The effects of measurement error in response variables and tests of association of explanatory variables in change models

Biomedical studies often measure variables with error. Examples in the literature include investigation of the association between the change in some outcome variable (blood pressure, cholesterol level etc.) and a set of explanatory variables (age, smoking status etc.). Typically, one fits linear regression models to investigate such associations. With the outcome variable measured with error, a problem occurs when we include the baseline value of the outcome variable as a covariate. In such instances, one can find a relationship between the observed change in the outcome and the explanatory variables even when there is no association between these variables and the true change in the outcome variable. We present a simple method of adjusting for a common measurement error bias that tends to be overlooked in the modelling of associations with change. Additional information (for example, replicates, instrumental variables) is needed to estimate the variance of the measurement error to perform this bias correction.