Wang C Y, Wang N, Wang S
Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, Seattle, Washington 98109-1024, USA.
Biometrics. 2000 Jun;56(2):487-95. doi: 10.1111/j.0006-341x.2000.00487.x.
We consider regression analysis when covariate variables are the underlying regression coefficients of another linear mixed model. A naive approach is to use each subject's repeated measurements, which are assumed to follow a linear mixed model, and obtain subject-specific estimated coefficients to replace the covariate variables. However, directly replacing the unobserved covariates in the primary regression by these estimated coefficients may result in a significantly biased estimator. The aforementioned problem can be evaluated as a generalization of the classical additive error model where repeated measures are considered as replicates. To correct for these biases, we investigate a pseudo-expected estimating equation (EEE) estimator, a regression calibration (RC) estimator, and a refined version of the RC estimator. For linear regression, the first two estimators are identical under certain conditions. However, when the primary regression model is a nonlinear model, the RC estimator is usually biased. We thus consider a refined regression calibration estimator whose performance is close to that of the pseudo-EEE estimator but does not require numerical integration. The RC estimator is also extended to the proportional hazards regression model. In addition to the distribution theory, we evaluate the methods through simulation studies. The methods are applied to analyze a real dataset from a child growth study.
当协变量是另一个线性混合模型的潜在回归系数时，我们考虑进行回归分析。一种简单的方法是使用每个受试者的重复测量值（假定这些测量值服从线性混合模型），并获得特定于受试者的估计系数来替代协变量。然而，直接用这些估计系数替代主回归中未观察到的协变量可能会导致估计量出现显著偏差。上述问题可作为经典加性误差模型的一种推广来评估，其中重复测量被视为重复样本。为了校正这些偏差，我们研究了一种伪期望估计方程（EEE）估计量、一种回归校准（RC）估计量以及RC估计量的一个改进版本。对于线性回归，在前述某些条件下，前两种估计量是相同的。然而，当主回归模型是非线性模型时，RC估计量通常会有偏差。因此，我们考虑一种改进的回归校准估计量，其性能接近于伪EEE估计量，但不需要数值积分。RC估计量也被扩展到比例风险回归模型。除了分布理论，我们还通过模拟研究来评估这些方法。这些方法被应用于分析一项儿童生长研究中的真实数据集。
