A Generalized Bootstrap Procedure of the Standard Error and Confidence Interval Estimation for Inverse Probability of Treatment Weighting

References

• Altonji, J. G., Elder, T. E., & Taber, C. R. (2005). Selection on observed and unobserved variables: Assessing the effectiveness of Catholic schools. Journal of Political Economy, 113(1), 151–184. https://doi.org/10.1086/426036
   Web of Science ®Google Scholar
• Austin, P. C. (2011). An introduction to propensity score methods for reducing the effects of confounding in observational studies. Multivariate Behavioral Research, 46(3), 399–424. https://doi.org/10.1080/00273171.2011.568786
   PubMed Web of Science ®Google Scholar
• Austin, P. C., & Small, D. S. (2014). The use of bootstrapping when using propensity-score matching without replacement: A simulation study. Statistics in Medicine, 33(24), 4306–4319. https://doi.org/10.1002/sim.6276
   PubMed Web of Science ®Google Scholar
• Austin, P. C. (2016). Variance estimation when using inverse probability of treatment weighting (IPTW) with survival analysis. Statistics in Medicine, 35(30), 5642–5655. https://doi.org/10.1002/sim.7084
   PubMed Web of Science ®Google Scholar
• Austin, P. C., & Stuart, E. A. (2015). Moving towards best practice when using inverse probability of treatment weighting (IPTW) using the propensity score to estimate causal treatment effects in observational studies. Statistics in Medicine, 34(28), 3661–3679. https://doi.org/10.1002/sim.6607
   PubMed Web of Science ®Google Scholar
• Bodory, H., Camponovo, L., Huber, M., & Lechner, M. (2020). The finite sample performance of inference methods for propensity score matching and weighting estimators. Journal of Business & Economic Statistics, 38(1), 183–200. https://doi.org/10.1080/07350015.2018.1476247
   Web of Science ®Google Scholar
• Brown, B. W., & Newey, W. K. (2002). Generalized method of moments, efficient bootstrapping, and improved inference. Journal of Business & Economic Statistics, 20(4), 507–517. https://doi.org/10.1198/073500102288618649
   Web of Science ®Google Scholar
• Chambers, R. L., & Dunstan, R. (1986). Estimating distribution functions from survey data. Biometrika, 73(3), 597–604. https://doi.org/10.1093/biomet/73.3.597
   Web of Science ®Google Scholar
• Donald, S. G., & Hsu, Y. C. (2014). Estimation and inference for distribution functions and quantile functions in treatment effect models. Journal of Econometrics, 178, 383–397. https://doi.org/10.1016/j.jeconom.2013.03.010
   Web of Science ®Google Scholar
• Frank, K. A., Maroulis, S. J., Duong, M. Q., & Kelcey, B. M. (2013). What would it take to change an inference? Using Rubin’s causal model to interpret the robustness of causal inferences. Educational Evaluation and Policy Analysis, 35(4), 437–460. https://doi.org/10.3102/0162373713493129
   Web of Science ®Google Scholar
• Freedman, D. A., & Berk, R. A. (2008). Weighting regressions by propensity scores. Evaluation Review, 32(4), 392–409. https://doi.org/10.1177/0193841X08317586
   PubMed Web of Science ®Google Scholar
• Harder, V. S., Stuart, E. A., & Anthony, J. C. (2010). Propensity score techniques and the assessment of measured covariate balance to test causal associations in psychological research. Psychological Methods, 15(3), 234–249. https://doi.org/10.1037/a0019623
   PubMed Web of Science ®Google Scholar
• Hernán, M. Á., Brumback, B., & Robins, J. M. (2000). Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology (Cambridge, Mass.), 11(5), 561–570. https://doi.org/10.1097/00001648-200009000-00012
   PubMed Web of Science ®Google Scholar
• Hernán, M. A., & Robins, J. M. (2006). Estimating causal effects from epidemiological data. Journal of Epidemiology & Community Health, 60(7), 578–586.
   PubMed Web of Science ®Google Scholar
• Hirano, K., & Imbens, G. W. (2001). Estimation of causal effects using propensity score weighting: An application to data on right heart catheterization. Health Services and Outcomes Research Methodology, 2(3/4), 259–278. https://doi.org/10.1023/A:1020371312283
   Google Scholar
• Hirano, K., Imbens, G. W., & Ridder, G. (2003). Efficient estimation of average treatment effects using the estimated propensity score. Econometrica, 71(4), 1161–1189. https://doi.org/10.1111/1468-0262.00442
   Web of Science ®Google Scholar
• Imai, K., & Ratkovic, M. (2014). Covariate balancing propensity score. Journal of the Royal Statistical Society Series B: Statistical Methodology, 76(1), 243–263. https://doi.org/10.1111/rssb.12027
   Web of Science ®Google Scholar
• Imbens, G. W. (2004). Nonparametric estimation of average treatment effects under exogeneity: A review. Review of Economics and Statistics, 86(1), 4–29. https://doi.org/10.1162/003465304323023651
   Web of Science ®Google Scholar
• Imbens, G. W. (2010). An economist’s perspective on Shadish (2010) and West and Thoemmes (2010). Psychological Methods, 15(1), 47–55. https://doi.org/10.1037/a0018538
   PubMed Web of Science ®Google Scholar
• Imbens, G. W., & Rubin, D. B. (2015). Causal inference for statistics, social, and biomedical sciences: An introduction. Cambridge University Press.
   Google Scholar
• Kang, J. D., & 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.
   Web of Science ®Google Scholar
• Kuk, A. Y. C. (1988). Estimation of distribution functions and medians under sampling with unequal probabilities. Biometrika, 75(1), 97–103. https://doi.org/10.1093/biomet/75.1.97
   Web of Science ®Google Scholar
• Lee, B. K., Lessler, J., & Stuart, E. A. (2011). Weight trimming and propensity score weighting. PloS One, 6(3), e18174. https://doi.org/10.1371/journal.pone.0018174
   PubMed Web of Science ®Google Scholar
• Li, T. (2018). The Bayesian Paradigm of Robustness Indices of Causal Inferences [Unpublished doctoral dissertation]. Michigan State University, East Lansing.
   Google Scholar
• Li, T., & Frank, K. (2022). The probability of a robust inference for internal validity. Sociological Methods & Research, 51(4), 1947–1968. https://doi.org/10.1177/0049124120914922
   Web of Science ®Google Scholar
• Murnane, R. J., & Willett, J. B. (2010). Methods matter: Improving causal inference in educational and social science research. Oxford University Press.
   Google Scholar
• Owen, A. B. (2001). Empirical likelihood. Chapman and Hall/CRC.
   Google Scholar
• Rao, J. N. K., Kovar, J. G., & Mantel, H. J. (1990). On estimating distribution functions and quantiles from survey data using auxiliary information. Biometrika, 77(2), 365–375. https://doi.org/10.1093/biomet/77.2.365
   Web of Science ®Google Scholar
• Robins, J. M., Hernan, M. A., & Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology (Cambridge, Mass.), 11(5), 550–560. https://doi.org/10.1097/00001648-200009000-00011
   PubMed Web of Science ®Google Scholar
• Rosenbaum, P. R. (2002). Observational Studies. Springer.
   Google Scholar
• Rosenbaum, P. R. (2010). Design of Observational Studies. Springer.
   Google Scholar
• Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41–55. https://doi.org/10.1093/biomet/70.1.41
   Web of Science ®Google Scholar
• Rubin, D. B. (2008). For objective causal inference, design trumps analysis. Annals of Applied Statistics, 2(3), 808–840.
   Web of Science ®Google Scholar
• Schafer, J. L., & Kang, J. (2008). Average causal effects from nonrandomized studies: A practical guide and simulated example. Psychological Methods, 13(4), 279–313. https://doi.org/10.1037/a0014268
   PubMed Web of Science ®Google Scholar
• Stuart, E. A., & Rubin, D. B. (2011). Best practices in quasi–experimental designs: Matching methods for causal inference. In Best practices in quantitative methods (pp. 155–176). SAGE Publications.
   Google Scholar
• Stürmer, T., Webster-Clark, M., Lund, J. L., Wyss, R., Ellis, A. R., Lunt, M., Rothman, K. J., & Glynn, R. J. (2021). Propensity score weighting and trimming strategies for reducing variance and bias of treatment effect estimates: A simulation study. American Journal of Epidemiology, 190(8), 1659–1670. https://doi.org/10.1093/aje/kwab041
   PubMed Web of Science ®Google Scholar
• Thompson, S. K. (2012). Sampling. Wiley.
   Google Scholar
• Williamson, E. J., Forbes, A., & White, I. R. (2014). Variance reduction in randomised trials by inverse probability weighting using the propensity score. Statistics in Medicine, 33(5), 721–737. https://doi.org/10.1002/sim.5991
   PubMed Web of Science ®Google Scholar
• Wooldridge, J. M. (1999). Asymptotic properties of weighted M-estimators for variable probability samples. Econometrica, 67(6), 1385–1406. https://doi.org/10.1111/1468-0262.00083
   Web of Science ®Google Scholar
• Wooldridge, J. M. (2002a). Inverse probability weighted M-estimators for sample selection, attrition and stratification. Portuguese Economic Journal, 1(2), 117–139. https://doi.org/10.1007/s10258-002-0008-x
   Google Scholar
• Wooldridge, J. M. (2002b). Econometric Analysis of Cross Section and Panel Data. MIT Press.
   Google Scholar
• Wooldridge, J. M. (2007). Inverse probability weighted estimation for general missing data problems. Journal of Econometrics, 141(2), 1281–1301. https://doi.org/10.1016/j.jeconom.2007.02.002
   Web of Science ®Google Scholar
• Xu, S., Ross, C., Raebel, M. A., Shetterly, S., Blanchette, C., & Smith, D. (2010). Use of stabilized inverse propensity scores as weights to directly estimate relative risk and its confidence intervals. Value in Health : The Journal of the International Society for Pharmacoeconomics and Outcomes Research, 13(2), 273–277. https://doi.org/10.1111/j.1524-4733.2009.00671.x
   PubMed Web of Science ®Google Scholar
• Zhou, T., Tong, G., Li, F., Thomas, L. E., Li, F. (2020). PSweight: An R package for propensity score weighting analysis. arXiv [stat.ME]. http://arxiv.org/abs/2010.08893
   Google Scholar