REGRESSION-ANALYSIS OF DATA WITH REPEATED MEASUREMENTS USING THE METHOD OF SUCCESSIVE DIFFERENCES

This paper discusses the first-order differencing approach to longitudinal data with measurements on individual subjects taken at irregular time points. Unlike the two-stage approach to this problem, which first fits a line or curve to each individual's growth pattern and then regresses the fitted line or curve on the covariates of interest, subjects with only two observations can still contribute to the estimation of parameters. Another major advantage is that any time trend of the response or any covariate effects on the response over a time interval within the total study period can be detected. Such an analysis can be very useful in clinical trials studies, especially in trials involving testing a new drug or therapy. The therapeutic effect of a drug or therapy may decrease with time and it is important to know the time period in which the treatment is most effective so that the shortest treatment duration can be determined to reduce the risks of toxic side-effects. Since estimation and inference of model parameters are performed under the framework of the multiple regression model, the procedures are easily implemented using popular statistical software packages. The estimators are asymptotically normal even when the assumed correlation structure is not met by the underlying data. The methods are illustrated with data from a study of primary anaplastic brain tumors.