Home Extending balance assessment for the generalized propensity score under multiple imputation
Article
Licensed
Unlicensed Requires Authentication

Extending balance assessment for the generalized propensity score under multiple imputation

  • Anna-Simone J. Frank ORCID logo EMAIL logo , David S. Matteson , Hiroko K. Solvang , Angela Lupattelli ORCID logo and Hedvig Nordeng ORCID logo
Published/Copyright: May 15, 2020
Become an author with De Gruyter Brill

Abstract

This manuscript extends the definition of the Absolute Standardized Mean Difference (ASMD) for binary exposure (M = 2) to cases for M > 2 on multiple imputed data sets. The Maximal Maximized Standardized Difference (MMSD) and the Maximal Averaged Standardized Difference (MASD) were proposed. For different percentages, missing data were introduced in covariates in the simulated data based on the missing at random (MAR) assumption. We then investigate the performance of these two metric definitions using simulated data of full and imputed data sets. The performance of the MASD and the MMSD were validated by relating the balance metrics to estimation bias. The results show that there is an association between the balance metrics and bias. The proposed balance diagnostics seem therefore appropriate to assess balance for the generalized propensity score (GPS) under multiple imputation.


Corresponding author: Anna-Simone J. Frank, Computational Biology Unit, Department of Informatics, Faculty of Mathematics and Natural Sciences, University of Bergen, Bergen, Norway, E-mail:

Award Identifier / Grant number: DMS-1455172

Funding source: New York State Division of Science, Technology and Innovation (NYSTAR)

Funding source: Cornell University Atkinson’s Center for a Sustainable Future (AVF-2017)

Funding source: Xerox PARC Faculty Research Award

Funding source: Cornell University Institute of Biotechnology

Funding source: UiO:Life Science internationalization support

Award Identifier / Grant number: DrugsInPregnancy grant no. 639377

  1. Research funding: This research was funded by United States Agency for International Development, National Science Foundation (DMS-1455172), New York State Division of Science, Technology and Innovation (NYSTAR), Cornell University Atkinson's Center for a Sustainable Future (AVF-2017), Norwegian Women's Public Health Association, Xerox PARC Faculty Research Award, Cornell University Institute of Biotechnology, UiO:Life Science internationalization support, H2020 European Research Council (DrugsInPregnancy grant no. 639377).

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: Authors state no conflict of interest.

  4. Informed consent: Informed consent was obtained from all individuals included in this study.

References

Alexander, E. K., E. N. Pearce, G. A. Brent, R. S. Brown, H. Chen, C. Dosiou, W. A. Grobman, P. Laurberg, J. H. Lazarus, S. J. Mandel, and R. P. Peeters. 2017. “2017 Guidelines of the American Thyroid Association for the Diagnosis and Management of Thyroid Disease during Pregnancy and the Postpartum.” Thyroid 27: 315–89, https://doi.org/10.1089/thy.2016.0457.Search in Google Scholar PubMed

Austin, P. C. 2011. “An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies.” Multivariate Behavioral Research, 46: 399–424, https://doi.org/10.1080/00273171.2011.568786.Search in Google Scholar PubMed PubMed Central

Austin, P. C. 2019. “Assessing Covariate Balance When Using the Generalized Propensity Score with Quantitative or Continuous Exposures.” Statistical Methods in Medical Research, 25 (5): 1365–77, https://doi.org/10.1177/0962280218756159.Search in Google Scholar PubMed PubMed Central

Austin, P. C., and E. A. Stuart. 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: 3661–79, https://doi.org/10.1002/sim.6607.Search in Google Scholar PubMed PubMed Central

Azur, M. J., E. A. Stuart, C. Frangakis, and P. J. Leaf. 2011. “Multiple Imputation by Chained Equations: What is it and How Does it Work?” International Journal of Methods in Psychiatric Research 20: 40–9, https://doi.org/10.1002/mpr.329.Search in Google Scholar PubMed PubMed Central

Bandoli, G., G. M. Kuo, R. Sugathan, C. D. Chambers, M. Rolland, and K. Palmsten. 2018. “Longitudinal trajectories of Antidepressant Use in Pregnancy and the Postnatal Period.” Archives of Women's Mental Health 21: 411–19, https://doi.org/10.1007/s00737-018-0809-2.Search in Google Scholar PubMed PubMed Central

Blehar, M. C., C. Spong, C. Grady, S. F. Goldkind, L. Sahin, and J. A. Clayton. 2013. “Enrolling Pregnant Women: Issues in Clinical Research.” Women's Health Issues 23: e39–45, https://doi.org/10.1016/j.whi.2012.10.003.Search in Google Scholar PubMed PubMed Central

Bray, B. C., J. J. Dziak, M. E. Patrick, and S. T. Lanza. 2019. “Inverse Propensity Score Weighting With a Latent Class Exposure: Estimating the Causal Effect of Reported Reasons for Alcohol Use on Problem Alcohol Use 16 Years Later.” Prevention Science 20 (3): 394–406, https://doi.org/10.1007/s11121-018-0883-8.Search in Google Scholar PubMed PubMed Central

Burgette, L., B. A. Griffin, and D. McCaffrey. 2017. “Propensity Scores for Multiple Treatments: A Tutorial for the Mnps Function in the Twang Package.” R package. Santa Monica: Rand Corporation, (Accessed July 2018).10.7249/TL136.2Search in Google Scholar

Chen, S. H. and E. H. Ip. 2015. “Behaviour of the Gibbs Sampler When Conditional Distributions are Potentially Incompatible.” Journal of Statistical Computation and Simulation 85: 3266–75, https://doi.org/10.1080/00949655.2014.968159.Search in Google Scholar PubMed PubMed Central

De Vries, B. B. L. P., M. Van Smeden, and R. H. Groenwold. 2018. “Propensity Score Estimation Using Classification and Regression Trees in the Presence of Missing Covariate Data.” Epidemiologic Methods, 7 (1), 20170020, https://doi.org/10.1515/em-2017-0020.Search in Google Scholar

Doidge, J. C. 2018. “Responsiveness-Informed Multiple Imputation and Inverse Probability-Weighting in Cohort Studies with Missing Data that are Non-Monotone or not Missing at Random.” Statistical Methods in Medical Research 27: 352–63, https://doi.org/10.1177/0962280216628902.Search in Google Scholar PubMed

Dong, Y., and C. Y. J. Peng. 2013. “Principled Missing Data Methods for Researchers.” SpringerPlus 2: 222, https://doi.org/10.1186/2193-1801-2-222.Search in Google Scholar PubMed PubMed Central

Eulenburg, C., A. Suling, P. Neuser, A. Reuss, U. Canzler, T. Fehm, A. Luyten, M. Hellriegel, L. Woelber, and S. Mahner. 2016. “Propensity Scoring After Multiple Imputation in a Retrospective Study on Adjuvant Radiation Therapy in Lymph-Node Positive Vulvar Cancer.” PloS One 11: e0165705, https://doi.org/10.1371/journal.pone.0165705.Search in Google Scholar PubMed PubMed Central

Feng, P., X. H. Zhou, Q. M. Zou, M. Y. Fan, and X. S. Li. 2012. “Generalized Propensity Score for Estimating the Average Treatment Effect of Multiple Treatments.” Statistics in Medicine 31: 681–97, https://doi.org/10.1002/sim.4168.Search in Google Scholar PubMed

Fong, C., C. Hazlett, and K. Imai. 2018. “Covariate Balancing Propensity Score for a Continuous Treatment: Application to the Efficacy of Political Advertisements.” The Annals of Applied Statistics 12: 156–77, https://doi.org/10.1214/17-aoas1101.Search in Google Scholar

Frank, A. S., A. Lupattelli, D. S. Matteson, and H. Nordeng. 2018. “Maternal Use of Thyroid Hormone Replacement Therapy Before, During, and After Pregnancy: Agreement Between Self-Report and Prescription Records and Group-Based Trajectory Modeling of Prescription Patterns.” Clinical Epidemiology 10: 1801–16, https://doi.org/10.2147/clep.s175616.Search in Google Scholar

Frank, A. S., A. Lupattelli, D. S. Matteson, H. M. Meltzer, and H. Nordeng. 2019. “Thyroid Hormone Replacement Therapy Patterns in Pregnant Women and Perinatal Outcomes in the Offspring.” Pharmacoepidemiology and Drug Safety 29 (1): 111–21, https://doi.org/10.1002/pds.4927.Search in Google Scholar

Frank, A. S. J., 2019. “Thyroid Hormone Replacement Therapy During Pregnancy–Quantifying Medication Patterns and Associated Outcomes in the Offspring”. In Series of dissertations submitted to the Faculty of Mathematics and Natural Sciences, No. 2161. Oslo: University of Oslo, pp. 1–251, URL http://urn.nb.no/URN:NBN:no-73653.Search in Google Scholar

Franklin, J. M., W. H. Shrank, J. Pakes, G. Sanfélix-Gimeno, O. S. Matlin, T. A. Brennan, and N. K. Choudhry. 2013. “Group-Based Trajectory Models: A New Approach to Classifying and Predicting Long-Term Medication Adherence.” Medical Care 51: 789–96, https://doi.org/10.1097/mlr.0000000000000002.Search in Google Scholar

Franklin, J. M., J. A. Rassen, D. Ackermann, D. B. Bartels, and S. Schneeweiss. 2014. “Metrics for Covariate Balance in Cohort Studies of Causal Effects.” Statistics in Medicine 33: 1685–99, https://doi.org/10.1002/sim.6058.Search in Google Scholar PubMed

Gasparini, A. and M. Lang. 2018. “rsimsum: Summarise Results from Monte Carlo Simulation Studies.” Journal of Open Source Software 3: 739, https://doi.org/10.21105/joss.00739.Search in Google Scholar

Graham, J. W., A. E. Olchowski, and T. D. Gilreath. 2007. “How Many Imputations are Really Needed? Some Practical Clarifications of Multiple Imputation Theory.” Prevention Science 8: 206–13, https://doi.org/10.1007/s11121-007-0070-9.Search in Google Scholar PubMed

Hayes, J. R. and J. I. Groner. 2008. “Using Multiple Imputation and Propensity Scores to Test the Effect of Car Seats and Seat Belt Usage on Injury Severity from Trauma Registry Data.” Journal of Pediatric Surgery 43: 924–7, https://doi.org/10.1016/j.jpedsurg.2007.12.043.Search in Google Scholar PubMed PubMed Central

Hernán, M. A., A. Alonso, R. Logan, F. Grodstein, K. B. Michels, M. J. Stampfer, W. C. Willett, J. E. Manson, and J. M. Robins. 2008. “Observational Studies Analyzed Like Randomized Experiments: An Application to Postmenopausal Hormone Therapy and Coronary Heart Disease.” Epidemiology. Cambridge, Mass 19: 766–79, https://doi.org/10.1097/EDE.0b013e3181875e61.Search in Google Scholar PubMed PubMed Central

Hill, J. 2004. “ Reducing Bias in Treatment Effect Estimation in Observational Studies Suffering from Missing Data.” Report no.04-01. US: Columbia University, January 2004.Search in Google Scholar

Hsu, C. H., and M. Yu. 2019. “Cox Regression Analysis with Missing Covariates via Nonparametric Multiple Imputation.” Statistical Methods in Medical Research, 28 (6): 1676–88, https://doi.org/10.1177/0962280218772592.Search in Google Scholar PubMed PubMed Central

Imai, K., and M. Ratkovic. 2015. “Robust Estimation of Inverse Probability Weights for Marginal Structural Models.” Journal of the American Statistical Association 110: 1013–23, https://doi.org/10.1080/01621459.2014.956872.Search in Google Scholar

Imai, K., and D. A. Van Dyk. 2004. “Causal Inference with General Treatment Regimes: Generalizing the Propensity Score.” Journal of the American Statistical Association 99: 854–66, https://doi.org/10.1198/016214504000001187.Search in Google Scholar

Imbens, G. W. 2000. “The Role of the Propensity Score in Estimating Dose-Response Functions.” Biometrika 87: 706–10, https://doi.org/10.1093/biomet/87.3.706.Search in Google Scholar

Jackson, J. W. 2016. “Diagnostics for Confounding of Time-Varying and Other Joint Exposures.” Epidemiology. Cambridge, Mass 27: 859, https://doi.org/10.1097/ede.0000000000000547.Search in Google Scholar PubMed PubMed Central

Jiang, M., and E. M. Foster. 2013. “Duration of Breastfeeding and Childhood Obesity: A Generalized Propensity Score Approach.” Health Services Research 48: 628–51, https://doi.org/10.1111/j.1475-6773.2012.01456.x.Search in Google Scholar PubMed PubMed Central

Karahalios, A., L. Baglietto, J. B. Carlin, D. R. English, and J. A. Simpson. 2012. “A Review of the Reporting and Handling of Missing Data in Cohort Studies with Repeated Assessment of Exposure Measures.” BMC Medical Research Methodology 12: 96, https://doi.org/10.1186/1471-2288-12-96.Search in Google Scholar PubMed PubMed Central

Kupzyk, K. A., and S. J. Beal. 2017. “Advanced Issues in Propensity Scores: Longitudinal and Missing Data.” The Journal of Early Adolescence 37: 59–84, https://doi.org/10.1177/0272431616636229.Search in Google Scholar

Kurth, T., A. M. Walker, R. J. Glynn, K. A. Chan, J. M. Gaziano, K. Berger, and J. M. Robins. 2005. “Results of Multivariable Logistic Regression, Propensity Matching, Propensity Adjustment, and Propensity-Based Weighting Under Conditions of Nonuniform Effect.” American Journal Of Epidemiology 163: 262–70, https://doi.org/10.1093/aje/kwj047.Search in Google Scholar PubMed

Lavori, P. W., R. Dawson, and D. Shera. 1995. “A Multiple Imputation Strategy for Clinical Trials with Truncation of Patient Data.” Statistics in Medicine 14: 1913–25, https://doi.org/10.1002/sim.4780141707.Search in Google Scholar PubMed

Lechner, M. 2001. “Identification and Estimation of Causal Effects of Multiple Treatments Under the Conditional Independence Assumption.” In Econometric Evaluation of Labour Market Policies, 43–58. Berlin: Springer.10.1007/978-3-642-57615-7_3Search in Google Scholar

Lee, J. H., and J. HuberJr. 2011. “Multiple Imputation with Large Proportions of Missing Data: How Much is too Much?” In United Kingdom Stata Users' Group Meetings 2011, No. 23, Stata Users Group.Search in Google Scholar

Leyrat, C., S. R. Seaman, I. R. White, I. Douglas, L. Smeeth, J. Kim, M. Resche-Rigon, J. R. Carpenter, and E. J. Williamson. 2019. “Propensity Score Analysis with Partially Observed Covariates: How Should Multiple Imputation be Used?” Statistical Methods in Medical Research 28: 3–19, https://doi.org/10.1177/0962280217713032.Search in Google Scholar PubMed PubMed Central

Li, F., and F. Li. 2019. “Propensity Score Weighting for Causal Inference with Multiple Treatments.” The Annals of Applied Statistics 13: 2389–415, https://doi.org/10.1214/19-aoas1282.Search in Google Scholar

Lumley, T. 2015. Mitools: Tools for Multiple Imputation of Missing Data. https://cran.r-project.org/web/packages/mitools/mitools.pdf (accessed July 2018).Search in Google Scholar

Lumley, T. 2018. Survey: Analysis of Complex Survey Samples. http://r-survey.r-forge.r-project.org/survey (accessed July 2018).Search in Google Scholar

Lupattelli, A., M. Wood, K. Lapane, O. Spigset, and H. Nordeng. 2017. “Risk of Preeclampsia After Gestational Exposure to Selective Serotonin Reuptake Inhibitors and Other Antidepressants: A Study from the Norwegian Mother and Child Cohort Study.” Pharmacoepidemiology and Drug Safety 26: 1266–76, https://doi.org/10.1002/pds.4286.Search in Google Scholar PubMed PubMed Central

Malla, L., R. Perera-Salazar, E. McFadden, M. Ogero, K. Stepniewska, and M. English. 2018. “Handling Missing Data in Propensity Score Estimation in Comparative Effectiveness Evaluations: A Systematic Review.” Journal of Comparative Effectiveness Research 7: 271–9, https://doi.org/10.2217/cer-2017-0071.Search in Google Scholar PubMed PubMed Central

Marston, L., J. R. Carpenter, K. R. Walters, R. W. Morris, I. Nazareth, and I. Petersen. 2010. “Issues in Multiple Imputation of Missing Data for Large General Practice Clinical Databases.” Pharmacoepidemiology and Drug Safety 19: 618–26, https://doi.org/10.1002/pds.1934.Search in Google Scholar PubMed

McCaffrey, D. F., B. A. Griffin, D. Almirall, M. E. Slaughter, R. Ramchand, and L. F. Burgette. 2013. “A Tutorial on Propensity Score Estimation for Multiple Treatments Using Generalized Boosted Models.” Statistics in Medicine, 32, 3388–414, https://doi.org/10.1002/sim.5753.Search in Google Scholar PubMed PubMed Central

McCaffrey, D. F., G. Ridgeway, and A. R. Morral. 2004. “Propensity Score Estimation with Boosted Regression for Evaluating Causal Effects in Observational Studies.” Psychological Methods 9: 403–25, https://doi.org/10.1037/1082-989x.9.4.403.Search in Google Scholar

Menard, S. 2002. Applied Logistic Regression Analysis, Vol. 106, New York: Sage.10.4135/9781412983433Search in Google Scholar

Miri, H. H., J. Hassanzadeh, A. Rajaeefard, M. Mirmohammadkhani, and K. A. Angali. 2016. “Multiple Imputation to Correct for Nonresponse Bias: Application in Non-Communicable Disease Risk Factors Survey.” Global Journal Health Science 8: 133–58, https://doi.org/10.5539/gjhs.v8n1p133.Search in Google Scholar PubMed PubMed Central

Mitra, R., and J. P. Reiter. 2016. “A Comparison of Two Methods of Estimating Propensity Scores After Multiple Imputation.” Statistical Methods in Medical Research 25: 188–204, https://doi.org/10.1177/0962280212445945.Search in Google Scholar PubMed

Moleti, M., M. Di Mauro, G. Sturniolo, M. Russo, and F. Vermiglio. 2019. “Hyperthyroidism in the Pregnant Woman: Maternal and Fetal Aspects.” Journal of Clinical & Translational Endocrinology 16: 100190.10.1016/j.jcte.2019.100190Search in Google Scholar PubMed PubMed Central

Morris, T. P., I. R. White, and M. J. Crowther. 2019. “Using Simulation Studies to Evaluate Statistical Methods.” Statistics in Medicine 38: 2074–102, https://doi.org/10.1002/sim.8086.Search in Google Scholar PubMed PubMed Central

Murray, J. S. 2018. “Multiple Imputation: A Review of Practical and Theoretical Findings.” Statistical Science 33: 142–59, https://doi.org/10.1214/18-sts644.Search in Google Scholar

Nezvalová-Henriksen, K., O. Spigset, R. E. Brandlistuen, E. Ystrom, G. Koren, and H. Nordeng. 2016. “Effect of Prenatal Selective Serotonin Reuptake Inhibitor. Ssri) Exposure on Birthweight and Gestational Age: A Sibling-Controlled Cohort Study.” International Journal of Epidemiology 45: 2018–29, https://doi.org/10.1093/ije/dyw049.Search in Google Scholar PubMed PubMed Central

Nguyen, T. L., G. S. Collins, J. Spence, J. P. Daurès, P. Devereaux, P. Landais, and Y. Le Manach. 2017. “Double-Adjustment in Propensity Score Matching Analysis: Choosing a Threshold for Considering Residual Imbalance.” BMC Medical Research Methodology 17: 78, https://doi.org/10.1186/s12874-017-0338-0.Search in Google Scholar PubMed PubMed Central

Nian, H., C. Yu, J. Ding, H. Wu, W. D. Dupont, S. Brunwasser, T. Gebretsadik, T. V. Hartert, and P. Wu. 2019. “Performance Evaluation of Propensity Score Methods for Estimating Average Treatment Effects with Multi-Level Treatments.” Journal of Applied Statistics 46: 853–73, https://doi.org/10.1080/02664763.2018.1523375.Search in Google Scholar PubMed PubMed Central

Nordeng, H., M. M. Van Gelder, O. Spigset, G. Koren, A. Einarson, and M. Eberhard-Gran. 2012. “Pregnancy Outcome after Exposure to Antidepressants and the Role of Maternal Depression: Results from the Norwegian Mother and Child Cohort Study.” Journal of Clinical Psychopharmacology 32: 186–94, https://doi.org/10.1097/jcp.0b013e3182490eaf.Search in Google Scholar

Pandis, N. 2014. “Bias in Observational Studies.” American Journal of Orthodontics and Dentofacial Orthopedics 145: 542–3, https://doi.org/10.1016/j.ajodo.2014.01.008.Search in Google Scholar PubMed

Qu, Y., and I. Lipkovich. 2009. “Propensity Score Estimation with Missing Values Using a Multiple Imputation Missingness Pattern. (MIMP) Approach.” Statistics in Medicine 28: 1402–14, https://doi.org/10.1002/sim.3549.Search in Google Scholar PubMed

Ridgeway, G., D. McCaffrey, A. Morral, L. Burgette, and B. A. Griffin. 2017. twang: Toolkit for Weighting and Analysis of Nonequivalent Groups. https://cran.r-project.org/web/packages/twang/twang.pdf (accessed July 2018).Search in Google Scholar

Rosenbaum, P. R., and D. B. Rubin. 1984. “Reducing Bias in Observational Studies Using Subclassification on the Propensity Score.” Journal of the American Statistical Association 79: 516–24, https://doi.org/10.1080/01621459.1984.10478078.Search in Google Scholar

Rubin, D. B. 1997. “Estimating Causal Effects from Large Data Sets Using Propensity Scores.” American Journal of Epidemiology 127: 757–63, https://doi.org/10.7326/0003-4819-127-8_part_2-199710151-00064.Search in Google Scholar PubMed

Rubin, D. B. 2004. “On Principles for Modeling Propensity Scores in Medical Research.” Pharmacoepidemiology and Drug Safety 13: 855–7, https://doi.org/10.1002/pds.968.Search in Google Scholar PubMed

Spreeuwenberg, M. D., A. Bartak, M. A. Croon, J. A. Hagenaars, J. J. Busschbach, H. Andrea, J. Twisk, and T. Stijnen. 2010. “The Multiple Propensity Score as Control for Bias in the Comparison of More Than Two Treatment Arms: An Introduction from a Case Study in Mental Health.” Medical Care 48: 166–74, https://doi.org/10.1097/mlr.0b013e3181c1328f.Search in Google Scholar

Stuart, E. A., B. K. Lee, and F. P. Leacy. 2013. “Prognostic Score–Based Balance Measures can be a Useful Diagnostic for Propensity Score Methods in Comparative Effectiveness Research.” Journal of Clinical Epidemiology 66: S84–S90.e1, https://doi.org/10.1016/j.jclinepi.2013.01.013.Search in Google Scholar PubMed PubMed Central

Sugihara, M. 2010. “Survival analysis using inverse probability of treatment weighted methods based on the generalized propensity score.” Pharmaceutical Statistics: The Journal of Applied Statistics in the Pharmaceutical Industry 9: 21–34, https://doi.org/10.1002/pst.365.Search in Google Scholar PubMed

Van Buuren, S., and K. Groothuis-Oudshoorn. 2011. “mice: Multivariate Imputation by Chained Equations in r.” Journal of Statistical Software 1–68. Also available at: https://www.jstatsoft.org/v45/i03/ (accessed July 20, 2018).10.18637/jss.v045.i03Search in Google Scholar

Webb-Vargas, Y., K. E. Rudolph, D. Lenis, P. Murakami, and E. A. Stuart. 2017. “An Imputation-Based Solution to Using Mismeasured Covariates in Propensity Score Analysis.” Statistical Methods in Medical Research 26: 1824–37, https://doi.org/10.1177/0962280215588771.Search in Google Scholar PubMed PubMed Central

Xu, S., C. Ross, M. A. Raebel, S. Shetterly, C. Blanchette, and D. Smith. 2010. “Use of Stabilized Inverse Propensity Scores as Weights to Directly Estimate Relative Risk and its Confidence Intervals.” Value in Health 13: 273–7, https://doi.org/10.1111/j.1524-4733.2009.00671.x.Search in Google Scholar PubMed PubMed Central

Yang, S., G. W. Imbens, Z. Cui, D. E. Faries, and Z. Kadziola. 2016. “Propensity Score Matching and Subclassification in Observational Studies with Multi-Level Treatments.” Biometrics 72: 1055–65, https://doi.org/10.1111/biom.12505.Search in Google Scholar PubMed

Yoshida, K., D. H. Solomon, S. Haneuse, S. C. Kim, E. Patorno, S. K. Tedeschi, H. Lyu, J. M. Franklin, T. Stürmer, S. Hernández-Díaz, and R. J. Glynn. 2018. “Multinomial Extension of Propensity Score Trimming Methods: A Simulation study.” American Journal of Epidemiology 188: 609–16, https://doi.org/10.1093/aje/kwy263.Search in Google Scholar PubMed PubMed Central

Zhu, Y., D. L. Coffman, and D. Ghosh. 2015. “A Boosting Algorithm for Estimating Generalized Propensity Scores with Continuous Treatments.” Journal of Causal Inference 3: 25–40, https://doi.org/10.1515/jci-2014-0022.Search in Google Scholar PubMed PubMed Central


Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/em-2019-0003)


Received: 2019-01-30
Accepted: 2020-03-31
Published Online: 2020-05-15

© 2020 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Editorial
  2. The mean prevalence
  3. Research Articles
  4. Heterogeneous indirect effects for multiple mediators using interventional effect models
  5. Sleep habits and their association with daytime sleepiness among medical students of Tanta University, Egypt
  6. Population attributable fractions for continuously distributed exposures
  7. A real-time search strategy for finding urban disease vector infestations
  8. Disease mapping models for data with weak spatial dependence or spatial discontinuities
  9. A comparison of cause-specific and competing risk models to assess risk factors for dementia
  10. A simple index of prediction accuracy in multiple regression analysis
  11. A comparison of approaches for estimating combined population attributable risks (PARs) for multiple risk factors
  12. Posterior predictive treatment assignment methods for causal inference in the context of time-varying treatments
  13. Random effects tumour growth models for identifying image markers of mammography screening sensitivity
  14. Extrapolating sparse gold standard cause of death designations to characterize broader catchment areas
  15. Extending balance assessment for the generalized propensity score under multiple imputation
  16. Regression analysis of unmeasured confounding
  17. The Use of Logic Regression in Epidemiologic Studies to Investigate Multiple Binary Exposures: An Example of Occupation History and Amyotrophic Lateral Sclerosis
  18. Meeting the Assumptions of Inverse-Intensity Weighting for Longitudinal Data Subject to Irregular Follow-Up: Suggestions for the Design and Analysis of Clinic-Based Cohort Studies
Downloaded on 14.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/em-2019-0003/html
Scroll to top button