title: Propensity score estimators for the average treatment effect and the average treatment effect on the treated may yield very different estimates.
abstract: Propensity score matching is typically used to estimate the average treatment effect for the treated while inverse probability of treatment weighting aims at estimating the population average treatment effect. We illustrate how different estimands can result in very different conclusions.
  
  
  
  We applied the two propensity score methods to assess the effect of continuous positive airway pressure on mortality in patients hospitalized for acute heart failure. We used Monte Carlo simulations to investigate the important differences in the two estimates.
  
  
  
  Continuous positive airway pressure application increased hospital mortality overall, but no continuous positive airway pressure effect was found on the treated. Potential reasons were (1) violation of the positivity assumption; (2) treatment effect was not uniform across the distribution of the propensity score. From simulations, we concluded that positivity bias was of limited magnitude and did not explain the large differences in the point estimates. However, when treatment effect varies according to the propensity score (E[Y(1)-Y(0)|g(X)] is not constant, Y being the outcome and g(X) the propensity score), propensity score matching ATT estimate could strongly differ from the inverse probability of treatment weighting-average treatment effect estimate. We show that this empirical result is supported by theory.
  
  
  
  Although both approaches are recommended as valid methods for causal inference, propensity score-matching for ATT and inverse probability of treatment weighting for average treatment effect yield substantially different estimates of treatment effect. The choice of the estimand should drive the choice of the method.
authors.affiliation: Department of Biostatistics, INSERM UMR-S717; Hôpital Saint Louis, AP-HP; Université Paris Diderot, Sorbonne Paris Cité; Paris, France Department of Anesthesiology & Critical Care, Hôpital Européen Georges Pompidou, AP-HP; Université Paris Descartes, Sorbonne Paris Cité; Paris, France Division of Biostatistics, School of Public Health, University of California at Berkeley, Berkeley, USA romainpirracchio@yahoo.fr.
authors.forename: R
authors.initials: R
authors.lastname: Pirracchio
authors.affiliation: Division of Biostatistics, School of Public Health, University of California at Berkeley, Berkeley, USA.
authors.forename: M
authors.initials: M
authors.lastname: Carone
authors.affiliation: Department of Biostatistics, INSERM UMR-S717; Hôpital Saint Louis, AP-HP; Université Paris Diderot, Sorbonne Paris Cité; Paris, France.
authors.forename: M Resche
authors.initials: MR
authors.lastname: Rigon
authors.affiliation: Department of Biostatistics, INSERM UMR-S717; Hôpital Saint Louis, AP-HP; Université Paris Diderot, Sorbonne Paris Cité; Paris, France.
authors.forename: E
authors.initials: E
authors.lastname: Caruana
authors.affiliation: Department of Anesthesiology & Critical Care, INSERM UMR-S942; Hôpital Lariboisière, AP-HP; Université Paris Diderot, Sorbonne Paris Cité; Paris, France.
authors.forename: A
authors.initials: A
authors.lastname: Mebazaa
authors.affiliation: Department of Biostatistics, INSERM UMR-S717; Hôpital Saint Louis, AP-HP; Université Paris Diderot, Sorbonne Paris Cité; Paris, France.
authors.forename: S
authors.initials: S
authors.lastname: Chevret
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D045422:Continuous Positive Airway Pressure / Q000706:statistics & numerical data; D005260:Female; D006333:Heart Failure / Q000401:mortality / Q000628:therapy*; D006801:Humans; D008297:Male; D008875:Middle Aged; D009010:Monte Carlo Method; D057216:Propensity Score; D015203:Reproducibility of Results
keywords: average treatment effect; average treatment on the treated; inverse probability weighting; matching; positivity assumption; propensity score