Abstract

Longitudinal studies and repeated-measures involve subjects being studied at several different times and/or under different experimental conditions. The serial measures obtained from the same subject may no longer be uncorrelated; this within-subject covariance has to be incorporated in the estimation of parameters. If the timing of observations is the same for all units and there is no missing data, then general multivariate techniques (e.g., GLS) yielding closed form solutions may be employed. In the case of arbitrary measurement times and variation in the number of observations for different individuals, random effects models using iterative techniques such as the expectation-maximization (EM) and Newton-Raphson algorithm may be employed.

This talk focuses on the extension of the random-effects model for a single characteristic to the case of a bivariate response, allowing for arbitrary patterns of observed data. The estimation of parameters for this model is via the EM-Algorithm. We derive the set of equations for this estimation procedure; these equations are appropriately modified to deal with missing data. The implementation of the EM algorithm along with methods of obtaining starting values will be discussed in detail. The methodology is illustrated with an example from AIDS clinical trials.