Linear time-dependent reference intervals where there is measurement error in the time variable - a parametric approach

This article re-examines parametric methods for the calculation of time specific reference intervals where there is measurement error present in the time covariate. Previous published work has commonly been based on the standard ordinary least squares approach, weighted where appropriate. In fact, this is an incorrect method when there are measurement errors present, and in this article, we show that the use of this approach may, in certain cases, lead to referral patterns that may vary with different values of the covariate. Thus, it would not be the case that all patients are treated equally; some subjects would be more likely to be referred than others, hence violating the principle of equal treatment required by the International Federation for Clinical Chemistry. We show, by using measurement error models, that reference intervals are produced that satisfy the requirement for equal treatment for all subjects.