Rosenbaum PR. Modern algorithms for matching in observational studies. Annual Review of Statistics and Its Application. 2020 Mar 7;7(1):143-76. https://doi.org/10.1146/annurev-statistics-031219-041058
One might try the aamatch package in R while reading this article, focusing on either of the following functions, artlessV2 or alittleArt. This package creates matched samples using modern methods, without great effort on the part of the user. It can create matched pairs, or 1-to-K matched sets with multiple controls.
Or cut and paste the link:
https://www.annualreviews.org/content/journals/10.1146/annurev-statistics-031219-041058
Rosenbaum PR. Sensitivity analysis for M-estimates, tests, and confidence intervals in matched observational studies. Biometrics. 2007 Jun;63(2):456-64. https://doi.org/10.1111/j.1541-0420.2006.00717.x Also in JSTOR: www.jstor.org/stable/4541357
This article is not a bad place to start learning about sensitivity analysis in observational studies, for several reasons.
First, this article discusses the method that is illustrated in the shiny app on this web page under the tab "Do a Sensitivity Analysis"; so, you can try the method as you read with just point-and-click effort. Second, both the article and the shiny app develop sensitivity analyses for tests, point estimates and confidence intervals. Third, the mean is an M-estimate, so you can compare the mean to other M-estimates, and thereby start to learn about relationship between the choice of test statistic and the design sensitivity -- there are better choices than the mean, as you will find using the shiny app. Fourth, the method works when matching with multiple controls, and multiple controls also affect the design sensitivity. Fifth, having understood this method, you will be ready to learn also about weighted M-statistics that further increase design sensitivity. Sixth, there is a reasonable implementation of the method in the senm and senmCI functions of the sensitivitymult package in R. Or see the R packages sensitivitymv, sensitivitymw, senstrat, and weightedRank for other related methods.
For more information: About points three and four above, see my Biometrics 2013;69(1): 118-127, and about the fifth point see my Journal of the American Statistical Association 2014;109(507):1145-58. There is more information in the bibliography for the shiny app obtained by clicking its bibliography button. There is also discussion of the R packages in the freely available article in Observational Studies 2015;1(2):1-7 at https://muse.jhu.edu/article/793399/pdf.
Or cut and past the link:
https://academic.oup.com/biometrics/article/63/2/456/7325210#422074393
Silber JH, Rosenbaum PR, Reiter JG, Jain S, Hill AS, Hashemi S, Brown S, Olfson M, Ing C. Exposure to operative anesthesia in childhood and subsequent neurobehavioral diagnoses: A natural experiment using appendectomy. Anesthesiology. 2024 Sep 1;141(3):489-499. doi:10.1097/ALN.0000000000005075
This study exemplifies several aspects of natural experiments and quasi-experiments in a large observational block design. My book Causal Inference (MIT Press, 2023) provides a general, informal discussion of quasi-experiments in Chapter 6 and of natural experiments in Chapter 7. Alternatively, see Chapters 6 and 8 of my Observation and Experiment (Harvard University Press, 2017).
Or cut and paste the link:
https://pmc.ncbi.nlm.nih.gov/articles/PMC11361557/
Silber JH, Rosenbaum PR, Clark AS, Giantonio BJ, Ross RN, Teng Y, Wang M, Niknam BA, Ludwig JM, Wang W, Even-Shoshan O. Characteristics associated with differences in survival among black and white women with breast cancer. Journal of the American Medical Association (JAMA). 2013 Jul 24;310(4). http://doi.org/10.1001/jama.2013.8272
This article exemplifies some of the similarities and differences between disparities research and observational studies. In particular, it exemplifies the use of the exterior match that Silber and I developed in relation to disparities research. (Rosenbaum PR, Silber JH. Using the exterior match to compare two entwined matched control groups. The American Statistician. 2013 May 1;67(2):67-75. https://doi.org/10.1080/00031305.2013.769914) Available in JSTOR: www.jstor.org/stable/24591435
Or cut and paste the link:
https://jamanetwork.com/journals/jama/fullarticle/1719739