  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.
