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.

翻译：在线性模型中，省略与模型中协变量正交的协变量不会导致系数估计有偏。但对于纵向数据，这一结论通常不成立，除了要求省略的纵向协变量与模型中的纵向协变量正交外，还需额外假设才能获得无偏的系数估计。我们提出在更弱假设下减少省略变量偏差的方法。当异步纵向协变量可观测时，我们提出一种两步估计程序用于推断此类协变量。对于同步与异步混合的纵向协变量，通过两步法可获得同步纵向协变量系数估计的参数收敛速度。大量模拟研究为理论结果提供了数值支持。我们在阿尔茨海默病神经影像学倡议研究的数据集上展示了该方法的性能。