Assessing Techniques for Quantifying the Impact of Bias Due to an Unmeasured Confounder: An Applied Example

Purpose: To compare the magnitude of bias due to unmeasured confounding estimated from various techniques in an applied example. Patients and Methods: We examined the association between dibutyl phthalate (DBP) and incident estrogen receptor (ER)-positive breast cancer in a Danish nationwide cohort (N=1,122,042). Cox regression analyses were adjusted for age and active drug compounds contributing to DBP exposure. We estimated the hazard ratios (HRs) that would have been observed had one of the DBP sources been unmeasured and calculated the strength of confounding by comparing to the fully adjusted HR. We performed a quantitative bias analysis (QBA) of the "unmeasured" confounder, using external information to specify the bias parameters. Upper bounds on the bias were estimated and E-values were calculated. Results: The adjusted HR for incident ER-positive breast cancer among women with highlevel (>= 10,000 cumulative milligrams) versus no DBP exposure was 2.12 (95% confidence interval 1.12 to 4.05). Removing each DBP source in isolation resulted in negligible change in the HR. The bias estimates from the QBA ranged from 1.00 to 1.01. The estimated maximum impact of unmeasured confounding ranged from 1.01 to 1.51. E-values ranged from 3.46 to 3.68. Conclusion: The impact of bias due to simulated unmeasured confounding was negligible, in part, because the unmeasured variable was not independent of controlled variables. When a suspected confounder cannot be measured in the study data, our exercise suggests that QBA is the most informative method for assessing the impact. E-values may best be reserved for situations where uncontrolled confounding emanates from an unknown confounder.