It is generally acknowledged that longitudinal rather than cross-sectional data provide the most information on growth and other time-dependent phenomena. This recognition in the area of craniofacial biology has led to the collection of excellent longitudinal data sets that contain valuable information on normal, abnormal, and altered growth and development in humans and other primates. Nevertheless, with few exceptions, appropriate statistical methods which adequately account for the covariance structure of such data sets have not been employed in their analysis. Apart from the programs which were produced during the first three years of this project, methods that are accessible and readily usable by the biomedical community are unavailable. Despite the formulation of mathematical models which are suitable for the analysis of longitudinal data (see, eg., the reviews in Kowalski and Guire, 1974; Goldstein, 1979; Guire and Kowalski, 1979; Marubini and Milani, 1986), implementation has lagged far behind theoretical development. The purpose of this research is to systematically compare available methods for longitudinal data analysis and implement the most suitable ones using the matrix algebra programming language, GAUSS (Edlefson and Jones, 1985). The goal is to develop computer programs that can be used easily by basic and clinical scientists to facilitate meaningful descriptions and comparisons of growth patterns in human and other primate populations. An integrated system of user-friendly programs will be developed and made available to the biomedical research community. These GAUSS programs will be in a stand-alone format that is easy to install and use -- no additional software is required. They will be thoroughly documented and detailed instructions for installing and running them will be provided. These menu-driven programs elicit from the user all of the information required to perform the analysis, ie., the dimensions and format of his/her data set. Articles issuing from this project will be written for investigators with only a basic understanding of statistics and will describe the conceptual bases, practical applications and use of the methods and programs. Instructions for program installation and use will be provided to, and updated for, all those requesting our programs. By providing easy-to-use tools for generating accurate descriptions of human growth, this project will contribute to improved health care in the areas of orthodontics, oral and maxillofacial surgery, cleft-lip and palate rehabilitation, and pediatrics.
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