NONPARAMETRIC-ESTIMATION OF COVARIANCE STRUCTURE IN LONGITUDINAL DATA

In longitudinal studies, the effect of various treatments over time is usually of prime interest. However, observations on the same subject are usually correlated and any analysis should account for the underly ing covariance structure. A nonparametric estimate of the covariance s tructure is useful, either as a guide to the formulation of a. paramet ric model or as the basis for formal inference without imposing parame tric assumptions. The sample covariance matrix provides such an estima te when the data consist of a short sequence of measurements at a comm on set of time points on each of many subjects:but is impractical when the data are severely unbalanced or when the sequences of measurement s on individual subjects are long relative to the number of subjects. The variogram of residuals from a saturated model for the mean respons e has previously been suggested as a nonparametric estimator for covar iance structure assuming stationarity. In this paper, we consider kern el weighted local linear regression smoothing of sample variogram ordi nates and of squared residuals to provide a nonparametric estimator fo r the covariance structure without assuming stationarity. The value of the estimator as a diagnostic tool is demonstrated in two application s, one to a set of data concerning the blood pressure of newborn babie s in an intensive care unit and the other to data on the time evolutio n of CD4 cell numbers in HIV seroconverters. The use of the estimator in more formal statistical inferences concerning the mean profiles req uires further study.