  In linear models, omitting a covariate that is orthogonal to covariates in
the model does not result in biased coefficient estimation. This in general
does not hold for longitudinal data, where additional assumptions are needed to
get unbiased coefficient estimation in addition to the orthogonality between
omitted longitudinal covariates and longitudinal covariates in the model. We
propose methods to mitigate the omitted variable bias under weaker assumptions.
A two-step estimation procedure is proposed for inference about the
asynchronous longitudinal covariates, when such covariates are observed. For
mixed synchronous and asynchronous longitudinal covariates, we get parametric
rate of convergence for the coefficient estimation of the synchronous
longitudinal covariates by the two-step method. Extensive simulation studies
provide numerical support for the theoretical findings. We illustrate the
performance of our method on dataset from the Alzheimers Disease Neuroimaging
Initiative study.
