Robust Linear Adjustment for Poisson Regression with Measurement Error Using Instrumental Variables in Calibration Sample

Abstract

We investigate methods for Poisson regression when covariates are measured with errors. In the whole cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies the classical measurement error model, but it may not have repeated measurements. We assume that an additional instrumental variable is available for subjects in a subset, namely a calibration sample, such that the instrumental variable is a linear function of the unobserved exposure variable. We propose a robust linear adjustment estimator that uses all the available data. The proposed estimator is shown to be consistent and asymptotically normal under very weak distributional assumptions. Finite sample performance of the proposed estimator is examined via intensive simulation studies, and it is shown to perform very well in many settings.