Lu Naiji, Tang Wan, He Hua, Yu Qin, Crits-Christoph Paul, Zhang Hui, Tu Xin
Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY 14642, USA.
Biom J. 2009 Aug;51(4):627-43. doi: 10.1002/bimj.200800186.
Models for longitudinal data are employed in a wide range of behavioral, biomedical, psychosocial, and health-care-related research. One popular model for continuous response is the linear mixed-effects model (LMM). Although simulations by recent studies show that LMM provides reliable estimates under departures from the normality assumption for complete data, the invariable occurrence of missing data in practical studies renders such robustness results less useful when applied to real study data. In this paper, we show by simulated studies that in the presence of missing data estimates of the fixed effect of LMM are biased under departures from normality. We discuss two robust alternatives, the weighted generalized estimating equations (WGEE) and the augmented WGEE (AWGEE), and compare their performances with LMM using real as well as simulated data. Our simulation results show that both WGEE and AWGEE provide valid inference for skewed non-normal data when missing data follows the missing at random, the most popular missing data mechanism for real study data.
纵向数据模型被广泛应用于行为、生物医学、心理社会以及医疗保健相关的研究中。一种用于连续响应的常用模型是线性混合效应模型（LMM）。尽管近期研究的模拟结果表明，对于完整数据，在偏离正态性假设的情况下，LMM能提供可靠的估计，但在实际研究中缺失数据的普遍存在使得这些稳健性结果在应用于实际研究数据时用处不大。在本文中，我们通过模拟研究表明，在存在缺失数据的情况下，当偏离正态性时，LMM固定效应的估计会产生偏差。我们讨论了两种稳健的替代方法，加权广义估计方程（WGEE）和增强型WGEE（AWGEE），并使用真实数据和模拟数据将它们与LMM的性能进行比较。我们的模拟结果表明，当缺失数据遵循随机缺失（这是实际研究数据中最常见的缺失数据机制）时，WGEE和AWGEE都能为偏态非正态数据提供有效的推断。
