Medical research projects often collect longitudinal data on groups of subjects that results in growth curves for each subject. These curves may in fact be growth curves, such as when animals are randomly divided into groups that are placed on different diets and their weights recorded as a function of time. The curves could be responses to a test or procedure such as a glucose challenge. The goal in both cases is to determine whether the mean curves for the groups are different. In many studies, subjects are randomly divided into a treated and a control group, where the control group is given a placebo, and a response is followed over time. Statistical tests of interest may be whether there is a response over time (time effect), whether one group has a higher overall level than the other group (group effect), and the two groups respond differently (group by time interaction). There are standard methods of analysis for growth curves. These methods assume that all subjects are measured at the times, that each curve can be represented by a polynomial of the same degree, that the polynomial coefficients have a multivariate normal distribution across subjects, and that the number of subjects is greater than the degree of the polynomial plus the number of constant per dependent variable in the multivariate analysis. This project will extend the current methodology to situtations where these assumptions do not hold. Often there are missing observations or subjects are not measured at the same time points. Time series methodology and the use of the Kalman filter for calculation of exact likelihoods allows serial correlation to be modeled within each subject. Both missing and unequally spaced observations can be handled. The Kalman filter approach can also be used to include random coefficients and estimate their between subject covariance matrix. As with standard methods of analysis for growth curves, covariates can be included in the model.
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