1
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Fogarty CB. Testing weak nulls in matched observational studies. Biometrics 2023; 79:2196-2207. [PMID: 35980014 DOI: 10.1111/biom.13741] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2021] [Accepted: 08/01/2022] [Indexed: 11/29/2022]
Abstract
We develop sensitivity analyses for the sample average treatment effect in matched observational studies while allowing unit-level treatment effects to vary. The methods may be applied to studies using any optimal without-replacement matching algorithm. In contrast to randomized experiments and to paired observational studies, we show for general matched designs that over a large class of test statistics, any procedure bounding the worst-case expectation while allowing for arbitrary effect heterogeneity must be unnecessarily conservative if treatment effects are actually constant across individuals. We present a sensitivity analysis which bounds the worst-case expectation while allowing for effect heterogeneity, and illustrate why it is generally conservative if effects are constant. An alternative procedure is presented that is asymptotically sharp if treatment effects are constant, and that is valid for testing the sample average effect under additional restrictions which may be deemed benign by practitioners. Simulations demonstrate that this alternative procedure results in a valid sensitivity analysis for the weak null hypothesis under a host of reasonable data-generating processes. The procedures allow practitioners to assess robustness of estimated sample average treatment effects to hidden bias while allowing for effect heterogeneity in matched observational studies.
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Affiliation(s)
- Colin B Fogarty
- Operations Research and Statistics Group, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA
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2
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Chén OY, Phan H, Cao H, Qian T, Nagels G, de Vos M. Probing potential priming: Defining, quantifying, and testing the causal priming effect using the potential outcomes framework. Front Psychol 2022; 13:724498. [PMID: 36438320 PMCID: PMC9693796 DOI: 10.3389/fpsyg.2022.724498] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2021] [Accepted: 09/13/2022] [Indexed: 03/03/2024] Open
Abstract
Having previously seen an item helps uncover the item another time, given a perceptual or cognitive cue. Oftentimes, however, it may be difficult to quantify or test the existence and size of a perceptual or cognitive effect, in general, and a priming effect, in particular. This is because to examine the existence of and quantify the effect, one needs to compare two outcomes: the outcome had one previously seen the item vs. the outcome had one not seen the item. But only one of the two outcomes is observable. Here, we argue that the potential outcomes framework is useful to define, quantify, and test the causal priming effect. To demonstrate its efficacy, we apply the framework to study the priming effect using data from a between-subjects study involving English word identification. In addition, we show that what has been used intuitively by experimentalists to assess the priming effect in the past has a sound mathematical foundation. Finally, we examine the links between the proposed method in studying priming and the multinomial processing tree (MPT) model, and how to extend the method to study experimental paradigms involving exclusion and inclusion instructional conditions.
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Affiliation(s)
- Oliver Y. Chén
- Faculty of Social Sciences and Law, University of Bristol, Bristol, United Kingdom
| | - Huy Phan
- School of Electronic Engineering and Computer Science, Queen Mary University of London, London, United Kingdom
- The Alan Turing Institute, London, United Kingdom
| | - Hengyi Cao
- Department of Psychology, Yale University, New Haven, CT, United States
- Center for Psychiatric Neuroscience, Feinstein Institutes for Medical Research, Manhasset, NY, United States
- Division of Psychiatry Research, Zucker Hillside Hospital, Glen Oaks, NY, United States
| | - Tianchen Qian
- Donald Bren School of Information and Computer Sciences, University of California, Irvine, Irvine, CA, United States
| | - Guy Nagels
- Department of Neurology, Universitair Ziekenhuis Brussel, Jette, Belgium
- Institute of Biomedical Engineering, University of Oxford, Oxford, United Kingdom
| | - Maarten de Vos
- Faculty of Engineering Science, KU Leuven, Leuven, Belgium
- Faculty of Medicine, KU Leuven, Leuven, Belgium
- KU Leuven Institute for Artificial Intelligence, Leuven, Belgium
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3
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Waite TW, Woods DC. Minimax Efficient Random Experimental Design Strategies With Application to Model-Robust Design for Prediction. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2020.1863221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Timothy W. Waite
- Department of Mathematics, University of Manchester, Manchester, UK
| | - David C. Woods
- Statistical Sciences Research Institute, University of Southampton, Southampton, UK
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4
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Johnson M, Cao J, Kang H. Detecting heterogeneous treatment effects with instrumental variables and application to the Oregon health insurance experiment. Ann Appl Stat 2022. [DOI: 10.1214/21-aoas1535] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | - Jiongyi Cao
- Department of Statistics, University of Chicago
| | - Hyunseung Kang
- Department of Statistics, University of Wisconsin-Madison
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5
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Katsevich E, Ramdas A. On the power of conditional independence testing under model-X. Electron J Stat 2022. [DOI: 10.1214/22-ejs2085] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Eugene Katsevich
- Department of Statistics and Data Science, University of Pennsylvania
| | - Aaditya Ramdas
- Department of Statistics and Data Science, Carnegie Mellon University, Machine Learning Department, Carnegie Mellon University
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6
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Li X, Small DS. Randomization-Based Test for Censored Outcomes: A New Look at the Logrank Test. Stat Sci 2022. [DOI: 10.1214/22-sts851] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Xinran Li
- Xinran Li is Assistant Professor, Department of Statistics, University of Illinois, Champaign, Illinois 61820, USA
| | - Dylan S. Small
- Dylan S. Small is Professor, Department of Statistics and Data Science, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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7
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Cohen PL, Fogarty CB. Gaussian prepivoting for finite population causal inference. J R Stat Soc Series B Stat Methodol 2021. [DOI: 10.1111/rssb.12439] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Peter L. Cohen
- Massachusetts Institute of Technology Cambridge Massachusetts USA
| | - Colin B. Fogarty
- Massachusetts Institute of Technology Cambridge Massachusetts USA
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8
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Kuang Y, Xie J. Distributed testing on mutual independence of massive multivariate data. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2021.2006232] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Yongxin Kuang
- School of Mathematics and Statistics, Henan University, Kaifeng, P.R. China
| | - Junshan Xie
- School of Mathematics and Statistics, Henan University, Kaifeng, P.R. China
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9
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Luo X, Dasgupta T, Xie M, Liu RY. Leveraging the Fisher randomization test using confidence distributions: Inference, combination and fusion learning. J R Stat Soc Series B Stat Methodol 2021. [DOI: 10.1111/rssb.12429] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xiaokang Luo
- Department of Statistics Rutgers University New Brunswick New Jersey USA
| | | | - Minge Xie
- Department of Statistics Rutgers University New Brunswick New Jersey USA
| | - Regina Y. Liu
- Department of Statistics Rutgers University New Brunswick New Jersey USA
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10
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Imbens G, Menzel K. A causal bootstrap. Ann Stat 2021. [DOI: 10.1214/20-aos2009] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Guido Imbens
- Department of Economics and Graduate School of Business, Stanford University
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11
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Affiliation(s)
- Yuehao Bai
- Department of Economics, University of Michigan, Ann Arbor, MI
| | - Joseph P. Romano
- Departments of Economics and Statistics, Stanford University, Stanford, CA
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12
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Affiliation(s)
- Jason Wu
- Department of Statistics, University of California, Berkeley, CA
| | - Peng Ding
- Department of Statistics, University of California, Berkeley, CA
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13
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Lu J. Improved Neymanian analysis for 2Kfactorial designs with binary outcomes. STAT NEERL 2019. [DOI: 10.1111/stan.12186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jiannan Lu
- Analysis and Experimentation,Microsoft Corporation Redmond Washington
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14
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Fogarty CB. Studentized Sensitivity Analysis for the Sample Average Treatment Effect in Paired Observational Studies. J Am Stat Assoc 2019. [DOI: 10.1080/01621459.2019.1632072] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Colin B. Fogarty
- Operations Research and Statistics Group, MIT Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA
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Zhao Q, Small DS, Bhattacharya BB. Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap. J R Stat Soc Series B Stat Methodol 2019. [DOI: 10.1111/rssb.12327] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
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16
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Lu J. On finite-population Bayesian inferences for 2 K factorial designs with binary outcomes. J STAT COMPUT SIM 2019. [DOI: 10.1080/00949655.2019.1574793] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Jiannan Lu
- Analysis and Experimentation, Microsoft Corporation, One Microsoft Way, Redmond, WA, USA
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17
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Ding P, Keele L. Rank tests in unmatched clustered randomized trials applied to a study of teacher training. Ann Appl Stat 2018. [DOI: 10.1214/18-aoas1147] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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18
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Generalizing distance covariance to measure and test multivariate mutual dependence via complete and incomplete V-statistics. J MULTIVARIATE ANAL 2018. [DOI: 10.1016/j.jmva.2018.08.006] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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19
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Fogarty CB. On mitigating the analytical limitations of finely stratified experiments. J R Stat Soc Series B Stat Methodol 2018. [DOI: 10.1111/rssb.12290] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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20
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Affiliation(s)
- Peng Ding
- Department of Statistics, University of California, Berkeley, CA
| | - Avi Feller
- Department of Statistics, University of California, Berkeley, CA
- Goldman School of Public Policy, University of California, Berkeley, CA
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21
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Ding P, Miratrix LW. Model‐free causal inference of binary experimental data. Scand Stat Theory Appl 2018. [DOI: 10.1111/sjos.12343] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Peng Ding
- Department of Statistics University of California Berkeley CA USA
| | - Luke W. Miratrix
- Graduate School of Education and Department of Statistics Harvard University Cambridge MA USA
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22
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Cox LA. RE: "BEST PRACTICES FOR GAUGING EVIDENCE OF CAUSALITY IN AIR POLLUTION EPIDEMIOLOGY". Am J Epidemiol 2018; 187:1338-1339. [PMID: 29584873 DOI: 10.1093/aje/kwy034] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2017] [Accepted: 12/06/2017] [Indexed: 01/15/2023] Open
Affiliation(s)
- Louis Anthony Cox
- Cox Associates, Denver, CO
- Department of Biostatistics and Informatics, Colorado School of Public Health, University of Colorado, Denver, Colorado
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23
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Fay MP, Brittain EH, Shih JH, Follmann DA, Gabriel EE. Causal estimands and confidence intervals associated with Wilcoxon-Mann-Whitney tests in randomized experiments. Stat Med 2018; 37:2923-2937. [PMID: 29774591 PMCID: PMC6373726 DOI: 10.1002/sim.7799] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2017] [Revised: 03/05/2018] [Accepted: 04/03/2018] [Indexed: 11/10/2022]
Abstract
Although the P value from a Wilcoxon-Mann-Whitney test is used often with randomized experiments, it is rarely accompanied with a causal effect estimate and its confidence interval. The natural parameter for the Wilcoxon-Mann-Whitney test is the Mann-Whitney parameter, ϕ, which measures the probability that a randomly selected individual in the treatment arm will have a larger response than a randomly selected individual in the control arm (plus an adjustment for ties). We show that the Mann-Whitney parameter may be framed as a causal parameter and show that it is not equal to a closely related and nonidentifiable causal effect, ψ, the probability that a randomly selected individual will have a larger response under treatment than under control (plus an adjustment for ties). We review the paradox, first expressed by Hand, that the ψ parameter may imply that the treatment is worse (or better) than control, while the Mann-Whitney parameter shows the opposite. Unlike the Mann-Whitney parameter, ψ is nonidentifiable from a randomized experiment. We review some nonparametric assumptions that rule out Hand's paradox through bounds on ψ and use bootstrap methods to make inferences on those bounds. We explore the relationship of the proportional odds parameter to Hand's paradox, showing that the paradox may occur for proportional odds parameters between 1/9 and 9. Thus, large effects are needed to ensure that if treatment appears better by the Mann-Whitney parameter, then treatment improves responses in most individuals. We demonstrate these issues using a vaccine trial.
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Affiliation(s)
- Michael P Fay
- Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, Bethesda, MD, USA
| | - Erica H Brittain
- Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, Bethesda, MD, USA
| | - Joanna H Shih
- Biometric Research Branch, DCTD, National Cancer Institute, Rockville, MD, USA
| | - Dean A Follmann
- Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, Bethesda, MD, USA
| | - Erin E Gabriel
- Department of Medical Epidemiology and Biostatistics, Karolinska Institute, Stockholm, Sweden
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24
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Li X, Ding P. General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference. J Am Stat Assoc 2018. [DOI: 10.1080/01621459.2017.1295865] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Xinran Li
- Department of Statistics, Harvard University, Cambridge, MA
| | - Peng Ding
- Department of Statistics, University of California, Berkeley, CA
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25
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Lu J. Sharpening randomization-based causal inference for 2 2 factorial designs with binary outcomes. Stat Methods Med Res 2017; 28:1064-1078. [PMID: 29205103 DOI: 10.1177/0962280217745720] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In medical research, a scenario often entertained is randomized controlled 22 factorial design with a binary outcome. By utilizing the concept of potential outcomes, Dasgupta et al. proposed a randomization-based causal inference framework, allowing flexible and simultaneous estimations and inferences of the factorial effects. However, a fundamental challenge that Dasgupta et al.'s proposed methodology faces is that the sampling variance of the randomization-based factorial effect estimator is unidentifiable, rendering the corresponding classic "Neymanian" variance estimator suffering from over-estimation. To address this issue, for randomized controlled 22 factorial designs with binary outcomes, we derive the sharp lower bound of the sampling variance of the factorial effect estimator, which leads to a new variance estimator that sharpens the finite-population Neymanian causal inference. We demonstrate the advantages of the new variance estimator through a series of simulation studies, and apply our newly proposed methodology to two real-life datasets from randomized clinical trials, where we gain new insights.
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Affiliation(s)
- Jiannan Lu
- Analysis and Experimentation, Microsoft Corporation, Redmond, USA
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26
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Ding P, Dasgupta T. A randomization-based perspective on analysis of variance: a test statistic robust to treatment effect heterogeneity. Biometrika 2017. [DOI: 10.1093/biomet/asx059] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
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27
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Ding P. Rejoinder: A Paradox from Randomization-Based Causal Inference. Stat Sci 2017. [DOI: 10.1214/17-sts571rej] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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30
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Aronow PM, Offer-Westort MR. Understanding Ding’s Apparent Paradox. Stat Sci 2017. [DOI: 10.1214/16-sts582] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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