or no treatment effect. As illustrated by the TOPICAL trial, increasing sample size for nonpromising interim result could waste limited resource on ineffective treatment. The modifications in these approaches are therefore unnecessary costs of flexibility/interpretability for unnecessary scenarios of sample size increase.
  
  
  OBJECTIVE
  To discuss and illustrate the appropriateness of SSA based on promising interim results, that is, conditional power being greater than 50% (or CDL approach), in a carefully planned and well-designed Phase 3 confirmatory trial.
  
  
  METHODS
  Two clinical trials are used to illustrate the clinical setting for the CDL approach and appropriateness of its application. Operating characteristics are assessed and compared to other methods using numeric computation. Hypothetical trials based on real clinical data are used to illustrate the approach.
  
  
  RESULTS
  The CDL approach for SSA leads to a small increase in expected sample size resulting in a small power gain versus the fixed design. This indicates that adding SSA will not on average substantially affect the budget at the portfolio level. However, when the interim result is promising, the CDL approach can dramatically increase the conditional power therefore mitigating the risk of an otherwise underpowered study.
  
  
  CONCLUSIONS
  Implementation challenges of the SSA methods are not in the scope of this paper. SSA is not intended to replace careful design of a confirmatory trial; instead, it can mitigate the risk for a well-designed trial.
  
  
  CONCLUSIONS
  The CDL approach for SSA based on promising interim results, that is, conditional power being greater than 50%, is particularly useful in mitigating the risk for a carefully planned and well-designed Phase 3 confirmatory trial. No modification to the conventional statistical procedure is necessary while the type I error rate is controlled. Such a feature of ''no interference,'' or no change to the conventional statistical procedure with or without sample size adjustment, is important for the interpretation of a confirmatory trial. Similar to the fixed design, carefully planned and well-designed group sequential studies can also benefit from SSA to mitigate the risk of failing to meet the study objective.
authors.affiliation: Sanofi Pasteur, Swiftwater, PA, USA.
authors.forename: Y H Joshua
authors.initials: YH
authors.lastname: Chen
authors.affiliation: Takeda, Chicago, IL, USA caiyan07@gmail.com.
authors.forename: Caiyan
authors.initials: C
authors.lastname: Li
authors.affiliation: Janssen Pharmaceutical Companies of Johnson and Johnson, Raritan, NJ, USA.
authors.forename: K K Gordon
authors.initials: KK
authors.lastname: Lan
mesh_terms: D017326:Clinical Trials, Phase III as Topic / Q000379:methods*; D006801:Humans; D015233:Models, Statistical; D012107:Research Design; D018401:Sample Size
keywords: Sample size adjustment; conditional power; interim analysis; promising