References

Abadie, Alberto, and Guido W. Imbens. 2006. “Large Sample Properties of Matching Estimators for Average Treatment Effects.” Econometrica 74 (1): 235–67. https://doi.org/10.1111/j.1468-0262.2006.00655.x.

Abadie, Alberto, and Guido W. Imbens. 2008. “On the Failure of the Bootstrap for Matching Estimators.” Econometrica 76 (6): 1537–57. https://doi.org/10.3982/ECTA6474.

Abadie, Alberto, and Guido W. Imbens. 2016. “Matching on the Estimated Propensity Score.” Econometrica 84 (2): 781–807. https://doi.org/10.3982/ECTA11293.

Anderson, T. W., and Herman Rubin. 1949. “Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations.” The Annals of Mathematical Statistics 20 (1): 46–63.

Andrews, Isaiah, and Timothy B. Armstrong. 2017. “Unbiased Instrumental Variables Estimation Under Known First-Stage Sign.” Quantitative Economics 8 (2): 479–503.

Angrist, Joshua D. 1990. “Lifetime Earnings and the Vietnam Era Draft Lottery: Evidence from Social Security Administrative Records.” American Economic Review 80 (3): 313–36.

Angrist, Joshua D., Susan M. Dynarski, Thomas J. Kane, Parag A. Pathak, and Christopher R. Walters. 2012. “Who Benefits from KIPP?” Journal of Policy Analysis and Management 31 (4): 837–60. https://doi.org/10.1002/pam.21647.

Angrist, Joshua D., and Guido W. Imbens. 1995. “Two-Stage Least Squares Estimation of Average Causal Effects in Models with Variable Treatment Intensity.” Journal of the American Statistical Association 90 (430): 431–42. https://doi.org/10.2307/2291054.

Angrist, Joshua D., Guido W. Imbens, and Donald B. Rubin. 1996. “Identification of Causal Effects Using Instrumental Variables.” Journal of the American Statistical Association 91 (434): 444–55.

Angrist, Joshua D., and Alan B. Krueger. 1991. “Does Compulsory School Attendance Affect Schooling and Earnings?” Quarterly Journal of Economics 106 (4): 979–1014. https://doi.org/10.2307/2937954.

Angrist, Joshua D., and Jörn-Steffen Pischke. 2009. Mostly Harmless Econometrics: An Empiricist’s Companion. Princeton University Press.

Angrist, Joshua, and Michal Kolesár. 2024. “One Instrument to Rule Them All: The Bias and Coverage of Just-ID IV.” Journal of Econometrics 240 (2): 105398.

Angrist, Joshua, Daniel Lang, and Philip Oreopoulos. 2009. “Incentives and Services for College Achievement: Evidence from a Randomized Trial.” American Economic Journal: Applied Economics 1 (1): 136–63.

Bang, Heejung, and James M. Robins. 2005. “Doubly Robust Estimation in Missing Data and Causal Inference Models.” Biometrics 61 (4): 962–73. https://doi.org/10.1111/j.1541-0420.2005.00377.x.

Baron, Reuben M., and David A. Kenny. 1986. “The Moderator–Mediator Variable Distinction in Social Psychological Research: Conceptual, Strategic, and Statistical Considerations.” Journal of Personality and Social Psychology 51 (6): 1173–82. https://doi.org/10.1037/0022-3514.51.6.1173.

Bartik, Timothy J. 1991. Who Benefits from State and Local Economic Development Policies? W. E. Upjohn Institute for Employment Research.

Berkson, Joseph. 1946. “Limitations of the Application of Fourfold Table Analysis to Hospital Data.” Biometrics Bulletin 2 (3): 47–53.

Bezuidenhout, Dana, Sarah Forthal, Kara Rudolph, and Matthew R. Lamb. 2025. “Single World Intervention Graphs (SWIGs): A Practical Guide.” American Journal of Epidemiology 194: 2047–52. https://doi.org/10.1093/aje/kwae353.

Bickel, Peter J., Chris A. J. Klaassen, Ya’acov Ritov, and Jon A. Wellner. 1993. Efficient and Adaptive Estimation for Semiparametric Models. Johns Hopkins University Press.

Bound, John, David A. Jaeger, and Regina M. Baker. 1995. “Problems with Instrumental Variables Estimation When the Correlation Between the Instruments and the Endogenous Explanatory Variable Is Weak.” Journal of the American Statistical Association 90 (430): 443–50. https://doi.org/10.2307/2291055.

Brookhart, M. Alan, Sebastian Schneeweiss, Kenneth J. Rothman, Robert J. Glynn, Jerry Avorn, and Til Stürmer. 2006. “Variable Selection for Propensity Score Models.” American Journal of Epidemiology 163 (12): 1149–56. https://doi.org/10.1093/aje/kwj149.

Buckles, Kasey S., and Daniel M. Hungerman. 2013. “Season of Birth and Later Outcomes: Old Questions, New Answers.” Review of Economics and Statistics 95 (3): 711–24.

Card, David. 1995. “Using Geographic Variation in College Proximity to Estimate the Return to Schooling.” In Aspects of Labour Market Behaviour: Essays in Honour of John Vanderkamp, edited by Louis N. Christofides, E. Kenneth Grant, and Robert Swidinsky. University of Toronto Press.

Chernozhukov, Victor, Denis Chetverikov, Mert Demirer, et al. 2018. “Double/Debiased Machine Learning for Treatment and Structural Parameters.” The Econometrics Journal 21 (1): C1–68. https://doi.org/10.1111/ectj.12097.

Cinelli, Carlos, and Chad Hazlett. 2020. “Making Sense of Sensitivity: Extending Omitted Variable Bias.” Journal of the Royal Statistical Society, Series B 82 (1): 39–67. https://doi.org/10.1111/rssb.12348.

Cochran, William G. 1968. “The Effectiveness of Adjustment by Subclassification in Removing Bias in Observational Studies.” Biometrics 24 (2): 295–313. https://doi.org/10.2307/2528036.

Cochran, William G. 1977. Sampling Techniques. 3rd ed. Wiley.

Cornfield, Jerome, William Haenszel, E. Cuyler Hammond, Abraham M. Lilienfeld, Michael B. Shimkin, and Ernst L. Wynder. 1959. “Smoking and Lung Cancer: Recent Evidence and a Discussion of Some Questions.” Journal of the National Cancer Institute 22 (1): 173–203.

Cressie, Noel, and Timothy R. C. Read. 1984. “Multinomial Goodness-of-Fit Tests.” Journal of the Royal Statistical Society, Series B 46 (3): 440–64.

Crump, Richard K., V. Joseph Hotz, Guido W. Imbens, and Oscar A. Mitnik. 2009. “Dealing with Limited Overlap in Estimation of Average Treatment Effects.” Biometrika 96 (1): 187–99. https://doi.org/10.1093/biomet/asn055.

Dale, Stacy Berg, and Alan B. Krueger. 2002. “Estimating the Payoff to Attending a More Selective College: An Application of Selection on Observables and Unobservables.” The Quarterly Journal of Economics 117 (4): 1491–527.

Dawid, A. Philip. 1979. “Conditional Independence in Statistical Theory.” Journal of the Royal Statistical Society, Series B 41 (1): 1–31.

Dawid, A. Philip. 1980. “Conditional Independence for Statistical Operations.” Annals of Statistics 8 (3): 598–617. https://doi.org/10.1214/aos/1176345011.

Dehejia, Rajeev H., and Sadek Wahba. 1999. “Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programmes.” Journal of the American Statistical Association 94 (448): 1053–62.

Deville, Jean-Claude, and Carl-Erik Särndal. 1992. “Calibration Estimators in Survey Sampling.” Journal of the American Statistical Association 87 (418): 376–82. https://doi.org/10.2307/2290268.

Ding, Peng. 2024. A First Course in Causal Inference. CRC Press.

Ding, Peng, Avi Feller, and Luke Miratrix. 2016. “Randomization Inference for Treatment Effect Variation.” Journal of the Royal Statistical Society: Series B 78 (3): 655–71. https://doi.org/10.1111/rssb.12124.

Ding, Peng, and Tyler J. VanderWeele. 2016. “Sensitivity Analysis Without Assumptions.” Epidemiology 27 (3): 368–77. https://doi.org/10.1097/EDE.0000000000000457.

Dorn, Jacob, and Kevin Guo. 2023. “Sharp Sensitivity Analysis for Inverse Propensity Weighting via Quantile Balancing.” Journal of the American Statistical Association 118 (544): 2645–57. https://doi.org/10.1080/01621459.2022.2069572.

Firth, David, and Karen E. Bennett. 1998. “Robust Models in Probability Sampling.” Journal of the Royal Statistical Society: Series B 60 (1): 3–21. https://doi.org/10.1111/1467-9868.00105.

Fisher, Ronald A. 1935. The Design of Experiments. Oliver; Boyd.

Frangakis, Constantine E., and Donald B. Rubin. 2002. “Principal Stratification in Causal Inference.” Biometrics 58 (1): 21–29. https://doi.org/10.1111/j.0006-341X.2002.00021.x.

Frisch, Ragnar, and Frederick V. Waugh. 1933. “Partial Time Regressions as Compared with Individual Trends.” Econometrica 1 (4): 387–401.

Fuller, Wayne A. 1975. “Regression Analysis for Sample Survey.” Sankhyā, Series C 37: 117–32.

Goldsmith-Pinkham, Paul, Isaac Sorkin, and Henry Swift. 2020. “Bartik Instruments: What, When, Why, and How.” American Economic Review 110 (8): 2586–624. https://doi.org/10.1257/aer.20181047.

Haavelmo, Trygve. 1943. “The Statistical Implications of a System of Simultaneous Equations.” Econometrica 11 (1): 1–12.

Hahn, Jinyong. 1998. “On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects.” Econometrica 66 (2): 315–31. https://doi.org/10.2307/2998560.

Hainmueller, Jens. 2012. “Entropy Balancing for Causal Effects: A Multivariate Reweighting Method to Produce Balanced Samples in Observational Studies.” Political Analysis 20 (1): 25–46. https://doi.org/10.1093/pan/mpr025.

Hansen, Ben B. 2008. “The Prognostic Analogue of the Propensity Score.” Biometrika 95 (2): 481–88. https://doi.org/10.1093/biomet/asn004.

Hansen, Lars Peter. 1982. “Large Sample Properties of Generalized Method of Moments Estimators.” Econometrica 50 (4): 1029–54. https://doi.org/10.2307/1912775.

Hausman, Jerry A. 1978. “Specification Tests in Econometrics.” Econometrica 46 (6): 1251–71. https://doi.org/10.2307/1913827.

Hernán, Miguel A., and James M. Robins. 2006. “Instruments for Causal Inference: An Epidemiologist’s Dream?” Epidemiology 17 (4): 360–72. https://doi.org/10.1097/01.ede.0000222409.00878.37.

Hernán, Miguel A., and James M. Robins. 2020. Causal Inference: What If. Chapman & Hall/CRC.

Hirano, Keisuke, Guido W. Imbens, and Geert Ridder. 2003. “Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score.” Econometrica 71 (4): 1161–89. https://doi.org/10.1111/1468-0262.00442.

Holland, Paul W. 1986. “Statistics and Causal Inference.” Journal of the American Statistical Association 81 (396): 945–60.

Huang, Yimin, and Marco Valtorta. 2006. “Pearl’s Calculus of Intervention Is Complete.” Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence (UAI) (Arlington, VA), 217–24.

Imai, Kosuke, Luke Keele, and Teppei Yamamoto. 2010. “Identification, Inference and Sensitivity Analysis for Causal Mediation Effects.” Statistical Science 25 (1): 51–71. https://doi.org/10.1214/10-STS321.

Imbens, Guido W. 2003. “Sensitivity to Exogeneity Assumptions in Program Evaluation.” American Economic Review 93 (2): 126–32.

Imbens, Guido W., and Joshua D. Angrist. 1994. “Identification and Estimation of Local Average Treatment Effects.” Econometrica 62 (2): 467–75.

Imbens, Guido W., and Whitney K. Newey. 2009. “Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity.” Econometrica 77 (5): 1481–512.

Imbens, Guido W., and Donald B. Rubin. 1997. “Estimating Outcome Distributions for Compliers in Instrumental Variables Models.” Review of Economic Studies 64 (4): 555–74.

Imbens, Guido W., and Donald B. Rubin. 2015. Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction. Cambridge University Press.

Isaki, Cary T., and Wayne A. Fuller. 1982. “Survey Design Under the Regression Superpopulation Model.” Journal of the American Statistical Association 77 (377): 89–96. https://doi.org/10.2307/2287773.

Kennedy, Edward H., Zongming Ma, Matthew D. McHugh, and Dylan S. Small. 2017. “Non-Parametric Methods for Doubly Robust Estimation of Continuous Treatment Effects.” Journal of the Royal Statistical Society: Series B 79 (4): 1229–45.

Khan, Shakeeb, and Elie Tamer. 2010. “Irregular Identification, Support Conditions, and Inverse Weight Estimation.” Econometrica 78 (6): 2021–42. https://doi.org/10.3982/ECTA7372.

Kitagawa, Toru. 2015. “A Test for Instrument Validity.” Econometrica 83 (5): 2043–63. https://doi.org/10.3982/ECTA11974.

Kwon, Yonghyun, Jae Kwang Kim, and Yumou Qiu. 2026. “Generalized Entropy Calibration for Analyzing Voluntary Survey Data.” Biometrics 82 (1): ujag041. https://doi.org/10.1093/biomtc/ujag041.

Laan, Mark J. van der, and Sherri Rose. 2011. Targeted Learning: Causal Inference for Observational and Experimental Data. Springer Series in Statistics. Springer.

Laan, Mark J. van der, and Sherri Rose. 2018. Targeted Learning in Data Science: Causal Inference for Complex Longitudinal Studies. Springer Series in Statistics. Springer.

Laan, Mark J. van der, and Daniel Rubin. 2006. “Targeted Maximum Likelihood Learning.” The International Journal of Biostatistics 2 (1): 1–40. https://doi.org/10.2202/1557-4679.1043.

LaLonde, Robert J. 1986. “Evaluating the Econometric Evaluations of Training Programmes with Experimental Data.” American Economic Review 76 (4): 604–20.

Lauritzen, Steffen L. 1996. Graphical Models. Oxford University Press.

Lee, David S., Justin McCrary, Marcelo J. Moreira, and Jack Porter. 2022. “Valid t-Ratio Inference for IV.” American Economic Review 112 (10): 3260–90.

Levis, Alexander W., Edward H. Kennedy, and Luke Keele. 2024. “Nonparametric Identification and Efficient Estimation of Causal Effects with Instrumental Variables.” arXiv Preprint arXiv:2402.09332.

Li, Ker-Chau, and Naihua Duan. 1989. “Regression Analysis Under Link Violation.” The Annals of Statistics 17 (3): 1009–52. https://doi.org/10.1214/aos/1176347254.

Li, Xinran, and Peng Ding. 2017. “General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference.” Journal of the American Statistical Association 112 (520): 1759–69. https://doi.org/10.1080/01621459.2017.1295865.

Lin, D. Y., Bruce M. Psaty, and Richard A. Kronmal. 1998. “Assessing the Sensitivity of Regression Results to Unmeasured Confounders in Observational Studies.” Biometrics 54 (3): 948–63.

Lin, Winston. 2013. “Agnostic Notes on Regression Adjustments to Experimental Data: Reexamining Freedman’s Critique.” The Annals of Applied Statistics 7 (1): 295–318. https://doi.org/10.1214/12-AOAS583.

Lovell, Michael C. 1963. “Seasonal Adjustment of Economic Time Series and Multiple Regression Analysis.” Journal of the American Statistical Association 58 (304): 993–1010.

Manski, Charles F. 1990. “Nonparametric Bounds on Treatment Effects.” American Economic Review, Papers and Proceedings 80 (2): 319–23.

Manski, Charles F. 2003. Partial Identification of Probability Distributions. Springer. https://doi.org/10.1007/b97478.

Montiel Olea, José Luis, and Carolin Pflueger. 2013. “A Robust Test for Weak Instruments.” Journal of Business & Economic Statistics 31 (3): 358–69.

Moreira, Marcelo J. 2003. “A Conditional Likelihood Ratio Test for Structural Models.” Econometrica 71 (4): 1027–48.

Newey, Whitney K., and Richard J. Smith. 2004. “Higher Order Properties of GMM and Generalized Empirical Likelihood Estimators.” Econometrica 72 (1): 219–55. https://doi.org/10.1111/j.1468-0262.2004.00482.x.

Neyman, Jerzy Splawa. 1923. “On the Application of Probability Theory to Agricultural Experiments: Essay on Principles, Section 9.” Statistical Science 5 (4): 465–72.

Pearl, Judea. 1993. “Comment: Graphical Models, Causality and Intervention.” Statistical Science 8 (3): 266–69.

Pearl, Judea. 1995a. “Causal Diagrams for Empirical Research.” Biometrika 82 (4): 669–88.

Pearl, Judea. 1995b. “On the Testability of Causal Models with Latent and Instrumental Variables.” Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI) (San Francisco, CA), 435–43.

Pearl, Judea. 2001. “Direct and Indirect Effects.” Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (UAI 2001), 411–20.

Pearl, Judea. 2009. Causality: Models, Reasoning, and Inference. 2nd ed. Cambridge University Press.

Phipson, Belinda, and Gordon K. Smyth. 2010. “Permutation P-Values Should Never Be Zero: Calculating Exact P-Values When Permutations Are Randomly Drawn.” Statistical Applications in Genetics and Molecular Biology 9 (1): Article 39.

Qin, Jin, and Jerry Lawless. 1994. “Empirical Likelihood and General Estimating Equations.” Annals of Statistics 22 (1): 300–325.

Ragusa, Giuseppe. 2011. “Minimum Divergence, Generalized Empirical Likelihoods, and Higher Order Expansions.” Econometric Reviews 30 (4): 406–56. https://doi.org/10.1080/07474938.2011.553541.

Reinisch, June M., Stephanie A. Sanders, Erik L. Mortensen, and Donald B. Rubin. 1995. “In Utero Exposure to Phenobarbital and Intelligence Deficits in Adult Men.” Journal of the American Medical Association 274 (19): 1518–25.

Richardson, Thomas S., and James M. Robins. 2013. Single World Intervention Graphs (SWIGs): A Unification of the Counterfactual and Graphical Approaches to Causality. Working Paper No. 128. Center for Statistics; the Social Sciences, University of Washington.

Richardson, Thomas S., and James M. Robins. 2014. ACE Bounds; Single World Intervention Graphs (SWIGs) and Identification of Causal Effects. University of Washington.

Robins, James M. 1986. “A New Approach to Causal Inference in Mortality Studies with a Sustained Exposure Period—Application to Control of the Healthy Worker Survivor Effect.” Mathematical Modelling 7 (9–12): 1393–512.

Robins, James M., Steven D. Mark, and Whitney K. Newey. 1992. “Estimating Exposure Effects by Modelling the Expectation of Exposure Conditional on Confounders.” Biometrics 48 (2): 479–95.

Robins, James M., Andrea Rotnitzky, and Lue Ping Zhao. 1994. “Estimation of Regression Coefficients When Some Regressors Are Not Always Observed.” Journal of the American Statistical Association 89 (427): 846–66. https://doi.org/10.2307/2290910.

Rosenbaum, Paul R. 1987a. “Model-Based Direct Adjustment.” Journal of the American Statistical Association 82 (398): 387–94. https://doi.org/10.1080/01621459.1987.10478441.

Rosenbaum, Paul R. 1987b. “Sensitivity Analysis for Certain Permutation Inferences in Matched Observational Studies.” Biometrika 74 (1): 13–26.

Rosenbaum, Paul R. 2002. Observational Studies. 2nd ed. Springer. https://doi.org/10.1007/978-1-4757-3692-2.

Rosenbaum, Paul R., and Donald B. Rubin. 1983a. “Assessing Sensitivity to an Unobserved Binary Covariate in an Observational Study with Binary Outcome.” Journal of the Royal Statistical Society, Series B 45 (2): 212–18.

Rosenbaum, Paul R., and Donald B. Rubin. 1983b. “The Central Role of the Propensity Score in Observational Studies for Causal Effects.” Biometrika 70 (1): 41–55.

Rubin, Donald B. 1974. “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies.” Journal of Educational Psychology 66 (5): 688–701.

Rubin, Donald B. 1980. “Randomization Analysis of Experimental Data: The Fisher Randomization Test.” Journal of the American Statistical Association 75 (371): 591–93.

Rubin, Donald B. 1986. “Which Ifs Have Causal Answers.” Journal of the American Statistical Association 81 (396): 961–62.

Rubin, Donald B. 2008. “For Objective Causal Inference, Design Trumps Analysis.” The Annals of Applied Statistics 2 (3): 808–40. https://doi.org/10.1214/08-AOAS187.

Sargan, John D. 1958. “The Estimation of Economic Relationships Using Instrumental Variables.” Econometrica 26 (3): 393–415. https://doi.org/10.2307/1907619.

Shachter, Ross D. 1998. “Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams).” Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI), 480–87.

Shpitser, Ilya. 2023. “When Does the ID Algorithm Fail?” arXiv Preprint arXiv:2307.03750.

Shpitser, Ilya, and Judea Pearl. 2006. “Identification of Joint Interventional Distributions in Recursive Semi-Markovian Causal Models.” Proceedings of the Twenty-First National Conference on Artificial Intelligence (AAAI) 21: 1219–26.

Sobel, Michael E. 1982. “Asymptotic Confidence Intervals for Indirect Effects in Structural Equation Models.” Sociological Methodology 13: 290–312. https://doi.org/10.2307/270723.

Staiger, Douglas, and James H. Stock. 1997. “Instrumental Variables Regression with Weak Instruments.” Econometrica 65 (3): 557–86.

Stensrud, Mats J., James M. Robins, Torben Martinussen, and Jessica G. Young. 2023. “Generalized Separable Effects for Mediation Analysis with a Mediator–Outcome Confounder.” Journal of the American Statistical Association 118 (543): 1736–48. https://doi.org/10.1080/01621459.2022.2071276.

Stensrud, Mats J., Jessica G. Young, Vanessa Didelez, James M. Robins, and Miguel A. Hernán. 2022. “Separable Effects for Causal Inference in the Presence of Competing Events.” Journal of the American Statistical Association 117 (537): 175–83. https://doi.org/10.1080/01621459.2020.1765783.

Stock, James H., and Motohiro Yogo. 2005. “Testing for Weak Instruments in Linear IV Regression.” In Identification and Inference for Econometric Models: Essays in Honor of Thomas Rothenberg, edited by Donald W. K. Andrews and James H. Stock. Cambridge University Press.

Tan, Zhiqiang. 2006. “A Distributional Approach for Causal Inference Using Propensity Scores.” Journal of the American Statistical Association 101 (476): 1619–37. https://doi.org/10.1198/016214506000000023.

Tan, Zhiqiang. 2020. “Regularized Calibrated Estimation of Propensity Scores with Model Misspecification and High-Dimensional Data.” Biometrika 107 (1): 137–58. https://doi.org/10.1093/biomet/asz059.

Tian, Jin, and Judea Pearl. 2002. “A General Identification Condition for Causal Effects.” Proceedings of the Eighteenth National Conference on Artificial Intelligence (AAAI) (Menlo Park, CA), 567–73.

Tsiatis, Anastasios A. 2006. Semiparametric Theory and Missing Data. Springer.

Tukey, John W. 1962. “The Future of Data Analysis.” The Annals of Mathematical Statistics 33 (1): 1–67.

Vaart, Aad W. van der. 1998. Asymptotic Statistics. Cambridge University Press.

VanderWeele, Tyler J. 2019. “Principles of Confounder Selection.” European Journal of Epidemiology 34 (3): 211–19. https://doi.org/10.1007/s10654-019-00494-6.

VanderWeele, Tyler J., and Peng Ding. 2017. “Sensitivity Analysis in Observational Research: Introducing the E-Value.” Annals of Internal Medicine 167 (4): 268–74. https://doi.org/10.7326/M16-2607.

VanderWeele, Tyler J., Stijn Vansteelandt, and James M. Robins. 2014. “Effect Decomposition in the Presence of an Exposure-Induced Mediator-Outcome Confounder.” Epidemiology 25 (2): 300–306.

Vansteelandt, Stijn, and Rhian M. Daniel. 2017. “Interventional Effects for Mediation Analysis with Multiple Mediators.” Epidemiology 28 (2): 258–65.

Waernbaum, Ingeborg. 2012. “Model Misspecification and Robustness in Causal Inference: Comparing Matching with Doubly Robust Estimation.” Statistics in Medicine 31 (15): 1572–81.

Wang, Hengfang, and Jae Kwang Kim. 2025. “Information Projection Approach to Smoothed Propensity Score Weighting for Handling Selection Bias Under Missing at Random.” Annals of the Institute of Statistical Mathematics 77: 127–53. https://doi.org/10.1007/s10463-024-00913-w.

Wang, Linbo, Thomas S. Richardson, and James M. Robins. 2026. “Causal Inference: A Tale of Three Frameworks.” Journal of Data Science 24 (1): 53–85. https://doi.org/10.6339/25-JDS1211.

Wang, Linbo, and Eric Tchetgen Tchetgen. 2018. “Bounded, Efficient and Multiply Robust Estimation of Average Treatment Effects Using Instrumental Variables.” Biometrika 105 (2): 387–97. https://doi.org/10.1093/biomet/asy015.

Yang, Shu, and Peng Ding. 2018. “Asymptotic Inference of Causal Effects with Observational Studies Trimmed by the Estimated Propensity Scores.” Biometrika 105 (2): 487–93. https://doi.org/10.1093/biomet/asy008.

Yang, Shu, Guido W. Imbens, Zhanglin Cui, Douglas E. Faries, and Zbigniew Kadziola. 2016. “Propensity Score Matching and Stratification in Observational Studies with Multi-Level Treatments.” Biometrics 72: 1055–65.

Yang, Shu, and Yunshu Zhang. 2023. “Multiply Robust Matching Estimators of Average and Quantile Treatment Effects.” Scandinavian Journal of Statistics 50: 235–65.

Zhao, Qingyuan, and Daniel Percival. 2017. “Entropy Balancing Is Doubly Robust.” Journal of Causal Inference 5 (1): 20160010. https://doi.org/10.1515/jci-2016-0010.

Zhao, Qingyuan, Dylan S. Small, and Bhaswar B. Bhattacharya. 2019. “Sensitivity Analysis for Inverse Probability Weighting Estimators via the Percentile Bootstrap.” Journal of the Royal Statistical Society, Series B 81 (4): 735–61. https://doi.org/10.1111/rssb.12327.

Zheng, Wenjing, and Mark J. van der Laan. 2011. “Cross-Validated Targeted Minimum-Loss-Based Estimation.” In Targeted Learning: Causal Inference for Observational and Experimental Data, edited by Mark J. van der Laan and Sherri Rose. Springer Series in Statistics. Springer.