Crump et al. (Biometrika. 2009;96(1):187-199), Stürmer et al. (Am J Epidemiol. 2010;172(7):843-854), and Walker et al. (Comp Eff Res. 2013;2013(3):11-20) proposed propensity score (PS) trimming methods as a means to improve efficiency (Crump) or reduce confounding (Stürmer and Walker). We generalized the trimming definitions by considering multinomial PSs, one for each treatment, and proved that these proposed definitions reduce to the original binary definitions when we have only 2 treatment groups. We then examined the performance of the proposed multinomial trimming methods in the setting of 3 treatment groups, in which subjects with extreme PSs more likely had unmeasured confounders. Inverse probability of treatment weights, matching weights, and overlap weights were used to control for measured confounders. All 3 methods reduced bias regardless of the weighting methods in most scenarios. Multinomial Stürmer and Walker trimming were more successful in bias reduction when the 3 treatment groups had very different sizes (10:10:80). Variance reduction, seen in all methods with inverse probability of treatment weights but not with matching weights or overlap weights, was more successful with multinomial Crump and Stürmer trimming. In conclusion, our proposed definitions of multinomial PS trimming methods were beneficial within our simulation settings that focused on the influence of unmeasured confounders.
Keywords: multinomial treatment; propensity score; propensity score trimming; propensity score weighting.
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