1,731
Views
8
CrossRef citations to date
0
Altmetric
Theory and Methods

Sensitivity Analysis via the Proportion of Unmeasured Confounding

&
Pages 1540-1550 | Received 05 Dec 2019, Accepted 09 Dec 2020, Published online: 03 Feb 2021

References

  • Altonji, J. G., Elder, T. E., and Taber, C. R. (2008), “Using Selection on Observed Variables to Assess Bias From Unobservables When Evaluating Swan-Ganz Catheterization,” American Economic Review, 98, 345–350. DOI: 10.1257/aer.98.2.345.
  • Audibert, J.-Y., and Tsybakov, A. B. (2007), “Fast Learning Rates for Plug-In Classifiers,” The Annals of Statistics, 35, 608–633. DOI: 10.1214/009053606000001217.
  • Baiocchi, M., Cheng, J., and Small, D. S. (2014), “Instrumental Variable Methods for Causal Inference,” Statistics in Medicine, 33, 2297–2340. DOI: 10.1002/sim.6128.
  • Benkeser, D., and van der Laan, M. (2016), “The Highly Adaptive Lasso Estimator,” in 2016 IEEE International Conference on Data Science and Advanced Analytics (DSAA), IEEE, pp. 689–696.
  • Bickel, P., Klaassen, C. A. J., Ritov, Y., and Wellner, J. A. (1993), Efficient and Adaptive Estimation for Semiparametric Models (Vol. 4), New York: Springer-Verlag.
  • Brumback, B. A., Hernán, M. A., Haneuse, S. J. P. A., and Robins, J. M. (2004), “Sensitivity Analyses for Unmeasured Confounding Assuming a Marginal Structural Model for Repeated Measures,” Statistics in Medicine, 23, 749–767. DOI: 10.1002/sim.1657.
  • Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., and Newey, W. K. (2016), “Double Machine Learning for Treatment and Causal Parameters,” Technical Report, Cemmap Working Paper.
  • Chernozhukov, V., Fernandez-Val, I., and Galichon, A. (2009), “Improving Point and Interval Estimators of Monotone Functions by Rearrangement,” Biometrika, 96, 559–575. DOI: 10.1093/biomet/asp030.
  • Cinelli, C., and Hazlett, C. (2020), “Making Sense of Sensitivity: Extending Omitted Variable Bias,” Journal of the Royal Statistical Society, Series B, 82, 39–67. DOI: 10.1111/rssb.12348.
  • Connors, A. F., Speroff, T., Dawson, N. V., Thomas, C., Harrell, F. E., Wagner, D., Desbiens, N., Goldman, L., Wu, A. W., Califf, R. M., and Fulkerson, W. J. (1996), “The Effectiveness of Right Heart Catheterization in the Initial Care of Critically Ill Patients,” Jama, 276, 889–897. DOI: 10.1001/jama.1996.03540110043030.
  • Cornfield, J., Haenszel, W., Hammond, E. C., Lilienfeld, A. M., Shimkin, M. B., and Wynder, E. L. (1959), “Smoking and Lung Cancer: Recent Evidence and a Discussion of Some Questions,” Journal of the National Cancer Institute, 22, 173–203.
  • de Oliveira, L. M. F. T., dos Santos, A. R. M., Farah, B. Q., Ritti-Dias, R. M., de Freitas, C. M. S. M., and Diniz, P. R. B. (2019), “Influence of Parental Smoking on the Use of Alcohol and Illicit Drugs Among Adolescents,” Einstein (São Paulo), 17, eAO4377. DOI: 10.31744/einstein_journal/2019AO4377.
  • Díaz, I., and van der Laan, M. J. (2013), “Sensitivity Analysis for Causal Inference Under Unmeasured Confounding and Measurement Error Problems,” The International Journal of Biostatistics, 9, 149–160. DOI: 10.1515/ijb-2013-0004.
  • Ding, P., and VanderWeele, T. J. (2016), “Sensitivity Analysis Without Assumptions,” Epidemiology, 27, 368.
  • Farrell, M. H. (2015), “Robust Inference on Average Treatment Effects With Possibly More Covariates Than Observations,” Journal of Econometrics, 189, 1–23. DOI: 10.1016/j.jeconom.2015.06.017.
  • Gastwirth, J. L., Krieger, A. M., and Rosenbaum, P. R. (1998), “Dual and Simultaneous Sensitivity Analysis for Matched Pairs,” Biometrika, 85, 907–920. DOI: 10.1093/biomet/85.4.907.
  • Györfi, L., Kohler, M., Krzyzak, A., and Walk, H. (2006), A Distribution-Free Theory of Nonparametric Regression, New York: Springer.
  • Hernán, M. A., and Robins, J. M. (2006), “Instruments for Causal Inference: An Epidemiologist’s Dream?,” Epidemiology, 17, 360–372. DOI: 10.1097/01.ede.0000222409.00878.37.
  • Horowitz, J. L. (2009), Semiparametric and Nonparametric Methods in Econometrics (Vol. 12), New York: Springer.
  • Horowitz, J. L., and Manski, C. F. (1995), “Identification and Robustness With Contaminated and Corrupted Data,” Econometrica: Journal of the Econometric Society, 63, 281–302. DOI: 10.2307/2951627.
  • Imbens, G. W. (2003), “Sensitivity to Exogeneity Assumptions in Program Evaluation,” American Economic Review, 93, 126–132. DOI: 10.1257/000282803321946921.
  • Imbens, G. W., and Manski, C. F. (2004), “Confidence Intervals for Partially Identified Parameters,” Econometrica, 72, 1845–1857. DOI: 10.1111/j.1468-0262.2004.00555.x.
  • Joffe, M. M., Yang, W. P., and Feldman, H. I. (2010), “Selective Ignorability Assumptions in Causal Inference,” The International Journal of Biostatistics, 6, 11. DOI: 10.2202/1557-4679.1199.
  • Kandasamy, K., and Yu, Y. (2016), “Additive Approximations in High Dimensional Nonparametric Regression via the SALSA,” in International Conference on Machine Learning, pp. 69–78.
  • Kennedy, E. H. (2019), “Nonparametric Causal Effects Based on Incremental Propensity Score Interventions,” Journal of the American Statistical Association, 114, 645–656. DOI: 10.1080/01621459.2017.1422737.
  • Kennedy, E. H., Balakrishnan, S., and G’Sell, M. (2018), “Sharp Instruments for Classifying Compliers and Generalizing Causal Effects,” arXiv no. 1801.03635.
  • Kennedy, E. H., Harris, S., and Keele, L. J. (2019), “Survivor-Complier Effects in the Presence of Selection on Treatment, With Application to a Study of Prompt ICU Admission,” Journal of the American Statistical Association, 114, 93–104. DOI: 10.1080/01621459.2018.1469990.
  • Lammert, C., Nguyen, D. L., Juran, B. D., Schlicht, E., Larson, J. J., Atkinson, E. J., and Lazaridis, K. N. (2013), “Questionnaire Based Assessment of Risk Factors for Primary Biliary Cirrhosis,” Digestive and Liver Disease, 45, 589–594. DOI: 10.1016/j.dld.2013.01.028.
  • Lin, D. Y., Psaty, B. M., and Kronmal, R. A. (1998), “Assessing the Sensitivity of Regression Results to Unmeasured Confounders in Observational Studies,” Biometrics, 54, 948–963. DOI: 10.2307/2533848.
  • Liu, W., Kuramoto, S. J., and Stuart, E. A. (2013), “An Introduction to Sensitivity Analysis for Unobserved Confounding in Nonexperimental Prevention Research,” Prevention Science, 14, 570–580. DOI: 10.1007/s11121-012-0339-5.
  • Luedtke, A. R., Diaz, I., and van der Laan, M. J. (2015), “The Statistics of Sensitivity Analyses,” U.C. Berkeley Division of Biostatistics Working Paper Series 341.
  • Luedtke, A. R. and van der Laan, M. J. (2016), “Statistical Inference for the Mean Outcome Under a Possibly Non-Unique Optimal Treatment Strategy,” The Annals of Statistics, 44, 713. DOI: 10.1214/15-AOS1384.
  • Pengpid, S., and Peltzer, K. (2019), “Alcohol Use and Misuse Among School-Going Adolescents in Thailand: Results of a National Survey in 2015,” International Journal of Environmental Research and Public Health, 16, 1898. DOI: 10.3390/ijerph16111898.
  • Raskutti, G., Wainwright, M. J., and Yu, B. (2012), “Minimax-Optimal Rates for Sparse Additive Models Over Kernel Classes via Convex Programming,” Journal of Machine Learning Research, 13, 389–427.
  • Richardson, A., Hudgens, M. G., Gilbert, P. B., and Fine, J. P. (2014), “Nonparametric Bounds and Sensitivity Analysis of Treatment Effects,” Statistical Science: A Review Journal of the Institute of Mathematical Statistics, 29, 596. DOI: 10.1214/14-STS499.
  • Richardson, T. S. and J. M. Robins (2010), “Analysis of the Binary Instrumental Variable Model,” in R. Dechter, H. Geffner, and J. Halpern (Eds.), Heuristics, Probability and Causality: A Tribute to Judea Pearl, Chapter 25, pp. 415–444. London: College Publications.
  • Robins, J. M. (2002), “Comment on ’Covariance adjustment in randomized experiments and observational studies’ by Paul Rosenbaum,” Stat Sci. 17, 286–327.
  • Robins, J. M. (2002), “[Covariance Adjustment in Randomized Experiments and Observational Studies]: Comment,” Statistical Science, 17, 309–321.
  • 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.
  • ——— (2002), “Covariance Adjustment in Randomized Experiments and Observational Studies,” Statistical Science, 17, 286–327.
  • ——— (2006), “Differential Effects and Generic Biases in Observational Studies,” Biometrika, 93, 573–586.
  • Rosenbaum, P. R., and Rubin, D. B. (1983), “Assessing Sensitivity to an Unobserved Binary Covariate in an Observational Study With Binary Outcome,” Journal of the Royal Statistical Society, Series B, 45, 212–218. DOI: 10.1111/j.2517-6161.1983.tb01242.x.
  • Rotnitzky, A., Scharfstein, D., Su, T.-L., and Robins, J. (2001), “Methods for Conducting Sensitivity Analysis of Trials With Potentially Nonignorable Competing Causes of Censoring,” Biometrics, 57, 103–113. DOI: 10.1111/j.0006-341x.2001.00103.x.
  • Rubin, D. B. (1974), “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies,” Journal of Educational Psychology, 66, 688. DOI: 10.1037/h0037350.
  • Tsiatis, A. (2007), Semiparametric Theory and Missing Data, New York: Springer.
  • van der Laan, M. J. (2017), “A Generally Efficient Targeted Minimum Loss Based Estimator Based on the Highly Adaptive Lasso,” The International Journal of Biostatistics, 13, 297. DOI: 10.1515/ijb-2015-0097.
  • van der Laan, M. J., Laan, M. J., and Robins, J. M. (2003), Unified Methods for Censored Longitudinal Data and Causality, New York: Springer.
  • van der Laan, M. J., and Luedtke, A. R. (2014), “Targeted Learning of an Optimal Dynamic Treatment, and Statistical Inference for Its Mean Outcome,” U.C. Berkeley Division of Biostatistics Working Paper Series 329.
  • van der Laan, M. J., Polley, E. C., and Hubbard, A. E. (2007), “Super Learner,” Statistical Applications in Genetics and Molecular Biology, 6, 25. DOI: 10.2202/1544-6115.1309.
  • van der Vaart, A. W. (2002), “Semiparametric Statistics,” in Lectures on Probability Theory and Statistics, eds. S. Tavaré and J. Picard, Springer, pp. 331–457.
  • van der Vaart, A. W., and Wellner, J. A. (1996), Weak Convergence and Empirical Processes With Application to Statistics, New York: Springer-Verlag.
  • VanderWeele, T. J., and Ding, P. (2017), “Sensitivity Analysis in Observational Research: Introducing the E-Value,” Annals of Internal Medicine, 167, 268–274. DOI: 10.7326/M16-2607.
  • Yadlowsky, S., Namkoong, H., Basu, S., Duchi, J., and Tian, L. (2018), “Bounds on the Conditional and Average Treatment Effect in the Presence of Unobserved Confounders,” arXiv no. 1808.09521.
  • Yang, Y., and Tokdar, S. T. (2015), “Minimax-Optimal Nonparametric Regression in High Dimensions,” The Annals of Statistics, 43, 652–674. DOI: 10.1214/14-AOS1289.
  • Zhang, B., and Tchetgen Tchetgen, E. J. (2019), “A Semiparametric Approach to Model-Based Sensitivity Analysis in Observational Studies,” arXiv no. 1910.14130.
  • Zhao, Q., Small, D. S., and Bhattacharya, B. B. (2017), “Sensitivity Analysis for Inverse Probability Weighting Estimators via the Percentile Bootstrap,” arXiv no. 1711.11286.
  • Zheng, W., and van der Laan, M. J. (2010), “Asymptotic Theory for Cross-Validated Targeted Maximum Likelihood Estimation,” U.C. Berkeley Division of Biostatistics Working Paper Series 273.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.