A Study of the Classical Asymptotic Noninferiority Test for Two Binomial Proportions

Almendra-Arao, Félix

doi:10.1177/009286150904300505

Cited by 8 publications

(6 citation statements)

References 12 publications

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“…Moreover, Almendra-Arao 14,15 and Almendra-Arao and Sotres-Ramos 16 have assumed that the critical regions of the studied NI tests must be Barnard convex sets to compute test sizes. Given the importance of this type of critical region for NI tests, Almendra-Arao 17 studied theoretical properties of these sets.…”

Section: A Brief Literature Reviewmentioning

confidence: 99%

On the Importance in Clinical Trials That Critical Regions for Comparing 2 Independent Proportions Must Be Barnard Convex Sets

Almendra-Arao

Sotres-Ramos

2014

Ther Innov Regul Sci

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The non-inferiority and superiority (NI/S) formulations to evaluate a new treatment are frequently used in active-controlled clinical trials. A key assumption for the NI/S statistical tests that compare 2 independent proportions is that corresponding critical regions are Barnard convex sets. This assumption allows significant reduction in the computation time required to calculate test sizes for these tests. This study presents arguments that both types of testing procedures (NI/S) require the corresponding critical regions to be Barnard convex sets. Otherwise, these tests may become meaningless. Notably, the critical regions of the well-known Blackwelder and Hauck-Anderson tests are not Barnard convex sets for many sample sizes.

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Section: A Brief Literature Reviewmentioning

confidence: 99%

On the Importance in Clinical Trials That Critical Regions for Comparing 2 Independent Proportions Must Be Barnard Convex Sets

Almendra-Arao

Sotres-Ramos

2014

Ther Innov Regul Sci

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“…The corresponding testing approach was shown to result in a smaller Type I error rate, in general, when compared with the uncorrected Wald method, but in some settings was also shown to be over‐conservative . In addition, patterns where both methods could, in fact, inflate the Type I error rate above the nominal level were detected .…”

Section: Introductionmentioning

confidence: 95%

“…It was recommended not to use uncorrected methods even if the sample sizes are relatively large . Properties of the Wald confidence interval with Hauck–Anderson continuity correction were further addressed . The corresponding testing approach was shown to result in a smaller Type I error rate, in general, when compared with the uncorrected Wald method, but in some settings was also shown to be over‐conservative .…”

Section: Introductionmentioning

confidence: 99%

Applications of asymptotic confidence intervals with continuity corrections for asymmetric comparisons in noninferiority trials

Soulakova

Bright

2013

Pharmaceutical Statistics

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A large-sample problem of illustrating noninferiority of an experimental treatment over a referent treatment for binary outcomes is considered. The methods of illustrating noninferiority involve constructing the lower two-sided confidence bound for the difference between binomial proportions corresponding to the experimental and referent treatments and comparing it with the negative value of the noninferiority margin. The three considered methods, Anbar, Falk-Koch, and Reduced Falk-Koch, handle the comparison in an asymmetric way, that is, only the referent proportion out of the two, experimental and referent, is directly involved in the expression for the variance of the difference between two sample proportions. Five continuity corrections (including zero) are considered with respect to each approach. The key properties of the corresponding methods are evaluated via simulations. First, the uncorrected two-sided confidence intervals can, potentially, have smaller coverage probability than the nominal level even for moderately large sample sizes, for example, 150 per group. Next, the 15 testing methods are discussed in terms of their Type I error rate and power. In the settings with a relatively small referent proportion (about 0.4 or smaller), the Anbar approach with Yates' continuity correction is recommended for balanced designs and the Falk-Koch method with Yates' correction is recommended for unbalanced designs. For relatively moderate (about 0.6) and large (about 0.8 or greater) referent proportion, the uncorrected Reduced Falk-Koch method is recommended, although in this case, all methods tend to be over-conservative. These results are expected to be used in the design stage of a noninferiority study when asymmetric comparisons are envisioned.

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“…The literature addressing this issue is still sparse, except for a noninferiority trial. 16,42,43 Most of the aforementioned methods do not address this calculation properly, which may lead to the corresponding power being either understated or overstated, as shown in Section 5. Although the exact p-value test does control the actual type I error, 14,15,44 the minimum required sample size calculation based on it can only be adopted when the total sample size is small due to its computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Are the tests overpowered or underpowered? A unified solution to correctly specify type I errors in design of clinical trials for two sample proportions

Liu,

Chen,

Sinks

et al. 2024

Statistics in Medicine

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As one of the most commonly used data types, methods in testing or designing a trial for binary endpoints from two independent populations are still being developed until recently. However, the power and the minimum required sample size comparisons between different tests may not be valid if their type I errors are not controlled at the same level. In this article, we unify all related testing procedures into a decision framework, including both frequentist and Bayesian methods. Sufficient conditions of the type I error attained at the boundary of hypotheses are derived, which help reduce the magnitude of the exact calculations and lay out a foundation for developing computational algorithms to correctly specify the actual type I error. The efficient algorithms are thus proposed to calculate the cutoff value in a deterministic decision rule and the probability value in a randomized decision rule, such that the actual type I error is under but closest to, or equal to, the intended level, respectively. The algorithm may also be used to calculate the sample size to achieve the prespecified type I error and power. The usefulness of the proposed methodology is further demonstrated in the power calculation for designing superiority and noninferiority trials.

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A Study of the Classical Asymptotic Noninferiority Test for Two Binomial Proportions

Cited by 8 publications

References 12 publications

On the Importance in Clinical Trials That Critical Regions for Comparing 2 Independent Proportions Must Be Barnard Convex Sets

On the Importance in Clinical Trials That Critical Regions for Comparing 2 Independent Proportions Must Be Barnard Convex Sets

Applications of asymptotic confidence intervals with continuity corrections for asymmetric comparisons in noninferiority trials

Are the tests overpowered or underpowered? A unified solution to correctly specify type I errors in design of clinical trials for two sample proportions

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