A New Method for Partial Correction of Residual Confounding in Time-Series and Other Observational Studies

Methods exist to detect residual confounding in epidemiologic studies. One requires a negative control exposure with 2 key properties: 1) conditional independence of the negative control and the outcome (given modeled variables) absent confounding and other model misspecification, and 2) associations of the negative control with uncontrolled confounders and the outcome. We present a new method to partially correct for residual confounding: When confounding is present and our assumptions hold, we argue that estimators from models that include a negative control exposure with these 2 properties tend to be less biased than those from models without it. Using regression theory, we provide theoretical arguments that support our claims. In simulations, we empirically evaluated the approach using a time-series study of ozone effects on asthma emergency department visits. In simulations, effect estimators from models that included the negative control exposure (ozone concentrations 1 day after the emergency department visit) had slightly or modestly less residual confounding than those from models without it. Theory and simulations show that including the negative control can reduce residual confounding, if our assumptions hold. Our method differs from available methods because it uses a regression approach involving an exposure-based indicator rather than a negative control outcome to partially correct for confounding.