Error in timing in regression with observed longitudinal measurements.

We consider regression analysis of a disease outcome in relation to longitudinal data which are observations from a random effects model. The covariate variables of interest are the values of the underlying trajectory at some time points, which may be fixed or subject-specific. Because the underlying random coefficients are unknown, the covariates to the primary model are generally unobserved. In addition, measurements are often not observed at the time points of interest. A motivating example to our model is the effects of age at adiposity rebound and the associated body mass index on the risk of adult obesity. The adiposity rebound is a time point at which the trajectory of a child's body fatness declines to a minimum. This general error in timing problem may be applied to an analysis when time-dependent marker variables follow a polynomial model in which the effect of a local maximum or minimum point may be of interest. It can be seen that directly applying estimated covariates, possibly obtained from estimated time points, may lead to bias. Estimation procedures based on expected estimating equations, regression calibration and simulation extrapolation are applied to this problem. Copyright 2003 John Wiley & Sons, Ltd.