Methods/Statistics
Do some quantitative bias analyses overestimate the bias due to uncontrolled confounding? Tsion A Armidie* Tsion Armidie Lindsay J Collin Richard F MacLehose Thomas P Ahern Timothy L Lash
In non-randomized studies aiming to answer causal questions, researchers estimate an exposure-outcome relationship, and confounding is a common concern. Adjustment for a minimally sufficient set of known and measured confounders will remove bias caused by those confounders; however, sometimes a confounder in the minimally sufficient set is unmeasured. Approaches exist to estimate the bias due to unmeasured confounding, including quantitative bias analysis (QBA). QBA assumes that the unmeasured confounder is independent of the measured controlled confounders. However, confounders are often correlated, so QBA to address unmeasured confounding would overstate the size of the bias in the presence of such correlation. This study uses an applied example to demonstrate how conventional bias analysis methods often overestimate the impact of unmeasured confounding.
This analysis used NHANES III (1988-1994) to examine the association between healthy eating index (HEI) and all-cause mortality (n=4457). A fully adjusted Cox regression model included tobacco use, sex, age, hypertension, BMI, education, and physical activity as the minimally sufficient adjustment set. Hazard ratios (HR) that would have been observed had one of hypertension, BMI, education, or physical activity been “unmeasured” were estimated by leaving them out of 5 separate Cox models. The strength of confounding was calculated by comparing the result with an unmeasured confounder with the fully adjusted estimate. We performed QBA for the “unmeasured” confounders, using the ‘true’ bias parameter estimates as given in NHANES.
The fully adjusted HR comparing Quintile 1 vs. 5 of HEI with all-cause mortality was 1.72 (95% CI 1.24 to 3.39). After treating hypertension, BMI, education, and physical activity as “unmeasured” confounders, little change in the HR was observed (1.72-1.88). The QBA bias-adjusted estimates ranged from 1.72 to 2.23.
Due to the correlation between covariates, the effect of bias due to treating confounders as unmeasured was negligible, but the bias analyses often suggested substantial bias. This applied example suggests that QBA is useful for evaluating unmeasured confounding but may overestimates the strength of bias when highly correlated variables have already been adjusted for.