AI 中文总结
研究线性混合效应模型在 MAR 机制下固定效应推断方法的不足，提出新的渐近方差估计器和小样本偏差校正估计器，以量化估计和预测的不确定性，经理论验证和数值示例证明了方法的有效性。
AI 中文摘要
在线性混合效应模型（LMM）中，对固定效应的推断通常依赖于假设方差参数已知时获得的广义最小二乘（GLS）方差估计器，或具有小样本偏差调整的 Kenward-Roger 方法。模拟研究表明，在随机缺失（MAR）机制下的大型临床试验中，这两种方法都会低估治疗效果的方差并夸大 I 型错误率，且随着治疗组间缺失机制差异的增加，I 型错误膨胀更大。反直觉的是，估计的固定效应和方差参数表现出渐近依赖性。忽略这种依赖性可能导致无效推断。为了考虑这种额外的变异性来源，我们提出了一种新的渐近方差估计器和小样本偏差校正估计器，以量化 MAR 下 LMM 中估计和预测的不确定性。所提出的方法在理论上是合理的，并通过数值示例证明了其性能。
英文摘要
In linear mixed effects models (LMM), inference on fixed effects typically relies on either the generalized least squares (GLS) variance estimator obtained by assuming that the variance parameters are known, or on the Kenward-Roger method with a small-sample bias adjustment. A simulation study shows that both approaches can underestimate the variance of the treatment effect and inflate the type I error rate in large clinical trials under missing at random (MAR) mechanisms, with greater type I error inflation as the differences in the missingness mechanisms between treatment groups increase. Counterintuitively, the estimated fixed effects and variance parameters exhibit asymptotic dependence. Ignoring this dependence may lead to invalid inference. To account for this additional source of variability, we propose a new asymptotic variance estimator and a small-sample bias-corrected estimator to quantify uncertainty in estimation and prediction in LMM under MAR. The proposed methods are theoretically justified, and their performance is demonstrated by numerical examples.
Comments15 pages
