The overall goal is to bridge the gap between recent statistical advances and current practice and to improve statistical methods so as to increase the applicability of their use in studies of human body composition and risk factors for cardiovascular and related diseases. Existing data from a longitudinal study of body composition and cardiovascular disease risk factors will be used to provide numerical examples and to demonstrate the application of the developed statistical methods. Specifically the aims are: (i) A random effects method will be extended by incorporating a time series process for the within-subject errors to ensure an adequate description of patterns of change over time and the accurate prediction of future values and future risk. The risk of elevated levels of future values conditioned on earlier values will be investigated. (ii) A kernel estimator will be investigated further to include: (i) the implementation of cross-validation to select the best combination of a smoothing parameter and a weight function, (ii) derivation of confidence intervals for the estimator and the predicted values, (iii) development of the velocity and acceleration of the fitted curve, and (iv) characterization of the landmark points such as maximum velocity, age at maximum, and predicted value at maximum velocity. These proposed statistical developments are motivated by the problems that occur in modeling irregular body composition and risk factors data from longitudinal designs. Patterns of change in body composition and risk factors are irregular among individuals which leads to the misspecification of the model or models describing these patterns. Consequently, the estimated coefficients and the predicted values are biased. The extension of random effects method and the further development of the kernel regression will improve the prediction of future values from earlier values. The ability to accurately predict future values from earlier values is important in studies of cardiovascular and related diseases where early intervention in childhood may prevent the occurrence of aberrant levels in adulthood. Although the investigation will be performed on body composition data and risk factors for cardiovascular and related diseases, these statistical methods will be generalizable to any serial data in any gender or minority population.
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