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Measurement error is a pervasive issue which renders the results of ananalysis unreliable. The measurement error literature contains numerouscorrection techniques, which can be broadly divided into those which aim toproduce exactly consistent estimators, and those which are only approximatelyconsistent. While consistency is a desirable property, it is typically attainedonly under specific model assumptions. Two techniques, regression calibrationand simulation extrapolation, are used frequently in a wide variety ofparametric and semiparametric settings. However, in many settings these methodsare only approximately consistent. We generalize these corrections, relaxingassumptions placed on replicate measurements. Under regularity conditions, theestimators are shown to be asymptotically normal, with a sandwich estimator forthe asymptotic variance. Through simulation, we demonstrate the improvedperformance of the modified estimators, over the standard techniques, whenthese assumptions are violated. We motivate these corrections using theFramingham Heart Study, and apply the generalized techniques to an analysis ofthese data.

Generalizations to Corrections for the Effects of Measurement Error in Approximately Consistent Methodologies