Table 1.

Comparisons of the Six Confounding Adjustment Methods

Method*	Brief Summary	Strengths	Weaknesses
Covariate-adjusted regression15	Fit multivariable regression regressing the outcome on the exposure variable and confounders	Conventional approach Results relatively easy to understand and interpret Can be implemented in many statistical packages	Difficult to assess covariate overlap Limited covariates possible with rare binary outcomes
Propensity scores (applies to the five PS-based methods below)5	Fit logistic regression regressing exposure on the confounders Calculate propensity score (PS) as the probability of receiving the exposure of interest from this regression	Confounding is removed conditional on PS Facilitates the assessment of covariate overlap May be possible to adjust for multiple covariates and complex non-linear terms even with rare outcomes
PS regression16	Fit multivariable regression regressing the outcome on the exposure variable and the estimated PS		Requires PS to be correctly adjusted for in the regression model
PS stratification17	Estimate treatment effect within strata having similar PS Estimate treatment effect by combining stratum-specific effects	No additional modeling assumption	Residual confounding within strata since subjects have similar but non-identical PS
PS matching5	Construct matched pairs with subjects with similar PSs from each exposure group Conduct conditional analyses among the matched pairs to estimate treatment effect	No additional modeling assumption Can estimate either average treatment effect or average treatment effect on the treated	Residual confounding due to similar but non-identical PS within matched pair Different matching algorithms with respective advantages and disadvantages Different caliper may affect results
Inverse probability weighting18,19	Weight each subject by the inverse of the probability of receiving observed exposure Compare the outcomes between the two exposure groups in the weighted population	No additional modeling assumption Applies easily to settings with more than two exposure groups Can be extended to handle time-varying exposure and time-varying confounding	Exposed subjects with very small PSs or unexposed subjects with very large PSs have large weights and may lead to large standard errors.
Doubly robust estimation20	Combine the covariate adjusted model and the inverse probability weight using a complex augmentation term	Gives valid inference if either model is correct but not necessarily both	Complex Subjects with large weights may lead to large standard errors

^*All methods are subject to bias if covariate overlap is not present. All methods require correct specification of models. For regression, this is the relationship between the confounders and the outcome. For PS, this is the relationship between the confounders and the exposure. The exception is doubly robust estimation, for which one of these may be incorrect.