  Measurement error arises through a variety of mechanisms. A rich literature
exists on the bias introduced by covariate measurement error and on methods of
analysis to address this bias. By comparison, less attention has been given to
errors in outcome assessment and non-classical covariate measurement error. We
consider an extension of the regression calibration method to settings with
errors in a continuous outcome, where the errors may be correlated with
prognostic covariates or with covariate measurement error. This method adjusts
for the measurement error in the data and can be applied with either a
validation subset, on which the true data are also observed (e.g., a study
audit), or a reliability subset, where a second observation of error prone
measurements are available. For each case, we provide conditions under which
the proposed method is identifiable and leads to unbiased estimates of the
regression parameter. When the second measurement on the reliability subset has
no error or classical unbiased measurement error, the proposed method is
unbiased even when the primary outcome and exposures of interest are subject to
both systematic and random error. We examine the performance of the method with
simulations for a variety of measurement error scenarios and sizes of the
reliability subset. We illustrate the method's application using data from the
Women's Health Initiative Dietary Modification Trial.
