In this monograph we will describe two simple, generally applicable approaches to measurement error analysis: regression calibration in this chapter and simulation extrapolation (SIMEX) in Chapter 5.
The basis of regression calibration is the replacement of X by the regression of X on (Z,W). After this approximation, one performs a standard analysis. The simplicity of this algorithm disguises its power. As Pierce and Kellerer (2004) state, regression calibration “is widely used, effective (and) reasonably well investigated.” Regression calibration shares with multiple imputation the advantage as Pierce and Kellerer note, “A great many analyses of the same cohort data are made for different purposes . . . it is very convenient that (once the replacement is made) essentially the same methods for ongoing analyses can be employed as if X were observed.” Regression calibration is simple and potentially applicable to any regression model, provided the approximation is sufficiently accurate. SIMEX shares these advantages but is more computationally intensive.