References
- Athey, S., and Imbens, G. (2016), “Recursive Partitioning for Heterogeneous Causal Effects,” Proceedings of the National Academy of Sciences of the United States of America, 113, 7353–7360. DOI: https://doi.org/10.1073/pnas.1510489113.
- Breiman, L., Friedman, J. H., Olshen, R. A., and Stone, C. J. (1984), Classification and Regression Trees, New York: Chapman & Hall/CRC.
- Di, Q., Dai, L., Wang, Y., Zanobetti, A., Choirat, C., Schwartz, J. D., and Dominici, F. (2017), “Association of Short-Term Exposure to Air Pollution With Mortality in Older Adults,” JAMA, 318, 2446–2456. DOI: https://doi.org/10.1001/jama.2017.17923.
- Di, Q., Kloog, I., Koutrakis, P., Lyapustin, A., Wang, Y., and Schwartz, J. (2016), “Assessing PM2.5 Exposures With High Spatiotemporal Resolution Across the Continental United States,” Environmental Science & Technology, 50, 4712–4721.
- Di, Q., Wang, Y., Zanobetti, A., Wang, Y., Koutrakis, P., Choirat, C., Dominici, F., and Schwartz, J. D. (2017), “Air Pollution and Mortality in the Medicare Population,” New England Journal of Medicine, 376, 2513–2522. DOI: https://doi.org/10.1056/NEJMoa1702747.
- Dockery, D. W., Pope, C. A., Xu, X., Spengler, J. D., Ware, J. H., Fay, M. E., Ferris, B. G., and Speizer, F. E. (1993), “An Association Between Air Pollution and Mortality in Six U.S. Cities,” New England Journal of Medicine, 329, 1753–1759. DOI: https://doi.org/10.1056/NEJM199312093292401.
- Dominici, F., Peng, R. D., Bell, M. L., Pham, L., McDermott, A., Zeger, S. L., and Samet, J. M. (2006), “Fine Particulate Air Pollution and Hospital Admission for Cardiovascular and Respiratory Diseases,” JAMA, 295, 1127–1134. DOI: https://doi.org/10.1001/jama.295.10.1127.
- Fogarty, C. B., Mikkelsen, M. E., Gaieski, D. F., and Small, D. S. (2016), “Discrete Optimization for Interpretable Study Populations and Randomization Inference in an Observational Study of Severe Sepsis Mortality,” Journal of the American Statistical Association, 111, 447–458. DOI: https://doi.org/10.1080/01621459.2015.1112802.
- 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: https://doi.org/10.1080/01621459.2016.1138865.
- Gastwirth, J. L., Krieger, A. M., and Rosenbaum, P. R. (2000), “Asymptotic Separability in Sensitivity Analysis,” Journal of the Royal Statistical Society, Series B, 62, 545–555. DOI: https://doi.org/10.1111/1467-9868.00249.
- Genz, A., and Bretz, F. (2009), Computation of Multivariate Normal and t Probabilities, Berlin: Springer.
- Hahn, P. R., Murray, J. S., and Carvalho, C. M. (2020), “Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects” (with discussion), Bayesian Analysis, 15, 965–1056. DOI: https://doi.org/10.1214/19-BA1195.
- Hansen, B. B. (2004), “Full Matching in an Observational Study of Coaching for the SAT,” Journal of the American Statistical Association, 99, 609–618. DOI: https://doi.org/10.1198/016214504000000647.
- Hsu, J. Y., Small, D. S., and Rosenbaum, P. R. (2013), “Effect Modification and Design Sensitivity in Observational Studies,” Journal of the American Statistical Association, 108, 135–148. DOI: https://doi.org/10.1080/01621459.2012.742018.
- Lee, K., Small, D. S., and Rosenbaum, P. R. (2018), “A Powerful Approach to the Study of Moderate Effect Modification in Observational Studies,” Biometrics, 74, 1161–1170. DOI: https://doi.org/10.1111/biom.12884.
- Loomis, D., Grosse, Y., Lauby-Secretan, B., Ghissassi, F. E., Bouvard, V., Benbrahim-Tallaa, L., Guha, N., Baan, R., Mattock, H., and Straif, K. (2013), “The Carcinogenicity of Outdoor Air Pollution,” The Lancet Oncology, 14, 1262–1263. DOI: https://doi.org/10.1016/S1470-2045(13)70487-X.
- Makar, M., Antonelli, J., Di, Q., Cutler, D., Schwartz, J., and Dominici, F. (2017), “Estimating the Causal Effect of Low Levels of Fine Particulate Matter on Hospitalization,” Epidemiology, 28, 627–634.
- Neyman, J. (1990), “On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9,” Statistical Science, 5, 465–472.
- Pope, C. A., Lefler, J. S., Ezzati, M., Higbee, J. D., Marshall, J. D., Kim, S.-Y., Bechle, M., Gilliat, K. S., Vernon, S. E., Robinson, A. L., and Burnett, R. T. (2019), “Mortality Risk and Fine Particulate Air Pollution in a Large, Representative Cohort of U.S. Adults,” Environmental Health Perspectives, 127, 077007. DOI: https://doi.org/10.1289/EHP4438.
- Rajagopalan, S., Al-Kindi, S. G., and Brook, R. D. (2018), “Air Pollution and Cardiovascular Disease,” Journal of the American College of Cardiology, 72, 2054–2070. DOI: https://doi.org/10.1016/j.jacc.2018.07.099.
- Rückerl, R., Schneider, A., Breitner, S., Cyrys, J., and Peters, A. (2011), “Health Effects of Particulate Air Pollution: A Review of Epidemiological Evidence,” Inhalation Toxicology, 23, 555–592. DOI: https://doi.org/10.3109/08958378.2011.593587.
- Rosenbaum, P. R. (2002a), “Covariance Adjustment in Randomized Experiments and Observational Studies,” Statistical Science, 17, 286–327. DOI: https://doi.org/10.1214/ss/1042727942.
- Rosenbaum, P. R. (2002b), Observational Studies, New York: Springer.
- Rosenbaum, P. R. (2010), Design of Observational Studies, New York: Springer.
- Rosenbaum, P. R. (2012), “Testing One Hypothesis Twice in Observational Studies,” Biometrika, 99, 763–774.
- Rosenbaum, P. R. (2017), Observation and Experiment, Cambridge, MA: Harvard University Press.
- Rosenbaum, P. R., and Silber, J. H. (2009), “Amplification of Sensitivity Analysis in Matched Observational Studies,” Journal of the American Statistical Association, 104, 1398–1405. DOI: https://doi.org/10.1198/jasa.2009.tm08470.
- Rubin, D. B. (1974), “Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies,” Journal of Educational Psychology, 66, 688–701. DOI: https://doi.org/10.1037/h0037350.
- Samet, J. M., Dominici, F., Curriero, F. C., Coursac, I., and Zeger, S. L. (2000), “Fine Particulate Air Pollution and Mortality in 20 U.S. Cities, 1987–1994,” New England Journal of Medicine, 343, 1742–1749. DOI: https://doi.org/10.1056/NEJM200012143432401.
- Stuart, E. A. (2010), “Matching Methods for Causal Inference: A Review and a Look Forward,” Statistical Science, 25, 1–21. DOI: https://doi.org/10.1214/09-STS313.
- Su, X., Tsai, C.-L., Wang, H., Nickerson, D. M., and Li, B. (2009), “Subgroup Analysis via Recursive Partitioning,” Journal of Machine Learning Research, 10, 141–158.
- Wager, S., and Athey, S. (2018), “Estimation and Inference of Heterogeneous Treatment Effects Using Random Forests,” Journal of the American Statistical Association, 113, 1228–1242. DOI: https://doi.org/10.1080/01621459.2017.1319839.
- Wu, X., Braun, D., Schwartz, J., Kioumourtzoglou, M. A., and Dominici, F. (2020), “Evaluating the Impact of Long-Term Exposure to Fine Particulate Matter on Mortality Among the Elderly,” Science Advances, 6, eaba5692. DOI: https://doi.org/10.1126/sciadv.aba5692.
- Zaykin, D. V., Zhivotovsky, L. A., Westfall, P. H., and Weir, B. S. (2002), “Truncated Product Method for Combining P-Values,” Genetic Epidemiology, 22, 170–185. DOI: https://doi.org/10.1002/gepi.0042.
- Zhang, H., and Singer, B. (2010), Recursive Partitioning and Applications, New York: Springer.