References

Almond, D., Chay, K. Y., & Lee, D. S. (2005). The costs of low birth weight. The Quarterly Journal of Economics, 120(3), 1031–1083.

Ariel Linden, T. J. V., Maya B. Mathur. (2020). Conducting sensitivity analysis for unmeasured confounding in observational studies using e-values: The evalue package. The Stata Journal: Promoting Communications on Statistics and Stata, 20(1), 162–175. https://doi.org/10.1177/1536867x20909696

Austin, P. C. (2009). Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity-score matched samples. Statistics in Medicine, 28(25), 3083–3107. https://doi.org/10.1002/sim.3697

Bang, H., & Robins, J. M. (2005). Doubly robust estimation in missing data and causal inference models. Biometrics, 61(4), 962–973.

Bonvini, M., & Kennedy, E. H. (2022). Sensitivity analysis via the proportion of unmeasured confounding. Journal of the American Statistical Association, 117(539), 1540–1550.

Boos, D. D., & Stefanski, L. A. (2013). Essential statistical inference: Theory and methods. Springer.

Brian W Whitcomb, A. I. N. (2021). Defining, quantifying, and interpreting “noncollapsibility” in epidemiologic studies of measures of “effect.” American Journal of Epidemiology, 190(5), 697–700. https://doi.org/10.1093/aje/kwaa267

Brian W. Whitcomb, N. J. P., Enrique F. Schisterman. (2009). Quantification of collider‐stratification bias and the birthweight paradox. Paediatric and Perinatal Epidemiology, 23(5), 394–402. https://doi.org/10.1111/j.1365-3016.2009.01053.x

Cattaneo, M. D. (2010). Efficient semiparametric estimation of multi-valued treatment effects under ignorability. Journal of Econometrics, 155(2), 138–154. https://econpapers.repec.org/RePEc:eee:econom:v:155:y:2010:i:2:p:138-154

Cole, S. R., & Hernán, M. A. (2008). Constructing inverse probability weights for marginal structural models (No. 6; Vol. 168, pp. 656–664). Oxford Academic. https://doi.org/10.1093/aje/kwn164

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., Fulkerson, W. J., Vidaillet, H., Broste, S., Bellamy, P., Lynn, J., & Knaus, W. A. (1996). The effectiveness of right heart catheterization in the initial care of critically ill patients. Journal of the American Medical Association, 276(11), 889–897. https://doi.org/10.1001/jama.276.11.889

Dang, L. E., Gruber, S., Lee, H., Dahabreh, I. J., Stuart, E. A., Williamson, B. D., Wyss, R., Díaz, I., Ghosh, D., Kıcıman, E., & al., et. (2023). A causal roadmap for generating high-quality real-world evidence. Journal of Clinical and Translational Science, 7(1), e212. https://doi.org/10.1017/cts.2023.635

Daniel, R. M. (2018). Double robustness. In Wiley StatsRef: Statistics reference online (pp. 1–14). Wiley. https://doi.org/10.1002/9781118445112.stat08068

Der Laan, M. J. van, & Rubin, D. (2006). Targeted maximum likelihood learning. The International Journal of Biostatistics, 2(1), Article 11.

Ding, P., & VanderWeele, T. J. (2016). Sensitivity analysis without assumptions. Epidemiology, 27(3), 368.

Dı́az, I., & Laan, M. J. van der. (2013). Sensitivity analysis for causal inference under unmeasured confounding and measurement error problems. The International Journal of Biostatistics, 9(2), 149–160.

Dı́az, I., Luedtke, A. R., & Laan, M. J. van der. (2018). Sensitivity analysis. In Targeted learning in data science (pp. 511–522). Springer.

Dorn, J., & Guo, K. (2022). Sharp sensitivity analysis for inverse propensity weighting via quantile balancing. Journal of the American Statistical Association, 1–13.

Dorn, J., Guo, K., & Kallus, N. (2021). Doubly-valid/doubly-sharp sensitivity analysis for causal inference with unmeasured confounding. arXiv Preprint arXiv:2112.11449.

Efron, B. (1982). The jackknife, the bootstrap and other resampling plans (Vol. 38). SIAM.

Efron, B., & Tibshirani, R. (1993). An introduction to the bootstrap (Vol. 57). Chapman & Hall. http://www.loc.gov/catdir/enhancements/fy0730/93004489-d.html

Greifer, N., & Stuart, E. A. (2023). Choosing the causal estimand for propensity score analysis of observational studies. arXiv. https://arxiv.org/abs/2106.10577

Gruber, S., & Laan, M. J. van der. (2012). Tmle: An r package for targeted maximum likelihood estimation. Journal of Statistical Software, 51(13), 1–35. https://doi.org/10.18637/jss.v051.i13

Gruber, S., & Laan, M. van der. (2009). Targeted maximum likelihood estimation: A gentle introduction. U.C. Berkeley Division of Biostatistics Working Paper Series. https://biostats.bepress.com/ucbbiostat/paper252

Gruber, S., & Laan, M. van der. (2011). Tmle: An r package for targeted maximum likelihood estimation. U.C. Berkeley Division of Biostatistics Working Paper Series.

Gutman, R., & Rubin, D. B. (2015). Estimation of causal effects of binary treatments in unconfounded studies. Stat Med, 34(26), 3381–3398.

Hailey R. Banack, J. S. K. (2013). The “obesity paradox” explained. Epidemiology, 24(3), 461–462. https://doi.org/10.1097/ede.0b013e31828c776c

Hammond, E. C. (1958). SMOKING AND DEATH RATES—REPORT ON FORTY-FOUR MONTHS OF FOLLOW-UP OF 187,783 MEN. Journal of the American Medical Association, 166(11), 1294. https://doi.org/10.1001/jama.1958.02990110030007

Hernán, M. A., & Robins, J. M. (2006). Estimating causal effects from epidemiological data. Journal of Epidemiology & Community Health, 60(7), 578–586.

Horvitz, D. G., & Thompson, D. J. (1952). A generalization of sampling without replacement from a finite universe. Journal of the American Statistical Association, 47(260), 663. https://doi.org/10.2307/2280784

Judea, P. (1994). A probabilistic calculus of actions. Proceedings of UAI-94, 454–462.

Jung, K., Lee, J., Gupta, V., & Cho, G. (2019). Comparison of bootstrap confidence interval methods for GSCA using a monte carlo simulation. Frontiers in Psychology, 10, 2215. https://doi.org/10.3389/fpsyg.2019.02215

Kennedy, E. H. (2016). Semiparametric theory and empirical processes in causal inference (pp. 141–167). Springer.

Lendle, S. D., Schwab, J., Petersen, M. L., & Der Laan, M. J. van. (2017). Ltmle: An r package implementing targeted minimum loss-based estimation for longitudinal data. Journal of Statistical Software, 81, 1–21. https://doi.org/10.18637/JSS.V081.I01

Luque-Fernandez, M. A. (2019). migariane/meltmle: Ensemble Learning Targeted Maximum Likelihood Estimation for Stata users | Zenodo. https://zenodo.org/record/2560828

Luque-Fernandez, M. A., Belot, A., Valeri, L., Cerulli, G., Maringe, C., & Rachet, B. (2018). Data-adaptive estimation for double-robust methods in population-based cancer epidemiology: Risk differences for lung cancer mortality by emergency presentation. American Journal of Epidemiology, 187(4), 871–878. https://doi.org/10.1093/aje/kwx317

Luque-Fernandez, M. A., Redondo-Sanchez, D., & Schomaker, M. (2019a). Effect modification and collapsibility in evaluations of public health interventions. American Journal of Public Health, 109(3), e12–e13. https://doi.org/10.2105/AJPH.2018.304916

Luque-Fernandez, M. A., Redondo-Sanchez, D., & Schomaker, M. (2019b). Effect Modification and Collapsibility in Evaluations of Public Health Interventions. American Journal of Public Health, 109(3), e12–e13. https://doi.org/10.2105/AJPH.2018.304916

Luque-Fernandez, M. A., Schomaker, M., Rachet, B., & Schnitzer, M. E. (2018). Targeted maximum likelihood estimation for a binary treatment: A tutorial. Statistics in Medicine, 37(16), 2530–2546. https://doi.org/10.1002/sim.7628

M. Schomaker, V. L., M. A. Luque‐Fernandez. (2019). Using longitudinal targeted maximum likelihood estimation in complex settings with dynamic interventions. Statistics in Medicine, 38(24), 4888–4911. https://doi.org/10.1002/sim.8340

Matthew A. Masten, A. P. (2018). Identification of treatment effects under conditional partial independence. Econometrica, 86(1), 317–351. https://doi.org/10.3982/ecta14481

Matthew A. Masten, L. Z., Alexandre Poirier. (2024). Assessing sensitivity to unconfoundedness: Estimation and inference. Journal of Business &Amp; Economic Statistics, 42(1), 1–13. https://doi.org/10.1080/07350015.2023.2183212

Maya B. Mathur, C. A. R., Peng Ding. (2018). Web site and r package for computing e-values. Epidemiology, 29(5), e45–e47. https://doi.org/10.1097/ede.0000000000000864

Miguel Angel Luque-Fernandez, U. V., Helga Zoega. (2016). Deconstructing the smoking-preeclampsia paradox through a counterfactual framework. European Journal of Epidemiology, 31(6), 613–623. https://doi.org/10.1007/s10654-016-0139-5

N. Pearce, L. R. (2014). Commentary: Three worlds collide: Berkson’s bias, selection bias and collider bias. International Journal of Epidemiology, 43(2), 521–524. https://doi.org/10.1093/ije/dyu025

Neyman, J. (1923). Sur les applications de la thar des probabilities aux experiences agaricales: Essay des principle. Excerpts reprinted (1990) in English. Statistical Science, 5, 463–472.

Oehlert, G. W. (1992). A note on the delta method. American Statistician, 46(1), 27–29. https://doi.org/10.1080/00031305.1992.10475842

Pearl, J. (2009). Causality: Models, reasoning, and inference. Cambridge University Press.

Pearl, J., & Robins, J. M. (1995). Probabilistic evaluation of sequential plans from causal models with hidden variables. Uncertainty in Artificial Intelligence, 11, 444–453.

Petersen, M. L., & Laan, M. J. van der. (2014). Causal models and learning from data. Epidemiology, 25(3), 418–426. https://doi.org/10.1097/ede.0000000000000078

Robins, J. M. (1986). A new approach to causal inference in mortality studies with sustained exposure periods – application to control of the healthy worker survivor effect. Mathematical Modeling, 7, 1393–1512.

Robins, J. (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), 1393–1512. https://doi.org/https://doi.org/10.1016/0270-0255(86)90088-6

Robins, J. M. (1999). Association, causation, and marginal structural models. Synthese, 121(1/2), 151–179. https://doi.org/10.2307/20118224

Robins, J. M., Rotnitzky, A., & Zhao, L. P. (1994a). Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89, 846–866.

Robins, J. M., Rotnitzky, A., & Zhao, L. P. (1994b). Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89(427), 846–866. http://www.jstor.org/stable/2290910

Rosenbaum, P. R. (1987). Sensitivity analysis for certain permutation inferences in matched observational studies. Biometrika, 74(1), 13–26.

Rosenbaum, P. R., & Rubin, D. B. (1983a). The central role of the propensity score in observational studies for causal effects. Biometrika, 70, 41–55.

Rosenbaum, P. R., & Rubin, D. B. (1983b). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41–55.

Rubin, D. B. (1974a). Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology, 66(5), 688.

Rubin, D. B. (2005). Causal inference using potential outcomes. Journal of the American Statistical Association, 100(469), 322–331. http://dx.doi.org/10.1198/016214504000001880

Rubin, D. B. (2007). The design versus the analysis of observational studies for causal effects: Parallels with the design of randomized trials. Stat Med, 26(1), 20–36.

Rubin, D. B. (1974b). Estimating causal effects of treatments in randomized and non-randomized studies. Journal of Educational Psychology, 66, 688–701.

S. Hernandez-Diaz, M. A. H., E. F. Schisterman. (2006). The birth weight "paradox" uncovered? American Journal of Epidemiology, 164(11), 1115–1120. https://doi.org/10.1093/aje/kwj275

Schomaker, M. (2020). Regression and causality. arXiv:2006.11754. http://arxiv.org/abs/2006.11754

Schuler, M. S., & Rose, S. (2017). Targeted maximum likelihood estimation for causal inference in observational studies. American Journal of Epidemiology, 185(1), 65–73. https://doi.org/10.1093/aje/kww165

Stürmer, T., Rothman, K. J., Avorn, J., & Glynn, R. J. (2010). Treatment effects in the presence of unmeasured confounding: Dealing with observations in the tails of the propensity score distribution-a simulation study. American Journal of Epidemiology, 172(7), 843–854. https://doi.org/10.1093/aje/kwq198

Tan, Z. (2006). A distributional approach for causal inference using propensity scores. Journal of the American Statistical Association, 101(476), 1619–1637.

Tsiatis, A. A., Davidian, M., Kang, J. D. Y. Y., & Schafer, J. L. (2007). Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science, 22(4), 523–539. https://doi.org/10.1214/07-STS227

VanderWeele, T. J., & Arah, O. A. (2011). Bias formulas for sensitivity analysis of unmeasured confounding for general outcomes, treatments, and confounders. Epidemiology, 42–52.

Xiao, Y., Moodie, E. E. M., & Abrahamowicz, M. (2013). Comparison of approaches to weight truncation for marginal structural cox models. Epidemiologic Methods, 2(1), 1–20. https://doi.org/10.1515/em-2012-0006

Zhao, Q., Small, D. S., & Bhattacharya, B. B. (2019). Sensitivity analysis for inverse probability weighting estimators via the percentile bootstrap. Journal of the Royal Statistical Society: Series B, 81(4), 735–761.