Magnitude and direction of missing confounders had different consequences on treatment effect estimation in propensity score analysis

OBJECTIVE: 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. STUDY DESIGN AND SETTING: 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). RESULTS: 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. CONCLUSION: 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.