Statistical inference for extended or shortened phase II studies based on Simon’s two-stage designs

Zhao, Junjun; Yu, Menggang; Xiong, Feng

doi:10.1186/s12874-015-0039-5

Cited by 13 publications

(17 citation statements)

References 17 publications

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“…It has been noted by other researchers 5,8 that no confidence interval exists when x 1 > r t , since the left side of equation (1) is always 1 regardless of the value of π * . For a similar reason, when x 2 = 0, the right side of equation (1) is always 1; therefore, there is no confidence interval for sample points ( x 1 , 0) based on the KC approach.…”

Section: Methodsmentioning

confidence: 91%

“…For a study with under- or over-enrollment in the second stage, Koyama and Chen 4 proposed a method to control for the conditional type I error in the unconditional p -value calculation and the confidence interval calculation. Later, Zhao et al 5 conducted a simulation study and showed that the confidence interval based on the approach by Koyama and Chen 4 does not guarantee the nominal coverage probability. In addition, they pointed out that the approach by Koyama and Chen has difficulty in computing confidence interval for some sample points.…”

Section: Introductionmentioning

confidence: 99%

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Exact confidence limits for the response rate in two-stage designs with over- or under-enrollment in the second stage

Shan

2016

Stat Methods Med Res

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Simon’s two-stage design has been widely used in early phase clinical trials to assess the activity of a new investigated treatment. In practice, the actual sample sizes do not always follow the study design precisely, especially in the second stage. When over- or under-enrollment occurs in a study, the original critical values for the study design are no longer valid for making proper statistical inference in a clinical trial. The hypothesis for such studies is always one-sided, and the null hypothesis is rejected when only a few responses are observed. Therefore, a one-sided lower interval is suitable to test the hypothesis. The commonly used approaches for confidence interval construction are based on asymptotic approaches. These approaches generally do not guarantee the coverage probability. For this reason, Clopper-Pearson approach can be used to compute exact confidence intervals. This approach has to be used in conjunction with a method to order the sample space. The frequently used method is based on point estimates for the response rate, but this ordering has too many ties which lead to conservativeness of the exact intervals. We propose developing exact one-sided intervals based on the p-value to order the sample space. The proposed approach outperforms the existing asymptotic and exact approaches. Therefore, it is recommended for use in practice.

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Section: Methodsmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Exact confidence limits for the response rate in two-stage designs with over- or under-enrollment in the second stage

Shan

2016

Stat Methods Med Res

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“…Assuming a NIM of 1.1, the study is given as (a1 / n1, a / n) = (21 / 30, 41 / 63) (11) under (p0 / NIM, p1, α and 1β) = (0.65 / 1.1, 0.8, 0.1, and 0.9). (12) Therefore, at the study end, more than forty (RR≥65%) responding patients (lower than 46 -RR≥73%-) out of 63 patients will be required to achieve a positive nding.…”

Section: Numerical Examplementioning

confidence: 99%

“…10 For point estimation, previous authors have developed a method to calculate the Uniformly Minimum Variance Unbiased Estimator (UMVUE) for Simon's designs and to achieve optimal results. 11 What is more, p-values and type II errors can be calculated with stochastic ordering of the UMVUE. 9,12 These methods can be used when the realized sample size at the stopping stage is different from that speci ed in the initial design, and this property makes them very useful for designing and analyzing two-stage phase II trials.…”

Section: Introductionmentioning

confidence: 99%

Inclusion of non-inferiority analysis in superiority-based clinical trials with single-arm, two-stage Simon’s design

Sampayo-Cordero

Miguel-Huguet

Peréz-García³

et al. 2019

Preprint

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Background The non-inferiority (NI) hypothesis is not usually considered in the early phases of clinical development. A proof-of-concept phase II study that allows for the analysis of NI, if superiority criteria cannot be met, may balance between multiple endpoints and additional parameters, which will result in more informed decisions in regard to the therapeutics’ potential value. Methods A total of 12,768 two-stage Simon’s design trials were constructed based on different assumptions of rejection response probability, minimum desired response probability, type I and II errors, and NI margins. P-value and type II error were calculated with stochastic ordering using Uniformly Minimum Variance Unbiased Estimator. Type I and II errors were simulated using the Monte Carlo method. Agreement between calculated and simulated values was analyzed with Bland-Altman plots. Results The level of agreement was equivalent between calculated and simulated values in two-stage superiority designs and ones in which switching to NI was allowed. Conclusion Switching to NI analysis, when superiority criteria are not achieved, may be useful for weighing additional factors such as clinical benefit duration, safety, cost, or biomarker strategy while assessing activity and early efficacy rate. Implementation of this strategy can be achieved through simple adaptations to existing designs for one-arm phase II clinical trials.

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“…one-sided p values can then be used to construct two-sided confidence intervals in a way that essentially is a generalization of the Clopper-Pearson approach (Clopper and Pearson, 1934) for an exact binomial proportion confidence interval (Koyama and Chen, 2008). A different approach, where the "extremeness" of an observation is measured by the likelihood ratio, was also proposed (Zhao, Yu and Feng, 2015). Shan, Zhang and Jiang (2017) extended the Clopper-Pearson-type confidence intervals to designs where the stage-two sample size upon continuation is allowed to vary with the observed number of responses.…”

mentioning

confidence: 99%

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

Kunzmann

Kieser

2017

Biometrical J

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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-knownClopper-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. K E Y W O R D Sadaptive designs, binary endpoint, confidence interval, two-stage designs BACKGROUNDSingle-arm two-stage designs are frequently applied in phase II of oncology research. Such designs allow testing the one-sided null hypothesis  0 ∶ ≤ 0 that the response probability of a new treatment is smaller than or equal to 0 at level and with power 1 − at some point alternative 1 > 0 . Simon's optimal designs (Simon, 1989) are the most popular two-stage designs for phase II oncology trials (Ivanova et al., 2016). These group-sequential designs with prefixed stage-wise sample size minimize the expected sample size on the boundary of the null hypothesis 0 under the given restrictions on type I and type II error rates. Extensions of Simon's group-sequential designs that allow the stage-two sample size to vary with the number of observed interim responses have been proposed by several authors (Banerjee and Tsiatis, 2006;Mander and Thompson, 2010;Jin et al., 2012;Englert and Kieser, 2013;Shan, Wilding, Hutson and Gerstenberger, 2016;Kunzmann and Kieser, 2016). Interval estimation after two-stage designs is complicated by the bias due to the response-adaptive sampling scheme. The group-sequential situation has been studied extensively (Jennison and Turnbull, 2000) and was applied to Simon's designs (Koyama and Chen, 2008). The principal idea is to resolve the inherent arbitrariness of p values in multistage designs by resorting to the stage-wise ordering that is induced by the uniformly minimum variance unbiased estimator (UMVUE) for the response probability . The obtained

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Statistical inference for extended or shortened phase II studies based on Simon’s two-stage designs

Cited by 13 publications

References 17 publications

Exact confidence limits for the response rate in two-stage designs with over- or under-enrollment in the second stage

Exact confidence limits for the response rate in two-stage designs with over- or under-enrollment in the second stage

Inclusion of non-inferiority analysis in superiority-based clinical trials with single-arm, two-stage Simon’s design

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

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