A univariate measurement error model for longitudinal change

Analyses of variables measured with error are often flawed when measurement error is ignored. An extensive literature on linear measurement error models is available by (1), and more recently, for non-linear measurement error models by (2) and (3). We investigate problems encountered in the analysis of longitudinal change, where the difference in some outcome variable is modeled on a set of regressor variables in a linear regression model. This type of analysis has become quite popular in biomedical research, and the results are often biased when the outcome variable is measured with error and its observed baseline value is included as a covariate in the fitted model. (4) demonstrated the effects of measurement error in the analysis of change in wall thickness of the common carotid artery. They showed the naive analysis led to erroneous findings due to the measurement error bias, even when the regressor variables were assumed to be measured precisely. In this paper, we present a method-of-moments correction for measurement error bias, provided the measurement error variance is known or can be estimated. This work extends the work of (4) to include regressor variables that are measured with error.