Matching by propensity score in cohort studies with three treatment groups

Epidemiology. 2013 May;24(3):401-9. doi: 10.1097/EDE.0b013e318289dedf.


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.

Publication types

  • Comparative Study
  • Evaluation Study
  • Research Support, N.I.H., Extramural
  • Research Support, N.I.H., Intramural

MeSH terms

  • Aged
  • Aged, 80 and over
  • Algorithms
  • Analgesics, Opioid / therapeutic use
  • Anti-Inflammatory Agents, Non-Steroidal / therapeutic use
  • Arthritis, Rheumatoid / drug therapy
  • Bias
  • Cohort Studies*
  • Computer Simulation
  • Confounding Factors, Epidemiologic
  • Cyclooxygenase 2 Inhibitors / therapeutic use
  • Epidemiologic Research Design*
  • Humans
  • Models, Statistical
  • Monte Carlo Method
  • Pharmacoepidemiology / methods*
  • Propensity Score*
  • Treatment Outcome


  • Analgesics, Opioid
  • Anti-Inflammatory Agents, Non-Steroidal
  • Cyclooxygenase 2 Inhibitors