The uniform general signed rank test and its design sensitivity

Howard, Steven R.; Pimentel, Samuel D.

doi:10.1093/biomet/asaa072

Cited by 8 publications

(6 citation statements)

References 31 publications

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“…The investigator would like to report insensitivity to small or moderate biases when, in fact, there is a treatment effect and there is no bias. The design sensitivity Υ is the limiting sensitivity to bias as 𝐼 → ∞ in some favorable situation, such as 𝑅 𝑖𝑗 = 𝛽 𝑖 + 𝛿𝑍 𝑖𝑗 + 𝜀 𝑖𝑗 in Section 4.1; see Hsu et al (2013), Karmakar et al (2019), Howard and Pimentel (2021), Rosenbaum (2020, Part III), Stuart and Hanna (2013), Q. Zhao (2019), andZubizarreta et al (2013).…”

Section: Comparing Statistics For the Second Factor In Terms Of Desig...mentioning

confidence: 99%

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A Second Evidence Factor for a Second Control Group

Rosenbaum

2023

Biometrics

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In an observational study of the effects caused by a treatment, a second control group is used in an effort to detect bias from unmeasured covariates, and the investigator is content if no evidence of bias is found. This strategy is not entirely satisfactory: two control groups may differ significantly, yet the difference may be too small to invalidate inferences about the treatment, or the control groups may not differ yet nonetheless fail to provide a tangible strengthening of the evidence of a treatment effect. Is a firmer conclusion possible? Is there a way to analyze a second control group such that the data might report measurably strengthened evidence of cause and effect, that is, insensitivity to larger unmeasured biases? Evidence factor analyses are not commonly used with a second control group: most analyses compare the treated group to each control group, but analyses of that kind are partially redundant; so, they do not constitute evidence factors. An alternative analysis is proposed here, one that does yield two evidence factors, and with a carefully designed test statistic, is capable of extracting strong evidence from the second factor. The new technical work here concerns the development of a test statistic with high design sensitivity and high Bahadur efficiency in a sensitivity analysis for the second factor. A study of binge drinking as a cause of high blood pressure is used as an illustration.

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Section: Comparing Statistics For the Second Factor In Terms Of Desig...mentioning

confidence: 99%

“…For various approaches to sensitivity analysis, see Bonvini and Kennedy (2022), Daniels et al. (2012), Fogarty and Small (2016), Howard and Pimentel (2021), Karmakar et al. (2019), McCandless et al.…”

Section: Two Evidence Factorsmentioning

confidence: 99%

A Second Evidence Factor for a Second Control Group

Rosenbaum

2023

Biometrics

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“…A last, hybrid, version (e.g., Howard and Pimentel (2020)) is to treat the two potential outcomes as random with joint distribution (Y T i , Y C i ) | X i ∼ P i , and the null posits…”

Section: Problem Setupmentioning

confidence: 99%

“…as used by Rosenbaum (2002) and Howard and Pimentel (2020), among others. The above estimation satisfies the critical property to guarantee FDR control: for a null pair i of two subjects with zero effects in ( 22), we have…”

Section: Extension Ii: Paired Samplesmentioning

confidence: 99%

Interactive identification of individuals with positive treatment effect while controlling false discoveries

Duan,

Wasserman,

Ramdas

2021

Preprint

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Out of the participants in a randomized experiment with anticipated heterogeneous treatment effects, is it possible to identify which ones have a positive treatment effect, even though each has only taken either treatment or control but not both? While subgroup analysis has received attention, claims about individual participants are more challenging. We frame the problem in terms of multiple hypothesis testing: we think of each individual as a null hypothesis (the potential outcomes are equal, for example) and aim to identify individuals for whom the null is false (the treatment potential outcome stochastically dominates the control, for example). We develop a novel algorithm that identifies such a subset, with nonasymptotic control of the false discovery rate (FDR). Our algorithm allows for interaction -a human data scientist (or a computer program acting on the human's behalf) may adaptively guide the algorithm in a data-dependent manner to gain high identification power. We also propose several extensions: (a) relaxing the null to nonpositive effects, (b) moving from unpaired to paired samples, and (c) subgroup identification. We demonstrate via numerical experiments and theoretical analysis that the proposed method has valid FDR control in finite samples and reasonably high identification power.

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“…These design sensitivity formulas provide powerful tools for asymptotically evaluating the performances of various tests in a sensitivity analysis. However, all previous approaches either require the use of pair matching (Fogarty et al, 2021;Hansen et al, 2014;Howard & Pimentel, 2020;Rosenbaum, 2010aRosenbaum, , 2011Rosenbaum & Small, 2017) or require a particular structure for the test statistic to which many rank statistics do not conform (Rosenbaum, 2013(Rosenbaum, , 2014. There are no design sensitivity formulas for popular test statistics, such as the Wilcoxon rank sum test and the Hodges-Lehmann aligned rank test, and the aberrant rank test discussed above; more generally, currently methods cannot handle test statistics where there are matched strata with multiple controls and ranking is done across matched strata as this induces dependence between matched strata that are typically assumed to be independent in many sensitivity analyses.…”

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confidence: 99%

Increasing Power for Observational Studies of Aberrant Response: An Adaptive Approach

Heng

Kang

Small

et al. 2021

Journal of the Royal Statistical Society Series B: Statistical Methodology

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In many observational studies, the interest is in the effect of treatment on bad, aberrant outcomes rather than the average outcome. For such settings, the traditional approach is to define a dichotomous outcome indicating aberration from a continuous score and use the Mantel-Haenszel test with matched data. For example, studies of determinants of poor child growth use the World Health Organization's definition of child stunting being height-for-age z-score ≤ − 2. The traditional approach may lose power because it discards potentially useful information about the severity of aberration. We develop an adaptive approach that makes use of this information and asymptotically dominates the traditional approach. We develop our approach in two parts. First, we develop an aberrant rank approach in matched observational studies and prove a novel design sensitivity formula enabling its asymptotic comparison with the Mantel-Haenszel test under various settings.Second, we develop a new, general adaptive approach, the two-stage programming method, and use it to adaptively combine the aberrant rank test and the Mantel-Haenszel test. We apply our approach to a study of the effect of teenage pregnancy on stunting.

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The uniform general signed rank test and its design sensitivity

Cited by 8 publications

References 31 publications

A Second Evidence Factor for a Second Control Group

A Second Evidence Factor for a Second Control Group

Interactive identification of individuals with positive treatment effect while controlling false discoveries

Increasing Power for Observational Studies of Aberrant Response: An Adaptive Approach

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