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首页> 外文期刊>Biometrics: Journal of the Biometric Society : An International Society Devoted to the Mathematical and Statistical Aspects of Biology >Regression analysis when covariates are regression parameters of a random effects model for observed longitudinal measurements.
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Regression analysis when covariates are regression parameters of a random effects model for observed longitudinal measurements.

机译：当协变量是用于观察的纵向测量的随机效应模型的回归参数时的回归分析。

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摘要

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.
机译：当协变量是其他线性混合模型的基础回归系数时，我们考虑进行回归分析。天真的方法是使用每个受试者的重复测量（假定遵循线性混合模型），并获取特定于受试者的估计系数来替换协变量。但是，用这些估计的系数直接替换初级回归中未观察到的协变量可能会导致估计量有明显偏差。可以将上述问题评估为经典加性误差模型的一般化，其中将重复测量视为重复项。为了纠正这些偏差，我们研究了伪期望估计方程（EEE）估计器，回归校准（RC）估计器和RC估计器的改进版本。对于线性回归，在某些条件下，前两个估计量是相同的。但是，当主要回归模型是非线性模型时，RC估计量通常存在偏差。因此，我们考虑了一种改进的回归校准估计器，其性能接近伪EEE估计器，但是不需要数值积分。 RC估计量也扩展到比例风险回归模型。除分布理论外，我们还通过仿真研究评估方法。该方法适用于分析来自儿童成长研究的真实数据集。

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