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Matching Weights to Simultaneously Compare Three Treatment Groups: Comparison to Three-way Matching

Yoshida, Kazuki; Hernández-Díaz, Sonia; Solomon, Daniel H.; Jackson, John W.; Gagne, Joshua J.; Glynn, Robert J.; Franklin, Jessica M.

doi: 10.1097/EDE.0000000000000627

Background: Propensity score matching is a commonly used tool. However, its use in settings with more than two treatment groups has been less frequent. We examined the performance of a recently developed propensity score weighting method in the three-treatment group setting.

Methods: The matching weight method is an extension of inverse probability of treatment weighting (IPTW) that reweights both exposed and unexposed groups to emulate a propensity score matched population. Matching weights can generalize to multiple treatment groups. The performance of matching weights in the three-group setting was compared via simulation to three-way 1:1:1 propensity score matching and IPTW. We also applied these methods to an empirical example that compared the safety of three analgesics.

Results: Matching weights had similar bias, but better mean squared error (MSE) compared with three-way matching in all scenarios. The benefits were more pronounced in scenarios with a rare outcome, unequally sized treatment groups, or poor covariate overlap. IPTW’s performance was highly dependent on covariate overlap. In the empirical example, matching weights achieved the best balance for 24 out of 35 covariates. Hazard ratios were numerically similar to matching. However, the confidence intervals were narrower for matching weights.

Conclusions: Matching weights demonstrated improved performance over three-way matching in terms of MSE, particularly in simulation scenarios where finding matched subjects was difficult. Given its natural extension to settings with even more than three groups, we recommend matching weights for comparing outcomes across multiple treatment groups, particularly in settings with rare outcomes or unequal exposure distributions. See video abstract at,

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From the aDepartment of Epidemiology, Harvard T.H. Chan School of Public Health, Boston, MA; bDepartment of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA; cDivision of Rheumatology, Immunology and Allergy, Brigham and Women’s Hospital, Boston, MA; dDivision of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women’s Hospital and Harvard Medical School, Boston, MA; and eDepartment of Epidemiology, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD.

Submitted 7 October 2015; accepted 19 January 2017.

K.Y. receives tuition support jointly from Japan Student Services Organization (JASSO) and Harvard T.H. Chan School of Public Health (partially supported by training grants from Pfizer, Takeda, Bayer, and PhRMA). S.H.D. has consulted for AstraZeneca and UCB. D.H.S. receives salary support from institutional research grants (NIH-K24AR055989) from Eli Lilly, Amgen, Pfizer, AstraZeneca, Genentech, and Corrona. He also receives royalties from UpToDate, and serves in unpaid roles in studies funded by Pfizer and Eli Lilly. J.J.G. has received salary support from institutional research grants from Novartis Pharmaceuticals Corporation. He is a consultant to Aetion, Inc., and Optum company. J.M.F. is PI of grants from PCORI and Merck. She also serves as consultant to Aetion, Inc. J.W.J. is funded by the Alonzo Smythe Yerby Fellowship at the Harvard T.H. Chan School of Public Health.

The simulation code is on The empirical dataset is not available as it is protected under data use agreement.

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Correspondence: Kazuki Yoshida, Departments of Epidemiology & Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA. E-mail:

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