A Bespoke Instrumental Variable Approach to Correction for Exposure Measurement Error

A covariate-adjusted estimate of an exposure-outcome association may be biased if the exposure variable suffers measurement error. We propose an approach to correct for exposure measurement error in a covariate-adjusted estimate of the association between a continuous exposure variable and outcome of interest. Our proposed approach requires data for a reference population in which the exposure was a priori set to some known level (e.g., 0, and is therefore unexposed); however, our approach does not require an exposure validation study or replicate measures of exposure, which are typically needed when addressing bias due to exposure measurement error. A key condition for this method, which we refer to as "partial population exchangeability," requires that the association between a measured covariate and outcome in the reference population equals the association between that covariate and outcome in the target population in the absence of exposure. We illustrate the approach using simulations and an example.