title: A comparison of entropy balance and probability weighting methods to generalize observational cohorts to a population: a simulation and empirical example.
abstract: OBJECTIVE
  We compared methods to control bias and confounding in observational studies including inverse probability weighting (IPW) and stabilized IPW (sIPW). These methods often require iteration and post-calibration to achieve covariate balance. In comparison, entropy balance (EB) optimizes covariate balance a priori by calibrating weights using the target's moments as constraints.
  
  
  METHODS
  We measured covariate balance empirically and by simulation by using absolute standardized mean difference (ASMD), absolute bias (AB), and root mean square error (RMSE), investigating two scenarios: the size of the observed (exposed) cohort exceeds the target (unexposed) cohort and vice versa. The empirical application weighted a commercial health plan cohort to a nationally representative National Health and Nutrition Examination Survey target on the same covariates and compared average total health care cost estimates across methods.
  
  
  RESULTS
  Entropy balance alone achieved balance (ASMD ≤ 0.10) on all covariates in simulation and empirically. In simulation scenario I, EB achieved the lowest AB and RMSE (13.64, 31.19) compared with IPW (263.05, 263.99) and sIPW (319.91, 320.71). In scenario II, EB outperformed IPW and sIPW with smaller AB and RMSE. In scenarios I and II, EB achieved the lowest mean estimate difference from the simulated population outcome ($490.05, $487.62) compared with IPW and sIPW, respectively. Empirically, only EB differed from the unweighted mean cost indicating IPW, and sIPW weighting was ineffective.
  
  
  CONCLUSIONS
  Entropy balance demonstrated the bias-variance tradeoff achieving higher estimate accuracy, yet lower estimate precision, compared with IPW methods. EB weighting required no post-processing and effectively mitigated observed bias and confounding. Copyright © 2016 John Wiley & Sons, Ltd.
authors.affiliation: Comprehensive Health Insights Inc., Louisville, KY, USA.
authors.forename: Raymond A
authors.identifier: http://orcid.org/0000-0002-6795-519X
authors.initials: RA
authors.lastname: Harvey
authors.affiliation: Comprehensive Health Insights Inc., Louisville, KY, USA.
authors.forename: Jennifer D
authors.initials: JD
authors.lastname: Hayden
authors.affiliation: Comprehensive Health Insights Inc., Louisville, KY, USA.
authors.forename: Pravin S
authors.initials: PS
authors.lastname: Kamble
authors.affiliation: Novo Nordisk Inc., Plainsboro, NJ, USA.
authors.forename: Jonathan R
authors.initials: JR
authors.lastname: Bouchard
authors.affiliation: Novo Nordisk Inc., Plainsboro, NJ, USA.
authors.forename: Joanna C
authors.initials: JC
authors.lastname: Huang
mesh_terms: D015982:Bias; D015331:Cohort Studies; D015986:Confounding Factors, Epidemiologic; D019277:Entropy; D017048:Health Care Costs / Q000706:statistics & numerical data; D006801:Humans; D009749:Nutrition Surveys / Q000706:statistics & numerical data; D064887:Observational Studies as Topic / Q000379:methods*; D011336:Probability; D012107:Research Design
keywords: entropy-balance; inverse probability weighting; observational; optimization; pharmacoepidemiology; weighting