title: Matching by propensity score in cohort studies with three treatment groups.
abstract: BACKGROUND
  Nonrandomized pharmacoepidemiology generally compares one medication with another. For many conditions, clinicians can benefit from comparing the safety and effectiveness of three or more appropriate treatment options. We sought to compare three treatment groups simultaneously by creating 1:1:1 propensity score-matched cohorts.
  
  
  METHODS
  We developed a technique that estimates generalized propensity scores and then creates 1:1:1 matched sets. We compared this methodology with two existing approaches-construction of matched cohorts through a common-referent group and a pairwise match for each possible contrast. In a simulation, we varied unmeasured confounding, presence of treatment effect heterogeneity, and the prevalence of treatments and compared each method's bias, variance, and mean squared error (MSE) of the treatment effect. We applied these techniques to a cohort of rheumatoid arthritis patients treated with nonselective nonsteroidal anti-inflammatory drugs, COX-2 selective inhibitors, or opioids.
  
  
  RESULTS
  We performed 1000 simulation runs. In the base case, we observed an average bias of 0.4% (MSE × 100 = 0.2) in the three-way matching approach and an average bias of 0.3% (MSE × 100 = 0.2) with the pairwise technique. The techniques showed differing bias and MSE with increasing treatment effect heterogeneity and decreasing propensity score overlap. With highly unequal exposure prevalences, strong heterogeneity, and low overlap, we observed a bias of 6.5% (MSE × 100 = 10.8) in the three-way approach and 12.5% (MSE × 100 = 12.3) in the pairwise approach. The empirical study displayed better covariate balance using the pairwise approach. Point estimates were substantially similar.
  
  
  CONCLUSIONS
  Our matching approach offers an effective way to study the safety and effectiveness of three treatment options. We recommend its use over the pairwise or common-referent approaches.
authors.affiliation: Division of Pharmacoepidemiology and Pharmacoeconomics, Department of Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, MA 02120, USA. jrassen@post.harvard.edu
authors.forename: Jeremy A
authors.initials: JA
authors.lastname: Rassen
authors.forename: Abhi A
authors.initials: AA
authors.lastname: Shelat
authors.forename: Jessica M
authors.initials: JM
authors.lastname: Franklin
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Glynn
authors.forename: Daniel H
authors.initials: DH
authors.lastname: Solomon
authors.forename: Sebastian
authors.initials: S
authors.lastname: Schneeweiss
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D000465:Algorithms; D000701:Analgesics, Opioid / Q000627:therapeutic use; D000894:Anti-Inflammatory Agents, Non-Steroidal / Q000627:therapeutic use; D001172:Arthritis, Rheumatoid / Q000188:drug therapy; D015982:Bias; D015331:Cohort Studies; D003198:Computer Simulation; D015986:Confounding Factors, Epidemiologic; D052246:Cyclooxygenase 2 Inhibitors / Q000627:therapeutic use; D015340:Epidemiologic Research Design; D006801:Humans; D015233:Models, Statistical; D009010:Monte Carlo Method; D017891:Pharmacoepidemiology / Q000379:methods*; D057216:Propensity Score; D016896:Treatment Outcome
chemical_list: D000701:Analgesics, Opioid; D000894:Anti-Inflammatory Agents, Non-Steroidal; D052246:Cyclooxygenase 2 Inhibitors