A parametric family of correlation structures for the analysis of longitudinal data

In epidemiological settings, we are often faced with numerous short time series, and a parsimonious parametrization of the correlation structure is desired in order to optimize the efficiency of the estimation procedure. We propose a damped exponential correlation structure for modeling multivariate Gaussian outcomes. The correlation between two observations separated by s units of time is modeled as gamma s theta, where gamma is the correlation between elements separated by one s-unit, and theta is a damping parameter. For (theta = 0), (theta = 1), and theta----infinity), the correlation structures of compound symmetry, first-order autoregressive, and first-order moving average processes are obtained. Although the AR(2) dependency structure, and the combination of random effects and AR(1) errors are not special cases of the proposed parametric family, these structures can be well approximated within the family for short time series. Maximum likelihood methods for parameter estimation and interpretations of intermediate models (0 less than theta less than 1) are discussed in the context of modeling pulmonary function in an adult population in The Netherlands and T-cell subsets in homosexual men infected with human immunodeficiency virus Type I.