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

Abstract

Background: Confounding is a common issue in epidemiological research. Commonly used confounder-adjustment methods include multivariable regression analysis and propensity score methods. Although it is common practice to assess the linearity assumption for the exposure-outcome effect, most researchers do not assess linearity of the relationship between the confounder and the exposure and between the confounder and the outcome before adjusting for the confounder in the analysis. Failing to take the true non-linear functional form of the confounder-exposure and confounder-outcome associations into account may result in an under- or overestimation of the true exposure effect. Therefore, this paper aims to demonstrate the importance of assessing the linearity assumption for confounder-exposure and confounder-outcome associations and the importance of correctly specifying these associations when the linearity assumption is violated.

Methods: A Monte Carlo simulation study was used to assess and compare the performance of confounder-adjustment methods when the functional form of the confounder-exposure and confounder-outcome associations were misspecified (i.e., linearity was wrongly assumed) and correctly specified (i.e., linearity was rightly assumed) under multiple sample sizes. An empirical data example was used to illustrate that the misspecification of confounder-exposure and confounder-outcome associations leads to bias.

Results: The simulation study illustrated that the exposure effect estimate will be biased when for propensity score (PS) methods the confounder-exposure association is misspecified. For methods in which the outcome is regressed on the confounder or the PS, the exposure effect estimate will be biased if the confounder-outcome association is misspecified. In the empirical data example, correct specification of the confounder-exposure and confounder-outcome associations resulted in smaller exposure effect estimates.

Conclusion: When attempting to remove bias by adjusting for confounding, misspecification of the confounder-exposure and confounder-outcome associations might actually introduce bias. It is therefore important that researchers not only assess the linearity of the exposure-outcome effect, but also of the confounder-exposure or confounder-outcome associations depending on the confounder-adjustment method used.

Keywords: Confounder-adjustment; Confounder-exposure association; Confounder-outcome association; Confounding; Linearity assumption; Multivariable regression analysis; Propensity score methods.

Fig. 1

Hypothetical example of the relationship between continuous variables A and B, where each point represents an observation. Panel a: linear relationship. Panel b: non-linear relationship. The dotted line represents the linear regression line for the relationship between variables A and B