Confounding and exposure measurement error can introduce bias when drawing inference about the marginal effect of an exposure on an outcome of interest. While there are broad methodologies for addressing each source of bias individually, confounding and exposure measurement error frequently co-occur and there is a need for methods that address them simultaneously. In this paper, corrected score methods are derived under classical additive measurement error to draw inference about marginal exposure effects using only measured variables. Three estimators are proposed based on g-formula, inverse probability weighting, and doubly-robust estimation techniques. The estimators are shown to be consistent and asymptotically normal, and the doubly-robust estimator is shown to exhibit its namesake property. The methods, which are implemented in the R package mismex, perform well in finite samples under both confounding and measurement error as demonstrated by simulation studies. The proposed doubly-robust estimator is applied to study the effects of two biomarkers on HIV-1 infection using data from the HVTN 505 preventative vaccine trial.

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