title: 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.
abstract: OBJECTIVE
  The propensity score method (PS) has proven to be an effective tool to reduce bias in nonrandomized studies, especially when the number of (potential) confounders is large and dimensionality problems arise. The PS method introduced by Rosenbaum and Rubin is described in detail for studies with 2 treatment options. Since in clinical practice we are often interested in the comparison of multiple interventions, there was a need to extend the PS method to multiple treatments. It has been shown that in theory a multiple PS method is possible. So far, its practical application is rare and a practical introduction lacking.
  
  
  METHODS
  A practical guideline to illustrate the use of the multiple PS method is provided with data from a mental health study. The multiple PS is estimated with a multinomial logistic regression analysis. The multiple PS is the probability of assignment to each treatment category. Subsequently, to estimate the treatment effects while controlling for initial differences, the multiple PSs, calculated for each treatment category, are included as extra predictors in the regression analysis.
  
  
  RESULTS
  With the multiple PS method, balance was achieved in all relevant pretreatment variables. The corrected estimated treatment effects were somewhat different from the results without control for initial differences.
  
  
  CONCLUSIONS
  Our results indicate that the multiple PS method is a feasible method to adjust for observed pretreatment differences in nonrandomized studies where the number of pretreatment differences is large and multiple treatments are compared.
authors.affiliation: Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands. M.Spreeuwenberg@vilans.nl
authors.forename: Marieke Dingena
authors.initials: MD
authors.lastname: Spreeuwenberg
authors.forename: Anna
authors.initials: A
authors.lastname: Bartak
authors.forename: Marcel A
authors.initials: MA
authors.lastname: Croon
authors.forename: Jacques A
authors.initials: JA
authors.lastname: Hagenaars
authors.forename: Jan J V
authors.initials: JJ
authors.lastname: Busschbach
authors.forename: Helene
authors.initials: H
authors.lastname: Andrea
authors.forename: Jos
authors.initials: J
authors.lastname: Twisk
authors.forename: Theo
authors.initials: T
authors.lastname: Stijnen
mesh_terms: D000328:Adult; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D005260:Female; D006801:Humans; D008297:Male; D015999:Multivariate Analysis; D057216:Propensity Score; D011613:Psychotherapy / Q000706:statistics & numerical data; D012044:Regression Analysis; D015983:Selection Bias