Curtailment in single‐arm two‐stage phase II oncology trials

Two‐stage designs that allow for early stopping if the treatment is ineffective are commonly used in phase II oncology trials. A limitation of current designs is that early stopping is only allowed at the end of the first stage, even if it becomes evident during the trial that a significant result is unlikely. One way to overcome this limitation is to implement stochastic curtailment procedures that enable stopping the trial whenever the conditional power is below a pre‐specified threshold θ. In this paper, we present the results for implementing curtailment rules in either only the second stage or both stages of the designs. In total, 102 scenarios with different parameter settings were investigated using conditional power thresholds θ between 0 and 1 in steps of 0.01. An increase in θ results not only in a decrease of the actual Type I error rate and power but also of the expected sample size. Therefore, a reasonable balance has to be found when selecting a specific threshold value in the planning phase of a curtailed two‐stage design. Given that the effect of curtailment highly depends on the underlying design parameters, no general recommendation for θ can be made. However, up to , the loss in power was less than 5% for all investigated scenarios while savings of up to 50% in expected sample size occurred. In general, curtailment is most appropriate when the outcome can be observed fast or when accrual is slow so that adequate information for making early and frequent decisions is available.     

Test‐compatible confidence intervals for adaptive two‐stage single‐arm designs with binary endpoint

Inference after two‐stage single‐arm designs with binary endpoint is challenging due to the nonunique ordering of the sampling space in multistage designs. We illustrate the problem of specifying test‐compatible confidence intervals for designs with nonconstant second‐stage sample size and present two approaches that guarantee confidence intervals consistent with the test decision. Firstly, we extend the well‐known Clopper–Pearson approach of inverting a family of two‐sided hypothesis tests from the group‐sequential case to designs with fully adaptive sample size. Test compatibility is achieved by using a sample space ordering that is derived from a test‐compatible estimator. The resulting confidence intervals tend to be conservative but assure the nominal coverage probability. In order to assess the possibility of further improving these confidence intervals, we pursue a direct optimization approach minimizing the mean width of the confidence intervals. While the latter approach produces more stable coverage probabilities, it is also slightly anti‐conservative and yields only negligible improvements in mean width. We conclude that the Clopper–Pearson‐type confidence intervals based on a test‐compatible estimator are the best choice if the nominal coverage probability is not to be undershot and compatibility of test decision and confidence interval is to be preserved.     

Challenges and regulatory experiences with non‐inferiority trial design without placebo arm

For a non‐inferiority trial without a placebo arm, the direct comparison between the test treatment and the selected positive control is in principle the only basis for statistical inference. Therefore, evaluating the test treatment relative to the non‐existent placebo presents extreme challenges and requires some kind of bridging from the past to the present with no current placebo data. For such inference based partly on an indirect bridging manipulation, fixed margin method and synthesis method are the two widely discussed methods in the recent literature. There are major differences in statistical inference paradigm between the two methods. The fixed margin method employs the historical data that assess the performances of the active control versus a placebo to guide the selection of the non‐inferiority margin. Such guidance is not part of the ultimate statistical inference in the non‐inferiority trial. In contrast, the synthesis method connects the historical data to the non‐inferiority trial data for making broader inferences relating the test treatment to the non‐existent current placebo. On the other hand, the type I error rate associated with the direct comparison between the test treatment and the active control cannot shed any light on the appropriateness of the indirect inference for faring the test treatment against the non‐existent placebo. This work explores an approach for assessing the impact of potential bias due to violation of a key statistical assumption to guide determination of the non‐inferiority margin.     

Comparison of design strategies for a three‐arm clinical trial with time‐to‐event endpoint: Power,time‐to‐analysis,and operational aspects

To optimize resources, randomized clinical trials with multiple arms can be an attractive option to simultaneously test various treatment regimens in pharmaceutical drug development. The motivation for this work was the successful conduct and positive final outcome of a three‐arm randomized clinical trial primarily assessing whether obinutuzumab plus chlorambucil in patients with chronic lympocytic lymphoma and coexisting conditions is superior to chlorambucil alone based on a time‐to‐event endpoint. The inference strategy of this trial was based on a closed testing procedure. We compare this strategy to three potential alternatives to run a three‐arm clinical trial with a time‐to‐event endpoint. The primary goal is to quantify the differences between these strategies in terms of the time it takes until the first analysis and thus potential approval of a new drug, number of required events, and power. Operational aspects of implementing the various strategies are discussed. In conclusion, using a closed testing procedure results in the shortest time to the first analysis with a minimal loss in power. Therefore, closed testing procedures should be part of the statistician's standard clinical trials toolbox when planning multiarm clinical trials.     

A Survey of Sample Size Formulas for Pairwise and Many‐one Multiple Comparisons in the Parametric,Nonparametric and Binomial Case

We present a survey of sample size formulas derived in other papers for pairwise comparisons of k treatments and for comparisons of k treatments with a control. We consider the calculation of sample sizes with preassigned per‐pair, any‐pair and all‐pairs power for tests that control either the comparisonwise or the experimentwise type I error rate. A comparison exhibits interesting similarities between the parametric, nonparametric and binomial case.