1932

Abstract

When assessing causal effects, determining the target population to which the results are intended to generalize is a critical decision. Randomized and observational studies each have strengths and limitations for estimating causal effects in a target population. Estimates from randomized data may have internal validity but are often not representative of the target population. Observational data may better reflect the target population, and hence be more likely to have external validity, but are subject to potential bias due to unmeasured confounding. While much of the causal inference literature has focused on addressing internal validity bias, both internal and external validity are necessary for unbiased estimates in a target population. This article presents a framework for addressing external validity bias, including a synthesis of approaches for generalizability and transportability, and the assumptions they require, as well as tests for the heterogeneity of treatment effects and differences between study and target populations.

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2023-03-09
2024-04-20
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Literature Cited

  1. Ackerman B, Schmid I, Rudolph KE, Seamans MJ, Susukida R et al. 2019. Implementing statistical methods for generalizing randomized trial findings to a target population. Addict. Behav. 94:124–32
    [Google Scholar]
  2. Allcott H, Mullainathan S. 2012. External validity and partner selection bias NBER Work. Pap. 18373
  3. Angrist JD, Fernández-Val I. 2013. ExtrapoLATE-ing: external validity and overidentification in the LATE framework. Advances in Economics and Econometrics, Vol. 3: Econometrics401–34 Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  4. Athey S, Imbens G. 2016. Recursive partitioning for heterogeneous causal effects. PNAS 113:277353–60
    [Google Scholar]
  5. Attanasio O, Meghir C, Szekely M. 2003. Using randomised experiments and structural models for ‘scaling up’: evidence from the PROGRESA evaluation IFS Work. Pap. EWP04/03, Inst. Fisc. Stud. London:
  6. Bareinboim E, Pearl J. 2014. Transportability from multiple environments with limited experiments: completeness results. Adv. Neural Inf. Process. Syst. 27:280–88
    [Google Scholar]
  7. Bareinboim E, Pearl J. 2016. Causal inference and the data-fusion problem. PNAS 113:277345–52
    [Google Scholar]
  8. Bareinboim E, Tian J. 2015. Recovering causal effects from selection bias. Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence3475–81 Palo Alto, CA: AAAI Press
    [Google Scholar]
  9. Bareinboim E, Tian J, Pearl J. 2014. Recovering from selection bias in causal and statistical inference. Proceedings of the Twenty-Eighth AAAI Conference on Artificial Intelligence2410–16 Palo Alto, CA: AAAI Press
    [Google Scholar]
  10. Begg CB. 1992. Cross design synthesis: a new strategy for medical effectiveness research. Rep. GAO/PEMD-92-18 US Gen. Account. Off. Washington, DC:
  11. Bell SH, Olsen RB, Orr LL, Stuart EA. 2016. Estimates of external validity bias when impact evaluations select sites nonrandomly. Educ. Eval. Policy Anal. 38:2318–35
    [Google Scholar]
  12. Benchimol EI, Smeeth L, Guttmann A, Harron K, Moher D et al. 2015. The REporting of studies Conducted using Observational Routinely-collected health Data (RECORD) statement. PLOS Med. 12:10e1001885
    [Google Scholar]
  13. Bennett M, Vielma JP, Zubizarreta JR. 2020. Building representative matched samples with multi-valued treatments in large observational studies. J. Comput. Graph. Stat. 29:4744–57
    [Google Scholar]
  14. Buchanan AL, Hudgens MG, Cole SR, Mollan KR, Sax PE et al. 2018. Generalizing evidence from randomized trials using inverse probability of sampling weights. J. R. Stat. Soc. Ser. A 181:41193–209
    [Google Scholar]
  15. Cahan A, Cahan S, Cimino JJ. 2017. Computer-aided assessment of the generalizability of clinical trial results. Int. J. Med. Inf. 99:60–66
    [Google Scholar]
  16. Chan W. 2017. Partially identified treatment effects for generalizability. J. Res. Educ. Eff. 10:3646–69
    [Google Scholar]
  17. Chen IY, Pierson E, Rose S, Joshi S, Ferryman K, Ghassemi M 2021. Ethical machine learning in healthcare. Annu. Rev. Biomed. Data Sci. 4:123–44
    [Google Scholar]
  18. Chen S, Tian L, Cai T, Yu M. 2017. A general statistical framework for subgroup identification and comparative treatment scoring. Biometrics 73:41199–209
    [Google Scholar]
  19. Chipman HA, George EI, McCulloch R 2007. Bayesian ensemble learning. Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference B Schölkopf, J Platt, T Hofmann 265–72 Cambridge, MA: MIT Press
    [Google Scholar]
  20. Chipman HA, George EI, McCulloch RE. 2010. BART: Bayesian additive regression trees. Ann. Appl. Stat. 4:1266–98
    [Google Scholar]
  21. Cole SR, Stuart EA. 2010. Generalizing evidence from randomized clinical trials to target populations: the ACTG 320 trial. Am. J. Epidemiol. 172:1107–15
    [Google Scholar]
  22. Colnet B, Mayer I, Chen G, Dieng A, Li R et al. 2021. Causal inference methods for combining randomized trials and observational studies: a review. arXiv:2011.08047 [stat.ME]
  23. Correa JD, Tian J, Bareinboim E. 2018. Generalized adjustment under confounding and selection biases. Thirty-Second AAAI Conference on Artificial Intelligence6335–42 Palo Alto, CA: AAAI Press
    [Google Scholar]
  24. Cronbach LJ, Shapiro K. 1982. Designing Evaluations of Educational and Social Programs Jossey-Bass Ser. Soc. Behav. Sci. High. Educ. San Francisco: Jossey-Bass. , 1st ed..
  25. Crump RK, Hotz VJ, Imbens GW, Mitnik OA. 2008. Nonparametric tests for treatment effect heterogeneity. Rev. Econ. Stat. 90:3389–405
    [Google Scholar]
  26. Dahabreh IJ, Hernan MA, Robertson SE, Buchanan A, Steingrimsson JA. 2019a. Generalizing trial findings using nested trial designs with sub-sampling of non-randomized individuals. arXiv:1902.06080 [stat.ME]
  27. Dahabreh IJ, Robertson SE, Petito LC, Hernán MA, Steingrimsson JA. 2022. Efficient and robust methods for causally interpretable meta-analysis: transporting inferences from multiple randomized trials to a target population. Biometrics In press. https://doi.org/10.1111/biom.13716
    [Crossref] [Google Scholar]
  28. Dahabreh IJ, Robertson SE, Steingrimsson JA, Stuart EA, Hernán MA. 2020. Extending inferences from a randomized trial to a new target population. Stat. Med. 39:141999–2014
    [Google Scholar]
  29. Dahabreh IJ, Robertson SE, Stuart E, Hernan M. 2017. Extending inferences from randomized participants to all eligible individuals using trials nested within cohort studies. arXiv:1709.04589 [stat.ME]
  30. Dahabreh IJ, Robertson SE, Tchetgen EJ, Stuart EA, Hernán MA. 2019b. Generalizing causal inferences from individuals in randomized trials to all trial-eligible individuals. Biometrics 75:2685–94
    [Google Scholar]
  31. Dahabreh IJ, Robins JM, Haneuse SJPA, Saeed I, Robertson SE et al. 2019c. Sensitivity analysis using bias functions for studies extending inferences from a randomized trial to a target population. arXiv:1905.10684 [stat.ME]
  32. Degtiar I, Layton T, Wallace J, Rose S 2021. Conditional cross-design synthesis estimators for generalizability in Medicaid. arXiv:2109.13288 [stat.ME]
  33. Ding P, Feller A, Miratrix L. 2016. Randomization inference for treatment effect variation. J. R. Stat. Soc. Ser. B 78:3655–71
    [Google Scholar]
  34. Dong N, Stuart EA, Lenis D, Quynh Nguyen T 2020. Using propensity score analysis of survey data to estimate population average treatment effects: a case study comparing different methods. Eval. Rev. 44:184–108
    [Google Scholar]
  35. Eddy DM. 1989. The confidence profile method: a Bayesian method for assessing health technologies. Oper. Res. 37:2210–28
    [Google Scholar]
  36. Fang A. 2017. 10 things to know about heterogeneous treatment effects. EGAP, Institute of Governmental Studies https://egap.org/resource/10-things-to-know-about-heterogeneous-treatment-effects/
    [Google Scholar]
  37. Flores CA, Mitnik OA. 2013. Comparing treatments across labor markets: an assessment of nonexperimental multiple-treatment strategies. Rev. Econ. Stat. 95:51691–707
    [Google Scholar]
  38. Ford I, Norrie J 2016. Pragmatic trials. New Engl. J. Med. 375:5454–63
    [Google Scholar]
  39. Frangakis C. 2009. The calibration of treatment effects from clinical trials to target populations. Clin. Trials 6:2136–40
    [Google Scholar]
  40. Gabler NB, Duan N, Liao D, Elmore JG, Ganiats TG, Kravitz RL. 2009. Dealing with heterogeneity of treatment effects: Is the literature up to the challenge?. Trials 10:143
    [Google Scholar]
  41. Gail M, Simon R. 1985. Testing for qualitative interactions between treatment effects and patient subsets. Biometrics 41:2361–72
    [Google Scholar]
  42. Gechter M. 2015. Generalizing the results from social experiments: theory and evidence from Mexico and India Work. Pap., Dep. Econ., Boston Univ. Boston, MA: https://www.bu.edu/econ/files/2015/05/Gechter_Generalizing_Social_Experiments.pdf
  43. Gelman A, Little TC. 1997. Poststratification into many categories using hierarchical logistic regression. Surv. Methodol.23127–35
    [Google Scholar]
  44. Glauner P, Migliosi A, Meira J, Valtchev P, State R, Bettinger F. 2017. Is big data sufficient for a reliable detection of non-technical losses?. 2017 19th International Conference on Intelligent System Application to Power Systems (ISAP)1–6 New York: IEEE
    [Google Scholar]
  45. Green DP, Kern HL. 2012. Modeling heterogeneous treatment effects in survey experiments with Bayesian additive regression trees. Public Opin. Q. 76:3491–511
    [Google Scholar]
  46. Greenhouse JB, Kaizar EE, Anderson HD, Bridge JA, Libby AM et al. 2017. Combining information from multiple data sources: an introduction to cross-design synthesis with a case study. Methods in Comparative Effectiveness Research C Gatsonis, SC Morton 223–46 London: Chapman & Hall/CRC
    [Google Scholar]
  47. Greenhouse JB, Kaizar EE, Kelleher K, Seltman H, Gardner W. 2008. Generalizing from clinical trial data: a case study. The risk of suicidality among pediatric antidepressant users. Stat. Med. 27:111801–13
    [Google Scholar]
  48. Greenland S. 2005. Multiple-bias modelling for analysis of observational data. J. R. Stat. Soc. Ser. A 168:267–91
    [Google Scholar]
  49. Gunter L, Zhu J, Murphy S 2011. Variable selection for qualitative interactions. Stat. Methodol. 8:142–55
    [Google Scholar]
  50. Haneuse S, Schildcrout J, Crane P, Sonnen J, Breitner J, Larson E. 2009. Adjustment for selection bias in observational studies with application to the analysis of autopsy data. Neuroepidemiology 32:3229–39
    [Google Scholar]
  51. Hartman E, Grieve R, Ramsahai R, Sekhon JS. 2015. From sample average treatment effect to population average treatment effect on the treated: combining experimental with observational studies to estimate population treatment effects. J. R. Stat. Soc. Ser. A 178:3757–78
    [Google Scholar]
  52. Heckman JJ. 1979. Sample selection bias as a specification error. Econometrica 47:1153–61
    [Google Scholar]
  53. Hernán MA, Alonso A, Logan R, Grodstein F, Michels KB et al. 2008. Observational studies analyzed like randomized experiments: an application to postmenopausal hormone therapy and coronary heart disease. Epidemiology 19:6766–79
    [Google Scholar]
  54. Hill JL. 2011. Bayesian nonparametric modeling for causal inference. J. Comput. Graph. Stat. 20:1217–40
    [Google Scholar]
  55. Horvitz DG, Thompson DJ. 1952. A generalization of sampling without replacement from a finite universe. J. Am. Stat. Assoc. 47:260663–85
    [Google Scholar]
  56. Hotz VJ, Imbens GW, Mortimer JH. 2005. Predicting the efficacy of future training programs using past experiences at other locations. J. Econom. 125:1241–70
    [Google Scholar]
  57. Imai K, King G, Stuart EA. 2008. Misunderstandings between experimentalists and observationalists about causal inference. J. R. Stat. Soc. Ser. A 171:2481–502
    [Google Scholar]
  58. Johansson FD, Kallus N, Shalit U, Sontag D. 2018. Learning weighted representations for generalization across designs. arXiv:1802.08598 [stat.ME]
  59. Josey KP, Yang F, Ghosh D, Raghavan S. 2021. A calibration approach to transportability with observational data. arXiv:2008.06615 [stat.ME]
  60. Kaizar EE. 2011. Estimating treatment effect via simple cross design synthesis. Stat. Med. 30:252986–3009
    [Google Scholar]
  61. Kaizar EE. 2015. Incorporating both randomized and observational data into a single analysis. Annu. Rev. Stat. Appl. 2:49–72
    [Google Scholar]
  62. Kallus N, Puli AM, Shalit U. 2018. Removing hidden confounding by experimental grounding. arXiv:1810.11646 [stat.ME]
  63. Keiding N, Louis TA. 2016. Perils and potentials of self-selected entry to epidemiological studies and surveys. J. R. Stat. Soc. Ser. A 179:2319–76
    [Google Scholar]
  64. Keiding N, Louis TA. 2018. Web-based enrollment and other types of self-selection in surveys and studies: consequences for generalizability. Annu. Rev. Stat. Appl. 5:25–47
    [Google Scholar]
  65. Kern HL, Stuart EA, Hill J, Green DP. 2016. Assessing methods for generalizing experimental impact estimates to target populations. J. Res. Educ. Eff. 9:1103–27
    [Google Scholar]
  66. Kim JK, Park S, Chen Y, Wu C. 2018. Combining non-probability and probability survey samples through mass imputation. arXiv:1812.10694 [stat.ME]
  67. Lesko CR, Buchanan AL, Westreich D, Edwards JK, Hudgens MG, Cole SR. 2017. Generalizing study results: a potential outcomes perspective. Epidemiology 28:4553–61
    [Google Scholar]
  68. Lu Y, Scharfstein DO, Brooks MM, Quach K, Kennedy EH. 2019. Causal inference for comprehensive cohort studies. arXiv:1910.03531 [stat.ME]
  69. Luedtke A, Carone M, van der Laan MJ. 2019. An omnibus non-parametric test of equality in distribution for unknown functions. J. R. Stat. Soc. Ser. B 81:175–99
    [Google Scholar]
  70. Lunceford JK, Davidian M. 2004. Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study. Stat. Med. 23:192937–60
    [Google Scholar]
  71. Marcus S. 1997. Assessing non-consent bias with parallel randomized and nonrandomized clinical trials. J. Clin. Epidemiol. 50:7823–28
    [Google Scholar]
  72. Miettinen OS. 1972. Standardization of risk ratios. Am. J. Epidemiol. 96:6383–88
    [Google Scholar]
  73. Nguyen TQ, Ebnesajjad C, Cole SR, Stuart EA. 2017. Sensitivity analysis for an unobserved moderator in RCT-to-target-population generalization of treatment effects. Ann. Appl. Stat. 11:1225–47
    [Google Scholar]
  74. Nie L, Zhang Z, Rubin D, Chu J 2013. Likelihood reweighting methods to reduce potential bias in noninferiority trials which rely on historical data to make inference. Ann. Appl. Stat. 7:31796–813
    [Google Scholar]
  75. Olsen RB, Orr LL, Bell SH, Stuart EA. 2013. External validity in policy evaluations that choose sites purposively: external validity in policy evaluations. J. Policy Anal. Manag. 32:1107–21
    [Google Scholar]
  76. O'Muircheartaigh C, Hedges LV. 2014. Generalizing from unrepresentative experiments: a stratified propensity score approach. J. R. Stat. Soc. Ser. C 63:2195–210
    [Google Scholar]
  77. Pan Q, Schaubel DE. 2009. Evaluating bias correction in weighted proportional hazards regression. Lifetime Data Anal. 15:1120–46
    [Google Scholar]
  78. Pearl J. 2000. Causality: Models, Reasoning, and Inference Cambridge, UK: Cambridge Univ. Press
  79. Pearl J. 2015. Generalizing experimental findings. J. Causal Inference 3:2259–66
    [Google Scholar]
  80. Pearl J, Bareinboim E 2011. Transportability of causal and statistical relations: a formal approach. 2011 IEEE 11th International Conference on Data Mining Workshops M Spiliopoulou, H Wang, D Cook, J Pei, W Wang et al.540–47 New York: IEEE
    [Google Scholar]
  81. Pearl J, Bareinboim E. 2014. External validity: from do-calculus to transportability across populations. Stat. Sci. 29:4579–95
    [Google Scholar]
  82. Phillippo DM, Ades AE, Dias S, Palmer S, Abrams KR, Welton NJ. 2018. Methods for population-adjusted indirect comparisons in health technology appraisal. Med. Decis. Mak. 38:2200–11
    [Google Scholar]
  83. Pool I, Abelson R, Popkin S. 1964. Candidates, Issues, and Strategies: A Computer Simulation of the 1960 Presidential Election Cambridge, MA: MIT Press
  84. Prentice RL, Langer R, Stefanick ML, Howard BV, Pettinger M et al. 2005. Combined postmenopausal hormone therapy and cardiovascular disease: toward resolving the discrepancy between observational studies and the Women's Health Initiative clinical trial. Am. J. Epidemiol. 162:5404–14
    [Google Scholar]
  85. Prevost TC, Abrams KR, Jones DR. 2000. Hierarchical models in generalized synthesis of evidence: an example based on studies of breast cancer screening. Stat. Med. 19:243359–76
    [Google Scholar]
  86. Qian M, Chakraborty B, Maiti R. 2019. A sequential significance test for treatment by covariate interactions. arXiv:1901.08738 [stat.ME]
  87. Raudenbush SW, Schwartz D. 2020. Randomized experiments in education, with implications for multilevel causal inference. Annu. Rev. Stat. Appl. 7:177–208
    [Google Scholar]
  88. Rothwell PM. 2005. External validity of randomised controlled trials: “To whom do the results of this trial apply?. Lancet 365:945382–93
    [Google Scholar]
  89. Rubin DB. 1974. Estimating causal effects of treatments in randomized and nonrandomized studies. J. Educ. Psychol. 66:5688–701
    [Google Scholar]
  90. Rudolph K, van der Laan M. 2017. Robust estimation of encouragement design intervention effects transported across sites. J. R. Stat. Soc. Ser. B 79:51509–25
    [Google Scholar]
  91. Schmid I, Rudolph KE, Nguyen TQ, Hong H, Seamans MJ et al. 2020. Comparing the performance of statistical methods that generalize effect estimates from randomized controlled trials to much larger target populations. Commun. Stat. Simul. Comput. https://doi.org/10.1080/03610918.2020.1741621
    [Crossref] [Google Scholar]
  92. Schulz KF, Altman DG, Moher D. 2010. CONSORT 2010 statement: updated guidelines for reporting parallel group randomised trials. BMJ 340:c332
    [Google Scholar]
  93. Schwartz D, Lellouch J. 1967. Explanatory and pragmatic attitudes in therapeutical trials. J. Chronic Dis. 20:8637–48
    [Google Scholar]
  94. Shadish WR, Cook TD, Campbell DT. 2001. Experimental and Quasi-Experimental Designs for Generalized Causal Inference Boston: Houghton Mifflin
  95. Signorovitch JE, Wu EQ, Yu AP, Gerrits CM, Kantor E et al. 2010. Comparative effectiveness without head-to-head trials: a method for matching-adjusted indirect comparisons applied to psoriasis treatment with adalimumab or etanercept. PharmacoEconomics 28:10935–45
    [Google Scholar]
  96. Simon R. 1982. Patient subsets and variation in therapeutic efficacy. Br. J. Clin. Pharmacol. 14:4473–82
    [Google Scholar]
  97. Stuart EA. 2010. Matching methods for causal inference: a review and a look forward. Stat. Sci. 25:11–21
    [Google Scholar]
  98. Stuart EA, Ackerman B, Westreich D. 2018. Generalizability of randomized trial results to target populations: design and analysis possibilities. Res. Soc. Work Pract. 28:5532–37
    [Google Scholar]
  99. Stuart EA, Bradshaw CP, Leaf PJ. 2015. Assessing the generalizability of randomized trial results to target populations. Prev. Sci. 16:3475–85
    [Google Scholar]
  100. Stuart EA, Cole SR, Bradshaw CP, Leaf PJ. 2011. The use of propensity scores to assess the generalizability of results from randomized trials: use of propensity scores to assess generalizability. J. R. Stat. Soc. Ser. A 174:2369–86
    [Google Scholar]
  101. Su X, Tsai CL, Wang H, Nickerson DM, Li B. 2009. Subgroup analysis via recursive partitioning. SSRN Electron. J. 10:141–58
    [Google Scholar]
  102. Su X, Zhou T, Yan X, Fan J, Yang S 2008. Interaction trees with censored survival data. Int. J. Biostatist. 4:1 https://doi.org/10.2202/1557-4679.1071
    [Crossref] [Google Scholar]
  103. Tian L, Alizadeh AA, Gentles AJ, Tibshirani R. 2014. A simple method for estimating interactions between a treatment and a large number of covariates. J. Am. Stat. Assoc. 109:5081517–32
    [Google Scholar]
  104. Tipton E. 2013a. Improving generalizations from experiments using propensity score subclassification: assumptions, properties, and contexts. J. Educ. Behav. Stat. 38:3239–66
    [Google Scholar]
  105. Tipton E. 2013b. Stratified sampling using cluster analysis: a sample selection strategy for improved generalizations from experiments. Eval. Rev. 37:2109–39
    [Google Scholar]
  106. Tipton E. 2014. How generalizable is your experiment? An index for comparing experimental samples and populations. J. Educ. Behav. Stat. 39:6478–501
    [Google Scholar]
  107. Tipton E, Hallberg K, Hedges LV, Chan W 2017. Implications of small samples for generalization: adjustments and rules of thumb. Eval. Rev. 41:5472–505
    [Google Scholar]
  108. Tipton E, Olsen RB. 2018. A review of statistical methods for generalizing from evaluations of educational interventions. Educ. Res. 47:8516–24
    [Google Scholar]
  109. Tipton E, Peck LR. 2017. A design-based approach to improve external validity in welfare policy evaluations. Eval. Rev. 41:4326–56
    [Google Scholar]
  110. Turner RM, Spiegelhalter DJ, Smith GCS, Thompson SG. 2009. Bias modelling in evidence synthesis. J. R. Stat. Soc. Ser. A 172:121–47
    [Google Scholar]
  111. Varadhan R, Henderson NC, Weiss CO. 2016. Cross-design synthesis for extending the applicability of trial evidence when treatment effect is heterogeneous: Part I. Methodology. Commun. Stat. Case Stud. Data Anal. Appl. 2:3–4112–26
    [Google Scholar]
  112. Verde PE, Ohmann C. 2015. Combining randomized and non-randomized evidence in clinical research: a review of methods and applications. Res. Synth. Methods 6:145–62
    [Google Scholar]
  113. Verde PE, Ohmann C, Morbach S, Icks A. 2016. Bayesian evidence synthesis for exploring generalizability of treatment effects: a case study of combining randomized and non-randomized results in diabetes. Stat. Med. 35:101654–75
    [Google Scholar]
  114. von Elm E, Altman DG, Egger M, Pocock SJ, Gøtzsche PC, Vandenbroucke JP. 2008. The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement: guidelines for reporting observational studies. J. Clin. Epidemiol. 61:4344–49
    [Google Scholar]
  115. Weisberg HI, Hayden VC, Pontes VP. 2009. Selection criteria and generalizability within the counterfactual framework: explaining the paradox of antidepressant-induced suicidality?. Clin. Trials 6:2109–18
    [Google Scholar]
  116. Weiss CO, Segal JB, Varadhan R. 2012. Assessing the applicability of trial evidence to a target sample in the presence of heterogeneity of treatment effect. Pharmacoepidemiol. Drug Saf. 21:121–29
    [Google Scholar]
  117. Weng C, Li Y, Ryan P, Zhang Y, Liu F et al. 2014. A distribution-based method for assessing the differences between clinical trial target populations and patient populations in electronic health records. Appl. Clin. Inform. 5:2463–79
    [Google Scholar]
  118. Westreich D, Edwards JK, Lesko CR, Stuart E, Cole SR. 2017. Transportability of trial results using inverse odds of sampling weights. Am. J. Epidemiol. 186:81010–14
    [Google Scholar]
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