An approach to quantifying the potential importance of residual confounding in systematic reviews of observational studies: A GRADE concept paper

Small relative effect sizes are common in observational studies of exposure in environmental and public health. However, such effects can still have considerable policy importance when the baseline rate of the health outcome is high, and many persons are exposed. Assessing the certainty of the evidence based on these effect sizes is challenging because they can be prone to residual confounding due to the non-randomized nature of the evidence. When applying GRADE, a precise relative risk >2.0 increases the certainty in an existing effect because residual confounding is unlikely to explain the association. GRADE also suggests rating up when opposing plausible residual confounding exists for other effect sizes. In this concept paper, we propose using the E-value, defined as the smallest effect size of a confounder that still can reduce an observed RR to the null value, and a reference confounder to assess the likelihood of residual confounding. We propose a 4-step approach. 1. Assess the association of interest for relevant exposure levels. 2. Calculate the E-value for this observed association. 3. Choose a reference confounder with sufficient strength and information and assess its effect on the observed association using the E-value. 4. Assess how likely it is that residual confounding will still bias the observed RR. We present three case studies and discuss the feasibility of the approach.