Zucker D M, Zerbe G O, Wu M C
Biostatistics Research Branch, U.S. National Heart, Lung and Blood Institute, Bethesda, Maryland 20892, USA.
Biometrics. 1995 Jun;51(2):413-24.
This paper generalizes the work of Blomqvist (1977, Journal of the American Statistical Association 72, 746-749) on inference for the relationship between the individual-specific slope and the individual-specific intercept in a linear growth curve model. The paper deals with longitudinal data involving one or more response variables and irregular follow-up times, with each response variable postulated to follow a linear growth curve model. The problem considered is inference concerning the association between one growth curve coefficient and another--for example, the slope and intercept for a selected response variable, or the two slopes for two different response variables--after adjusting for all remaining coefficients among all of the response variables. An inferential approach based on the method of moments and an inferential approach based on maximum likelihood are described, and the asymptotic properties of these procedures are presented. Extensions of the methodology to allow polynomial growth curves and baseline covariates are outlined. The methodology is illustrated with a practical example arising from a clinical trial in lung disease.
本文推广了布洛姆奎斯特（1977年，《美国统计协会杂志》72卷，第746 - 749页）关于线性增长曲线模型中个体特定斜率与个体特定截距之间关系推断的工作。本文处理涉及一个或多个响应变量以及不规则随访时间的纵向数据，假定每个响应变量都遵循线性增长曲线模型。所考虑的问题是在对所有响应变量中的所有其余系数进行调整之后，关于一个增长曲线系数与另一个系数之间关联的推断——例如，选定响应变量的斜率和截距，或者两个不同响应变量的两个斜率——。描述了一种基于矩法的推断方法和一种基于最大似然的推断方法，并给出了这些方法的渐近性质。概述了将该方法扩展以允许多项式增长曲线和基线协变量的情况。用一个来自肺病临床试验的实际例子说明了该方法。
