REGRESSION FOR TIME-DEPENDENT DATA

生物医学研究中的一个常见问题是描述一个 响应（Y）是解释变量（X）的函数。 当 观测是独立的广义线性模型（GLM） 包括线性、逻辑、对数线性和比例风险 为此目的，模型得到了很好的开发。 当观察 是相关的，目前的技术是不够的，特别是对于 离散和非正常的结果。 这项研究将发展 纵向相关数据的回归方法 时间序列研究。 在纵向研究中，一些 对许多主题中的每一个主题都提出了意见。重复瓣膜 是相互关联的。 在时间序列研究中， 关于Y和X的关系是由一个更长的 一组相关的观察结果。 通过发展广义线性模型的扩展，这些方法将有助于 常见的各种离散和连续的反应， 生物医学，特别是传染病研究。 为 纵向研究，我将开发过渡，边缘和 随机效应（混合）模型。 这些将用于分析 多中心艾滋病队列研究的纵向数据 （MACS），海地艾滋病毒研究（HHS）和一项感染性研究 疾病和维生素A缺乏症（ICS）。 对于时间序列的情况，参数和观测驱动 模型（考克斯，1981年）将进行研究。 这些模型将用于 估计艾滋病的趋势并作出短期预测 美国各风险组和州的发病率和肝炎发病率 宾夕法尼亚州各县的发病率。

A common problem in biomedical research is to describe a response (Y) as a function of explanatory variables (X). When observations are independent, generalized linear models (GLM's) including linear, logistic, log-linear and proportional hazards models are well developed for this purpose. When observations are correlated, current techniques are inadequate, particularly for discrete and non-normal outcomes. This study will develop regression methods for correlated data which arise in longitudinal and time series studies. In longitudinal studies, a few observations are made on each of many subjects. Repeated valves for an individual are correlated. In time series studies, inferences about the relationship of Y and X are made from a single longer set of correlated observations. By developing extensions of GLM's, the methods will be useful for a variety of discrete and continuous responses common to biomedical and particularly infectious disease research. For longitudinal studies, I will develop transitional, marginal and random effects (mixed) models. These will be used to analyze longitudinal data from the Multicenter AIDS Cohort Study (MACS), the Haiti HIV Study (HHS) and a study of infectious diseases and Vitamin A deficiency in Indonesian children (ICS). For the time series case, parameter and observation driven models (Cox, 1981) will be studied. These models will be used to estimate trends and make short-term projections of AIDS incidence by risk group and state in the U.S. and of hepatitis incidence by county in the State of Pennsylvania.