Studentized Sensitivity Analysis for the Sample Average Treatment Effect in Paired Observational Studies

References

• Ahmed, A.-H. N., Leon, R., and Proschan, F. (1981), “Generalized Association, With Applications in Multivariate Statistics,” The Annals of Statistics, 9, 168–176. DOI: 10.1214/aos/1176345343.
   Web of Science ®Google Scholar
• Caughey, D., Dafoe, A., and Miratrix, L. (2017), “Beyond the Sharp Null: Randomization Inference, Bounded Null Hypotheses, and Confidence Intervals for Maximum Effects,” arXiv preprint arXiv:1709.07339.
   Google Scholar
• Chung, E., and Romano, J. P. (2013), “Exact and Asymptotically Robust Permutation Tests,” The Annals of Statistics, 41, 484–507. DOI: 10.1214/13-AOS1090.
   Web of Science ®Google Scholar
• Copas, J. B., and Li, H. (1997), “Inference for Non-Random Samples,” Journal of the Royal Statistical Society, Series B, 59, 55–95. DOI: 10.1111/1467-9868.00055.
   Google Scholar
• Cox, D. R. (1958), Planning of Experiments, New York: Wiley.
   Google Scholar
• Ding, P. (2017), “A Paradox From Randomization-Based Causal Inference,” Statistical Science, 32, 331–345. DOI: 10.1214/16-STS571.
   Web of Science ®Google Scholar
• Ding, P., and Dasgupta, T. (2017), “A Randomization-Based Perspective on Analysis of Variance: A Test Statistic Robust to Treatment Effect Heterogeneity,” Biometrika, 105, 45–56. DOI: 10.1093/biomet/asx059.
   Web of Science ®Google Scholar
• Fisher, R. (1935), “Comment on ‘Statistical Problems in Agricultural Experimentation’,” Journal of the Royal Statistical Society, Series B, 2, 154–157.
   Google Scholar
• Fogarty, C. B., and Hasegawa, R. B. (2019), “Extended Sensitivity Analysis for Heterogeneous Unmeasured Confounding With an Application to Sibling Studies of Returns to Education,” Annals of Applied Statistics, 13, 767–796. DOI: 10.1214/18-AOAS1215.
   Web of Science ®Google Scholar
• Fogarty, C. B., Shi, P., Mikkelsen, M. E., and Small, D. S. (2017), “Randomization Inference and Sensitivity Analysis for Composite Null Hypotheses With Binary Outcomes in Matched Observational Studies,” Journal of the American Statistical Association, 112, 321–331. DOI: 10.1080/01621459.2016.1138865.
   Web of Science ®Google Scholar
• Gelman, A. (2015), “The Connection Between Varying Treatment Effects and the Crisis of Unreplicable Research: A Bayesian Perspective,” Journal of Management, 41, 632–643. DOI: 10.1177/0149206314525208.
   Web of Science ®Google Scholar
• Heckman, J. J., Urzua, S., and Vytlacil, E. (2006), “Understanding Instrumental Variables in Models With Essential Heterogeneity,” The Review of Economics and Statistics, 88, 389–432. DOI: 10.1162/rest.88.3.389.
   Web of Science ®Google Scholar
• Hill, J. (2002), “Comment on ‘Covariance Adjustment in Randomized Experiments and Observational Studies’,” Statistical Science, 17, 307–309. DOI: 10.1214/ss/1042727942.
   Web of Science ®Google Scholar
• Holland, P. W. (1986), “Statistics and Causal Inference,” Journal of the American Statistical Association, 81, 945–960. DOI: 10.1080/01621459.1986.10478354.
   Web of Science ®Google Scholar
• Imai, K. (2008), “Variance Identification and Efficiency Analysis in Randomized Experiments Under the Matched-Pair Design,” Statistics in Medicine, 27, 4857–4873. DOI: 10.1002/sim.3337.
   PubMed Web of Science ®Google Scholar
• Janssen, A. (1997), “Studentized Permutation Tests for Non-iid Hypotheses and the Generalized Behrens–Fisher Problem,” Statistics and Probability Letters, 36, 9–21. DOI: 10.1016/S0167-7152(97)00043-6.
   Web of Science ®Google Scholar
• Lehmann, E. L., and Romano, J. P. (2005), Testing Statistical Hypotheses, Berlin: Springer Science & Business Media.
   Google Scholar
• Loh, W. W., Richardson, T. S., and Robins, J. M. (2017), “An Apparent Paradox Explained,” Statistical Science, 32, 356–361. DOI: 10.1214/17-STS610.
   Web of Science ®Google Scholar
• Maffei, F., Fimognari, C., Castelli, E., Stefanini, G. F., Forti, G. C., and Hrelia, P. (2000), “Increased Cytogenetic Damage Detected by Fish Analysis on Micronuclei in Peripheral Lymphocytes From Alcoholics,” Mutagenesis, 15, 517–523. DOI: 10.1093/mutage/15.6.517.
   PubMed Web of Science ®Google Scholar
• Neyman, J. (1923), “On the Application of Probability Theory to Agricultural Experiments. Essay on Principles,” Section 9 (in Polish). Roczniki Nauk Roiniczych, 10, 1–51 (Reprinted in Statistical Science, 1990, 5, 463–480).
   Google Scholar
• Neyman, J. (1935), “Statistical Problems in Agricultural Experimentation,” Supplement to the Journal of the Royal Statistical Society, 2, 107–180.
   Google Scholar
• Robins, J. M. (2002), “Comment on ‘Covariance Adjustment in Randomized Experiments and Observational Studies’,” Statistical Science, 17(3):309–321. DOI: 10.1214/ss/1042727942.
   Web of Science ®Google Scholar
• Rosenbaum, P. R. (1987), “Sensitivity Analysis for Certain Permutation Inferences in Matched Observational Studies,” Biometrika, 74, 13–26. DOI: 10.1093/biomet/74.1.13.
   Web of Science ®Google Scholar
• Rosenbaum, P. R. (2002a), “Attributing Effects to Treatment in Matched Observational Studies,” Journal of the American Statistical Association, 97, 183–192.
   Web of Science ®Google Scholar
• Rosenbaum, P. R. (2002b), Observational Studies, New York: Springer.
   Google Scholar
• Rosenbaum, P. R. (2003), “Exact Confidence Intervals for Nonconstant Effects by Inverting the Signed Rank Test,” The American Statistician, 57, 132–138.
   Web of Science ®Google Scholar
• Rosenbaum, P. R. (2004), “Design Sensitivity in Observational Studies,” Biometrika, 91, 153–164.
   Web of Science ®Google Scholar
• Rosenbaum, P. R. (2007), “Sensitivity Analysis for M-Estimates, Tests, and Confidence Intervals in Matched Observational Studies,” Biometrics, 63, 456–464.
   PubMed Web of Science ®Google Scholar
• Rosenbaum, P. R. (2011), “A New u-Statistic With Superior Design Sensitivity in Matched Observational Studies,” Biometrics, 67, 1017–1027.
   PubMed Web of Science ®Google Scholar
• Rosenbaum, P. R. (2013), “Impact of Multiple Matched Controls on Design Sensitivity in Observational Studies,” Biometrics, 69, 118–127.
   PubMed Web of Science ®Google Scholar
• Rosenbaum, P. R. (2016), “Using Scheffé Projections for Multiple Outcomes in an Observational Study of Smoking and Periodontal Disease,” The Annals of Applied Statistics, 10, 1447–1471.
   Web of Science ®Google Scholar
• Rubin, D. B. (1974), “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies,” Journal of Educational Psychology, 66, 688–701. DOI: 10.1037/h0037350.
   Web of Science ®Google Scholar
• Rubin, D. B. (1980), “Comment on ‘Randomization Analysis of Experimental Data: The Fisher Randomization Test’,” Journal of the American Statistical Association, 75, 591–593.
   Web of Science ®Google Scholar
• Sabbaghi, A., and Rubin, D. B. (2014), “Comments on the Neyman–Fisher Controversy and Its Consequences,” Statistical Science, 29, 267–284. DOI: 10.1214/13-STS454.
   Web of Science ®Google Scholar
• Welch, B. L. (1937), “On the z-test in Randomized Blocks and Latin Squares,” Biometrika, 29, 21–52. DOI: 10.1093/biomet/29.1-2.21.
   Google Scholar
• Werfel, U., Langen, V., Eickhoff, I., Schoonbrood, J., Vahrenholz, C., Brauksiepe, A., Popp, W., and Norpoth, K. (1998), “Elevated DNA Single-Strand Breakage Frequencies in Lymphocytes of Welders Exposed to Chromium and Nickel,” Carcinogenesis, 19, 413–418. DOI: 10.1093/carcin/19.3.413.
   PubMed Web of Science ®Google Scholar
• Wu, J., and Ding, P. (2018), “Randomization Tests for Weak Null Hypotheses,” arXiv preprint arXiv:1809.07419.
   Google Scholar
• Zhao, Q. (2018), “On Sensitivity Value of Pair-Matched Observational Studies,” Journal of the American Statistical Association, 114, 713–722 DOI: 10.1080/01621459.2018.1429277.
   Web of Science ®Google Scholar