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 areas of craniofacial biology has led to the collection of excellent longitudinal cephalometric data sets that contain high quality information on normal, abnormal and altered growth and development in humans and other primates. Nevertheless, with the exception of a few studies (Dawson et al. 1980; Schneiderman, 1985; Buschang, et al., 1986), none use appropriate methods of analysis that adequately account for the covariance structure of such data sets. Apart from two published computer programs (Schneiderman and Kowalski, 1985, 1987) which perform Rao's single sample polynomial growth curve analysis and Hills procedures for unequal-time intervals, methods that are accessible and readily usable by the biomedical community are unavailable. Despite the formulation of models which are suitable for the analysis of longitudinal data (see review in Kowalski and Guire, 1974; Marubini and Milani, 1986), implementation has been thwarted due to computational complexity. Since these methods have been used with substantial data sets, their formal properties remain largely unknown. The purpose of this research is to systematically compare available methods and implement the most suitable ones using the new matrix algebra programming language, GAUSS. 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. The current widespread use of conventional statistics (based on ordinary least squares) has resulted in misleading standards that may underestimate variability. Specific problems to be addressed are (1) treatment of missing data. (2) multigroup comparisons, (3) unbalanced designs, (4) multivariate situations and (5) the formal properties of the methods implemented such as robustness, precision, power and efficiency. Simulations will be used to investigate these properties. An integrated system of use friendly programs that performs the most useful methods will then be used to reanalyze The University of Michigan's Elementary School Children data as well as normative rhesus monkey data. Articles issuing from this project will be written for investigators with only a basic understanding of statistics and will describe the conceptual basis, practical applications and use of the methods and 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 surgery, cleft-lip and palate rehabilitation, pediatric neurosurgery.
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