Td. Tosteson et al., COVARIATE MEASUREMENT ERROR AND THE ESTIMATION OF RANDOM EFFECT PARAMETERS IN A MIXED-MODEL FOR LONGITUDINAL DATA, Statistics in medicine, 17(17), 1998, pp. 1959-1971
We explore the effects of measurement error in a time-varying covariat
e for a mixed model applied to a longitudinal study of plasma levels a
nd dietary intake of beta-carotene. We derive a simple expression for
the bias of large sample estimates of the variance of random effects i
n a longitudinal model for plasma levels when dietary intake is treate
d as a time-varying covariate subject to measurement error. In general
, estimates for these variances made without consideration of measurem
ent error are biased positively, unlike estimates for the slope coeffi
cients which tend to be 'attenuated'. If we can assume that the residu
als from a longitudinal fit for the time-varying covariate behave like
measurement errors, we can estimate the original parameters without t
he need for additional validation or reliability studies. We propose a
method to test this assumption and show that the assumption is reason
able for the example data. We then use a likelihood-based method of es
timation that involves a simple extension of existing methods for fitt
ing mixed models. Simulations illustrate the properties of the propose
d estimators. (C) 1998 John Wiley & Sons, Ltd.