Approaches to handling data when a phase II trial deviates from the pre-specified Simon's two-stage design

Two-Stage Single-Arm Trials Are Rarely Analyzed Effectively or Reported Adequately

PURPOSE

Two-stage single-arm designs have historically been the most common design used in phase II oncology. They remain a mainstay today, particularly for trials in rare subgroups. Consequently, it is imperative such studies be designed, analyzed, and reported effectively. We comprehensively review such trials to examine whether this is the case.

METHODS

Oncology trials that used Simon's two-stage design over a 5-year period were identified and reviewed. They were evaluated for whether they reported sufficient design (eg, required sample size) and analysis (eg, CI) details. Articles that did not adjust their inference for the incorporation of an interim analysis were also reanalyzed.

RESULTS

Four-hundred twenty-five articles were included. Of these, just 47.5% provided the five components that ensure design reproducibility. Only 1.2% and 2.1% reported an adjusted point estimate or CI, respectively. Just 55.3% provided the final stage rejection bound, indicating many trials did not test a hypothesis for their primary outcome. Trial reanalyses suggested reported point estimates underestimated treatment effects and reported CIs were too narrow.

CONCLUSION

Key design details of two-stage single-arm trials are often unreported. Their inference is rarely performed such as to remove bias introduced by the interim analysis. These findings are particular alarming when considered against the growing trend in which nonrandomized trials make up a large proportion of all evidence on a treatment's effectiveness in a rare biomarker-defined patient subgroup. Future studies must improve the way they are analyzed and reported.

Key design features shown to be often omitted from reports on trials using Simonâs two-stage design

A two-stage phase II clinical trial design with nested criteria for early stopping and efficacy

We propose a two-stage design for a single arm clinical trial with an early stopping rule for futility. This design employs different endpoints to assess early stopping and efficacy. The early stopping rule is based on a criteria determined more quickly than that for efficacy. These separate criteria are also nested in the sense that efficacy is a special case of, but usually not identical to, the early stopping endpoint. The design readily allows for planning in terms of statistical significance, power, expected sample size, and expected duration. This method is illustrated with a phase II design comparing rates of disease progression in elderly patients treated for lung cancer to rates found using a historical control. In this example, the early stopping rule is based on the number of patients who exhibit progression-free survival (PFS) at 2 months post treatment follow-up. Efficacy is judged by the number of patients who have PFS at 6 months. We demonstrate our design has expected sample size and power comparable with the Simon two-stage design but exhibits shorter expected duration under a range of useful parameter values.

Optimal inference for Simon's two-stage design with over or under enrollment at the second stage

Simon's two-stage designs are widely used in clinical trials to assess the activity of a new treatment. In practice, it is often the case that the second stage sample size is different from the planned one. For this reason, the critical value for the second stage is no longer valid for statistical inference. Existing approaches for making statistical inference are either based on asymptotic methods or not optimal. We propose an approach to maximize the power of the study while maintaining the type I error rate where the type I error rate and power are calculated exactly from binomial distributions. The critical values of the proposed approach are numerically searched by an intelligent algorithm over the complete parameter space. It is guaranteed that the proposed approach is at least as powerful as the conditional power approach which is a valid but non-optimal approach. The power gain of the proposed approach can be substantial as compared to the conditional power approach. We apply the proposed approach to a real Phase II clinical trial.

A Rescue Strategy for Handling Unevaluable Patients in Simon's Two Stage Design

For phase II oncology trials, Simon’s two-stage design is the most commonly used strategy. However, when clinically unevaluable patients occur, the total number of patients included at each stage differs from what was initially planned. Such situations raise concerns about the operating characteristics of the trial design. This paper evaluates three classical ad hoc strategies and a novel one proposed in this work for handling unevaluable patients. This latter is called the rescue strategy which adapts the critical stopping rules to the number of unevaluable patients at each stage without modifying the planned sample size. blue Simulations show that none of these strategies perfectly match the original target constraints for type I and II error rates. Our rescue strategy is nevertheless the one which best approaches the target error rates requirement. A re-analysis of one real phase II clinical trials on metastatic cancer illustrates the use of the proposed strategy.