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Propensity score (PS) analysis allows an unbiased estimate of treatment effects but assumes that all confounders are measured. We assessed the impact of omitting confounders from a PS analysis on clinical decision making.We conducted Monte Carlo simulations on hypothetical observational studies based on virtual populations and on the population from a large randomized trial (CRASH-2). In both series of simulations, PS analysis was conducted with all confounders and with omitted confounders, which were defined to have different strengths of association with the outcome and treatment exposure. After inverse probability of treatment weighting, we calculated the absolute risk differences and numbers needed to treat (NNT).In both series of simulations, omitting a confounder that was moderately associated with the outcome and exposure led to negligible bias on the NNT scale. The bias induced by omitting strongly positive confounding variables remained less than 15 patients to treat. Major bias and reversed effects were found only when omitting highly prevalent, strongly negative confounders that were similarly associated with the outcome and exposure with odds ratios greater than 4.00 (or <0.25). This omission was accompanied by a substantial decrease in analysis power.The omission of strongly negative confounding variables from a PS analysis can lead to incorrect clinical decision making. However, omitting these variables also decreases the analysis power, which may prevent the reporting of significant but misleading effects.

Original publication




Journal article


Journal of clinical epidemiology

Publication Date





87 - 97


Laboratory of Biostatistics, Epidemiology, Clinical Research and Health Economics, UPRES EA 2415, Montpellier University, Montpellier, France; Department of Anesthesia, Michael DeGroote School of Medicine, Faculty of Health Sciences, McMaster University, Hamilton, Canada; Department of Clinical Epidemiology and Biostatistics, Michael DeGroote School of Medicine, Faculty of Health Sciences, McMaster University, Hamilton, Canada; Population Health Research Institute, David Braley Cardiac, Vascular and Stroke Research Institute, Perioperative Medicine and Surgical Research Unit, Hamilton, Canada.


Humans, Monte Carlo Method, Odds Ratio, Risk, Bias (Epidemiology), Confounding Factors (Epidemiology), Computer Simulation, Randomized Controlled Trials as Topic, Propensity Score, Observational Studies as Topic, Clinical Decision-Making