Do quantitative bias analyses accurately characterize bias due to uncontrolled confounding?

Adjustment for a sufficient set of confounders removes bias. When a confounder is unmeasured, approaches exist to estimate bias. Confounders are often correlated, so analyses that ignore correlations overstate bias.

Using NHANES III, we examined the association between Healthy Eating Index (HEI) and all-cause mortality (n=2417). A fully adjusted model included tobacco use, sex, age, hypertension, BMI, education, and physical activity. 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. We then performed bias analysis for the unmeasured confounders using uncorrelated bias parameter estimates.

The fully adjusted HR comparing HEI Quintile 1 vs. 5 was 1.72 (95% CI 1.24 to 2.40). After treating variables as "unmeasured" confounders, HRs changed little (range: 1.73 to 1.98). Bias-adjusted hazard ratios ranged from 1.72 to 1.98 suggesting that substantial unmeasured confounding would be required to explain the associations.

Due to correlations between covariates, the additional bias attributable to unmeasured variables was minimal. QBA produced estimates that often overestimated the impact of the unmeasured confounders. Although QBA is useful for evaluating unmeasured confounding, it may not precisely quantify the strength of bias.