Misspecification of confounder-exposure and confounder-outcome associations leads to bias in effect estimates

Table 2 Confounder-adjustment methods and the association(s) that need to be correctly specified to obtain an unbiased estimate of the exposure effect

Confounder-adjustment methods	Confounder-exposure association	Confounder-outcome association
Multivariable regression analysis	n/a	√
Covariate adjustment using the PS^§	√	√^*
IPW^§	√	n/a
DR estimation^§	Both associations need to be specified but estimators are consistent if either is correctly specified

Abbreviations: PS propensity score, IPW inverse probability weighting, DR double robust, PS-outcome effect, n/a: not applicable, requires a correctly specified propensity score (i.e., the log odds of the exposure is linear in the confounders)

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