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Stronger instruments via integer programming in an observational study of late preterm birth outcomes. (English) Zbl 1454.62431
Summary: In an optimal nonbipartite match, a single population is divided into matched pairs to minimize a total distance within matched pairs. Nonbipartite matching has been used to strengthen instrumental variables in observational studies of treatment effects, essentially by forming pairs that are similar in terms of covariates but very different in the strength of encouragement to accept the treatment. Optimal nonbipartite matching is typically done using network optimization techniques that can be quick, running in polynomial time, but these techniques limit the tools available for matching. Instead, we use integer programming techniques, thereby obtaining a wealth of new tools not previously available for nonbipartite matching, including fine and near-fine balance for several nominal variables, forced near balance on means and optimal subsetting. We illustrate the methods in our on-going study of outcomes of late-preterm births in California, that is, births of 34 to 36 weeks of gestation. Would lengthening the time in the hospital for such births reduce the frequency of rapid readmissions? A straightforward comparison of babies who stay for a shorter or longer time would be severely biased, because the principal reason for a long stay is some serious health problem. We need an instrument, something inconsequential and haphazard that encourages a shorter or a longer stay in the hospital. It turns out that babies born at certain times of day tend to stay overnight once with a shorter length of stay, whereas babies born at other times of day tend to stay overnight twice with a longer length of stay, and there is nothing particularly special about a baby who is born at 11:00 pm. Therefore, we use hour-of-birth as an instrument for a longer hospital stay. Using integer programming, we form 80,600 pairs of two babies who are similar in terms of observed covariates but very different in anticipated lengths of stay based on their hours of birth. We ask whether encouragement to stay an extra day reduces readmissions within two days of discharge. A sensitivity analysis addresses the possibility that the instrument is not valid as an instrument, that is, not random but rather biased by an unmeasured covariate associated with the hour of birth. Bias can give the impression of a treatment effect when there is no effect, but it can also mask an actual effect, leaving the impression of no effect, and both possibilities are examined in analyses for effects and for near equivalence.

62P10 Applications of statistics to biology and medical sciences; meta analysis
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[1] Abadie, A. and Imbens, G. W. (2006). Large sample properties of matching estimators for average treatment effects. Econometrica 74 235-267. · Zbl 1112.62042 · doi:10.1111/j.1468-0262.2006.00655.x
[2] Abadie, A. and Imbens, G. W. (2008). On the failure of the bootstrap for matching estimators. Econometrica 76 1537-1557. · Zbl 1153.91752 · doi:10.3982/ECTA6474
[3] Almond, D. and Doyle, J. J. (2008). After midnight: A regression discontinuity design in length of postpartum hospital stays. NBER Working Paper 13877. Available at . · www.nber.org
[4] Angrist, J. D., Imbens, G. W. and Rubin, D. B. (1996). Identification of causal effects using instrumental variables (with discussion). J. Amer. Statist. Assoc. 91 444-455. · Zbl 0897.62130 · doi:10.2307/2291629
[5] Baiocchi, M., Small, D. S., Lorch, S. and Rosenbaum, P. R. (2010). Building a stronger instrument in an observational study of perinatal care for premature infants. J. Amer. Statist. Assoc. 105 1285-1296. · Zbl 1388.62311 · doi:10.1198/jasa.2010.ap09490
[6] Bauer, P. and Kieser, M. (1996). A unifying approach for confidence intervals and testing of equivalence and difference. Biometrika 83 934-937. · Zbl 0883.62033 · doi:10.1093/biomet/83.4.934 · www3.oup.co.uk
[7] Bertsekas, D. P. (1981). A new algorithm for the assignment problem. Math. Program. 21 152-171. · Zbl 0461.90069 · doi:10.1007/BF01584237
[8] Bound, J., Jaeger, D. A. and Baker, R. M. (1995). Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. J. Amer. Statist. Assoc. 90 443-450.
[9] Cornfield, J., Haenszel, W., Hammond, E. C., Lilienfeld, A. M., Shimkin, M. B. and Wynder, E. L. (1959). Smoking and lung cancer: Recent evidence and a discussion of some questions. J. Natl. Cancer Inst. 22 173-203.
[10] Corrada Bravo, H. (2005). Package Rcplex. Available at . · cran.r-project.org
[11] Derigs, U. (1988). Solving nonbipartite matching problems via shortest path techniques. Ann. Oper. Res. 13 225-261. · doi:10.1007/BF02288324
[12] Diprete, T. A. and Gangl, M. (2004). Assessing bias in the estimation of causal effects. Sociol. Method. 34 271-310.
[13] Edmonds, J. (1965). Maximum matching and a polyhedron with \(0,1\)-vertices. J. Res. Nat. Bur. Standards Sect. B 69B 125-130. · Zbl 0141.21802
[14] Egleston, B. L., Scharfstein, D. O. and MacKenzie, E. (2009). On estimation of the survivor average causal effect in observational studies when important confounders are missing due to death. Biometrics 65 497-504. · Zbl 1167.62083 · doi:10.1111/j.1541-0420.2008.01111.x
[15] Fisher, R. A. (1935). Design of Experiments . Oliver and Boyd, Edinburgh. · Zbl 0011.03205
[16] Gadbury, G. L. (2001). Randomization inference and bias of standard errors. Amer. Statist. 55 310-313. · doi:10.1198/000313001753272268
[17] Gastwirth, J. L. (1992). Methods for assessing the sensitivity of statistical comparisons used in Title VII cases to omitted variables. Jurimetrics 33 19-34.
[18] Gastwirth, J. L., Krieger, A. M. and Rosenbaum, P. R. (1998). Dual and simultaneous sensitivity analysis for matched pairs. Biometrika 85 907-920. · Zbl 0921.62053 · doi:10.1093/biomet/85.4.907 · www3.oup.co.uk
[19] Goyal, N. K., Fager, C. and Lorch, S. A. (2011). Adherence to discharge guidelines for late-preterm newborns. Pediatrics 128 62-71.
[20] Hansen, B. B. (2007). Optmatch. R News 7 18-24. R package optmatch.
[21] Holland, P. W. H. (1988). Causal inference, path analysis, and recursive structural equations models. Sociol. Method. 18 449-484.
[22] Hosman, C. A., Hansen, B. B. and Holland, P. W. (2010). The sensitivity of linear regression coefficients’ confidence limits to the omission of a confounder. Ann. Appl. Stat. 4 849-870. · Zbl 1194.62089 · doi:10.1214/09-AOAS315
[23] Imbens, G. W. (2003). Sensitivity to exogeneity assumptions in program evaluation. Am. Econ. Rev. 93 126-132.
[24] Korte, B. and Vygen, J. (2008). Combinatorial Optimization : Theory and Algorithms , 4th ed. Algorithms and Combinatorics 21 . Springer, Berlin. · Zbl 1149.90126
[25] Langenskiold, S. and Rubin, D. B. (2008). Outcome-free design of observational studies. Annals of Economics and Statistics 91/92 107-125.
[26] Lu, B. (2005). Propensity score matching with time-dependent covariates. Biometrics 61 721-728. · Zbl 1079.62114 · doi:10.1111/j.1541-0420.2005.00356.x
[27] Lu, B., Greevy, R., Xu, X. and Beck, C. (2011). Optimal nonbipartite matching and its statistical applications. Amer. Statist. 65 21-30. · Zbl 05886130 · doi:10.1198/tast.2011.08294
[28] Malkin, J. D., Broder, M. S. and Keeler, E. (2000). Do longer postpartum stays reduce newborn readmissions? Analysis using instrumental variables. Health Serv. Res. 35 1071-1091.
[29] Marcus, S. M. (1997). Using omitted variable bias to assess uncertainty in the estimation of an AIDS education treatment effect. J. Ed. Behav. Statist. 22 193-201.
[30] McCandless, L. C., Gustafson, P. and Levy, A. (2007). Bayesian sensitivity analysis for unmeasured confounding in observational studies. Stat. Med. 26 2331-2347. · doi:10.1002/sim.2711
[31] Neyman, J. (1923). On the application of probability theory to agricultural experiments. Essay on principles. Section 9. Ann. Agric. Sci. 10 1-51 (in Polish). [Reprinted in English with discussion by T. Speed and D. B. Rubin in Statist. Sci. 5 (1990) 463-480. MR1092986]
[32] Politis, D. N. and Romano, J. P. (1994). Large sample confidence regions based on subsamples under minimal assumptions. Ann. Statist. 22 2031-2050. · Zbl 0828.62044 · doi:10.1214/aos/1176325770
[33] Reiter, J. (2000). Using statistics to determine causal relationships. Amer. Math. Monthly 107 24-32. · Zbl 1001.00005 · doi:10.2307/2589374
[34] Rosenbaum, P. R. (1989). Optimal matching in observational studies. J. Amer. Statist. Assoc. 84 1024-1032.
[35] Rosenbaum, P. R. (2002a). Observational Studies , 2nd ed. Springer, New York. · Zbl 0985.62091
[36] Rosenbaum, P. R. (2002b). Attributing effects to treatment in matched observational studies. J. Amer. Statist. Assoc. 97 183-192. · Zbl 1073.62586 · doi:10.1198/016214502753479329
[37] Rosenbaum, P. R. (2010). Design of Observational Studies . Springer, New York. · Zbl 1308.62005
[38] Rosenbaum, P. R. (2012). Optimal matching of an optimally chosen subset in observational studies. J. Comput. Graph. Statist. 21 57-71. · doi:10.1198/jcgs.2011.09219
[39] Rosenbaum, P. R., Ross, R. N. and Silber, J. H. (2007). Minimum distance matched sampling with fine balance in an observational study of treatment for ovarian cancer. J. Amer. Statist. Assoc. 102 75-83. · Zbl 1284.62670 · doi:10.1198/016214506000001059
[40] Rosenbaum, P. R. and Rubin, D. B. (1983). Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. J. R. Stat. Soc. Ser. B Stat. Methodol. 45 212-218.
[41] Rosenbaum, P. R. and Silber, J. H. (2009a). Sensitivity analysis for equivalence and difference in an observational study of neonatal intensive care units. J. Amer. Statist. Assoc. 104 501-511. · Zbl 1388.62333 · doi:10.1198/jasa.2009.0016
[42] Rosenbaum, P. R. and Silber, J. H. (2009b). Amplification of sensitivity analysis in matched observational studies. J. Amer. Statist. Assoc. 104 1398-1405. · Zbl 1205.62180 · doi:10.1198/jasa.2009.tm08470
[43] Rubin, D. B. (1974). Estimating causal effects of treatments in randomized and nonrandomized studies. J. Educ. Psych. 66 688-701.
[44] Rubin, D. B. (1980). Bias reduction using Mahalanobis metric matching. Biometrics 36 293-298. · Zbl 0463.62015 · doi:10.2307/2529981
[45] Schrijver, A. (1986). Theory of Linear and Integer Programming . Wiley, Chichester. · Zbl 0665.90063
[46] Silber, J. H., Lorch, S. L., Rosenbaum, P. R., Medoff-Cooper, B., Bakewell-Sachs, S., Millman, A., Mi, L., Even-Shoshan, O. and Escobar, G. E. (2009). Additional maturity at discharge and subsequent health care costs. Health Serv. Res. 44 444-463.
[47] Small, D. S. and Rosenbaum, P. R. (2008). War and wages: The strength of instrumental variables and their sensitivity to unobserved biases. J. Amer. Statist. Assoc. 103 924-933. · Zbl 1205.62221 · doi:10.1198/016214507000001247
[48] Stuart, E. A. (2010). Matching methods for causal inference: A review and a look forward. Statist. Sci. 25 1-21. · Zbl 1328.62007 · doi:10.1214/09-STS313
[49] Wang, L. and Krieger, A. M. (2006). Causal conclusions are most sensitive to unobserved binary covariates. Stat. Med. 25 2257-2271. · doi:10.1002/sim.2344
[50] Welch, B. L. (1937). On the \(z\)-test in randomized blocks and Latin squares. Biometrika 29 21-52. · Zbl 0017.12602 · doi:10.1093/biomet/29.1-2.21
[51] Wolsey, L. A. (1998). Integer Programming . Wiley, New York. · Zbl 0930.90072
[52] Yanagawa, T. (1984). Case-control studies: Assessing the effect of a confounding factor. Biometrika 71 191-194. · Zbl 0532.62087 · doi:10.1093/biomet/71.1.191
[53] Yang, D., Small, D. S., Silber, J. H. and Rosenbaum, P. R. (2012). Optimal matching with minimal deviation from fine balance in a study of obesity and surgical outcomes. Biometrics 68 628-636. · Zbl 1274.62910 · doi:10.1111/j.1541-0420.2011.01691.x
[54] Yu, B. B. and Gastwirth, J. L. (2005). Sensitivity analysis for trend tests: Application to the risk of radiation exposure. Biostatistics 6 201-209. · Zbl 1071.62112 · doi:10.1093/biostatistics/kxi003
[55] Zubizarreta, J. R., Reinke, C. E., Kelz, R. R., Silber, J. H. and Rosenbaum, P. R. (2011). Matching for several sparse nominal variables in a case-control study of readmission following surgery. Amer. Statist. 65 229-238. · doi:10.1198/tas.2011.11072
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