Zeger S L, Diggle P J
Department of Biostatistics, Johns Hopkins University, Baltimore, Maryland 21205-2179.
Biometrics. 1994 Sep;50(3):689-99.
The paper describes a semiparametric model for longitudinal data which is illustrated by its application to data on the time evolution of CD4 cell numbers in HIV seroconverters. The essential ingredients of the model are a parametric linear model for covariate adjustment, a nonparametric estimation of a smooth time trend, serial correlation between measurements on an individual subject, and random measurement error. A back-fitting algorithm is used in conjunction with a cross-validation prescription to fit the model. A notable feature in the application is that the onset of HIV infection is associated with a sudden drop in CD4 cells followed by a longer-term slower decay. The model is also used to estimate an individual's curve by combining his data with the population curve. Shrinkage toward the population mean trajectory is controlled in a natural way by the estimated covariance structure of the data.
本文描述了一种用于纵向数据的半参数模型，并通过将其应用于HIV血清转化者CD4细胞数量随时间变化的数据来说明。该模型的基本要素包括用于协变量调整的参数线性模型、平滑时间趋势的非参数估计、个体受试者测量值之间的序列相关性以及随机测量误差。使用反向拟合算法结合交叉验证方法来拟合模型。该应用中的一个显著特征是，HIV感染的发作与CD4细胞的突然下降相关，随后是长期的缓慢衰减。该模型还用于通过将个体数据与总体曲线相结合来估计个体曲线。通过数据的估计协方差结构以自然的方式控制向总体平均轨迹的收缩。
