title: Insights into different results from different causal contrasts in the presence of effect-measure modification.
abstract: OBJECTIVE
  Both propensity score (PS) matching and inverse probability of treatment weighting (IPTW) allow causal contrasts, albeit different ones. In the presence of effect-measure modification, different analytic approaches produce different summary estimates.
  
  
  METHODS
  We present a spreadsheet example that assumes a dichotomous exposure, covariate, and outcome. The covariate can be a confounder or not and a modifier of the relative risk (RR) or not. Based on expected cell counts, we calculate RR estimates using five summary estimators: Mantel-Haenszel (MH), maximum likelihood (ML), the standardized mortality ratio (SMR), PS matching, and a common implementation of IPTW.
  
  
  RESULTS
  Without effect-measure modification, all approaches produce identical results. In the presence of effect-measure modification and regardless of the presence of confounding, results from the SMR and PS are identical, but IPTW can produce strikingly different results (e.g., RR = 0.83 vs. RR = 1.50). In such settings, MH and ML do not estimate a population parameter and results for those measures fall between PS and IPTW.
  
  
  CONCLUSIONS
  Discrepancies between PS and IPTW reflect different weighting of stratum-specific effect estimates. SMR and PS matching assign weights according to the distribution of the effect-measure modifier in the exposed subpopulation, whereas IPTW assigns weights according to the distribution of the entire study population. In pharmacoepidemiology, contraindications to treatment that also modify the effect might be prevalent in the population, but would be rare among the exposed. In such settings, estimating the effect of exposure in the exposed rather than the whole population is preferable.
authors.affiliation: Division of Pharmacoepidemiology and Pharmacoeconomics, Brigham and Women's Hospital, Harvard Medical School, Boston, MA 02120, USA. til.sturmer@post.harvard.edu
authors.forename: Til
authors.initials: T
authors.lastname: Stürmer
authors.forename: Kenneth J
authors.initials: KJ
authors.lastname: Rothman
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Glynn
mesh_terms: D015982:Bias; D015984:Causality; D015986:Confounding Factors, Epidemiologic; D003627:Data Interpretation, Statistical; D004812:Epidemiologic Methods; D006801:Humans; D016013:Likelihood Functions; D017891:Pharmacoepidemiology / Q000379:methods / Q000706:statistics & numerical data; D018570:Risk Assessment