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

TL;DR

This paper introduces generalized correction methods for measurement error that relax traditional assumptions, demonstrating improved estimator performance through simulations and application to the Framingham Heart Study.

Contribution

It extends existing measurement error correction techniques to broader settings, ensuring asymptotic normality under weaker assumptions.

Findings

Generalized estimators are asymptotically normal with sandwich variance estimators.

Simulation studies show improved performance over standard methods when assumptions are violated.

Application to Framingham data illustrates practical utility of the generalized corrections.

Abstract

Measurement error is a pervasive issue which renders the results of an analysis unreliable. The measurement error literature contains numerous correction techniques, which can be broadly divided into those which aim to produce exactly consistent estimators, and those which are only approximately consistent. While consistency is a desirable property, it is typically attained only under specific model assumptions. Two techniques, regression calibration and simulation extrapolation, are used frequently in a wide variety of parametric and semiparametric settings. However, in many settings these methods are only approximately consistent. We generalize these corrections, relaxing assumptions placed on replicate measurements. Under regularity conditions, the estimators are shown to be asymptotically normal, with a sandwich estimator for the asymptotic variance. Through simulation, we demonstrate the improved performance of the modified estimators, over the standard techniques, when these assumptions are violated. We motivate these corrections using the Framingham Heart Study, and apply the generalized techniques to an analysis of these data.