Parametric Measurement Error Models

We describe a simulation-based method of inference for parametric measurement error models in which the measurement error variance is known or at least well estimated. The method entails adding additional measurement error in known increments to the data, computing estimates from the contaminated data, establishing a trend between these estimates and the variance of the added errors, and extrapolating this trend back to the case of no measurement error. We show that the method is equivalent or asymptotically equivalent to method-of-moments estimation in linear measurement error modelling. Simulation studies are presented showing that the method produces estimators that are nearly asymptotically unbiased and efficient in standard and nonstandard logistic regression models. An oversimplified but fairly accurate description of the method is that it is method-of-moments estimation using Monte Carlo derived estimating equations. Note: This paper uses data supplied by the National Heart, Lung, and Blood Institute, NIH, and DHHS from the Framingham Heart Study. The views expressed in this paper are those of the authors and do not necessarily reflect the views of the National Heart, Lung, and Blood Institute, or of the Framingham Study.