Asymptotical tests in 2×2 comparative trials

Andrés, Antonio Martín; Quevedo, M. J. Sánchez; Mato, Agustín Silva

doi:10.1016/s0167-9473(02)00005-1

Cited by 9 publications

(3 citation statements)

References 26 publications

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“…So in general we can recommend ordering by the pooled Z instead of the unpooled Z. Since Barndard's CSM test is difficult to calculate, Martín Andrés, Sánchez Quevedo and Silva Mato [42] compared many approximations to that value. They concluded that the mid-p Fisher's p-value was the best approximation to the CSM test, although it could be conservative for very small samples.…”

Section: Power and Efficiency Comparisonsmentioning

confidence: 99%

Practical valid inferences for the two-sample binomial problem

Hunsberger

2021

Statist. Surv.

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Our interest is whether two binomial parameters differ, which parameter is larger, and by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there continues to be new work on this issue and no consensus solution. Previous reviews have focused primarily on testing and the properties of validity and power, or primarily on confidence intervals, their coverage, and expected length. Here we evaluate both. For example, we consider whether a p-value and its matching confidence interval are compatible, meaning that the p-value rejects at level α if and only if the 1 − α confidence interval excludes all null parameter values. For focus, we only examine non-asymptotic inferences, so that most of the p-values and confidence intervals are valid (i.e., exact) by construction. Within this focus, we review different methods emphasizing many of the properties and interpretational aspects we desire from applied frequentist inference: validity, accuracy, good power, equivariance, compatibility, coherence, and parameterization and direction of effect. We show that no one method can meet all the desirable properties and give recommendations based on which properties are given more importance.

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Section: Power and Efficiency Comparisonsmentioning

confidence: 99%

Practical valid inferences for the two-sample binomial problem

Hunsberger

2021

Statist. Surv.

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show abstract

“…So in general we can recommend ordering by the pooled Z instead of the unpooled Z. Since Barndard's CSM test is difficult to calculate, Martın Andrés, Sánchez Quevedo and Silva Mato [45] compared many approximations to that value. They concluded that the mid-p Fisher's p-value was the best approximation to the CSM test, although it could be conservative for very small samples.…”

Section: Power and Efficiency Comparisonsmentioning

confidence: 99%

Practical Valid Inferences for the Two-Sample Binomial Problem

Fay,

Hunsberger

2019

Preprint

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Consider comparing two independent binomial responses. Our interest is whether the two binomial parameters are different, and if different, which is larger, and if larger, by how much. This apparently simple problem was addressed by Fisher in the 1930's, and has been the subject of many review papers since then. Yet there continues to be new work on this issue and no consensus solution. Previous reviews have focused primarily on testing and the properties of validity and power, or primarily on confidence intervals, their coverage, and expected length. Here we evaluate both together. For example, we consider whether a p-value and its matching confidence interval are compatible, meaning that the p-value rejects at level α if and only if the 1 − α confidence interval excludes all null parameter values. For focus, we only examine non-asymptotic inferences, so that most of the p-values and confidence intervals are valid (i.e., exact) by construction. Within this focus, we review different methods emphasizing many of the properties and interpretational aspects we desire from applied frequentist inference: validity, accuracy, good power, equivariance, compatibility, coherence, causal interpretation, and parameterization and direction of effect. We show that no one method can meet all the desirable properties and give recommendations based on which properties are given more importance.

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“…This is the optimal c.c. proposed by MartÌn, Snchez and Silva (2002) for the classic C1 and C2. The previous version c.c.…”

Section: Tests With Continuity Correctionmentioning

confidence: 99%

Asymptotical Tests on the Equivalence, Substantial Difference and Non‐inferiority Problems with Two Proportions

Andrés¹,

Tejedor

2004

Biometrical J

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SummaryLet d ¼ p 2 À p 1 be the difference between two binomial proportions obtained from two independent trials. For parameter d, three pairs of hypothesis may be of interest:, where H i is the null hypothesis and K i is the alternative hypothesis. These tests are useful in clinical trials, pharmacological and vaccine studies and in statistics generally. The three problems may be investigated by exact unconditional tests when the sample sizes are moderate. Otherwise, one should use approximate (or asymptotical) tests generally based on a Z-statistics like those suggested in the paper. The article defines a new procedure for testing H 2 or H 3 , demonstrates that this is more powerful than tests based on confidence intervals (the classic TOST -two one sided tests -test), defines two corrections for continuity which reduce the liberality of the three tests, and selects the one that behaves better. The programs for executing the unconditional exact and asymptotic tests described in the paper can be loaded at

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Asymptotical tests in 2×2 comparative trials

Cited by 9 publications

References 26 publications

Practical valid inferences for the two-sample binomial problem

Practical valid inferences for the two-sample binomial problem

Practical Valid Inferences for the Two-Sample Binomial Problem

Asymptotical Tests on the Equivalence, Substantial Difference and Non‐inferiority Problems with Two Proportions

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