A family of models for uniform and serial dependence in repeated measurements studies

Data arising from a randomized double-masked clinical trial for multiple sc lerosis have provided particularly variable longitudinal repeated measureme nts responses. Specific models for such data, other than those based on the multivariate normal distribution, would be a valuable addition to the appl ied statistician's toolbox. A useful family of multivariate distributions c an be generated by substituting the integrated intensity of one distributio n into a second (outer) distribution. The parameters in the second distribu tion are then used to create a dependence structure among observations on a unit. These may either be a form of serial dependence for longitudinal dat a or of uniform dependence within clusters. These are respectively analogou s to the Kalman filter of state space models and to copulas, but they have the major advantage that they do not require any explicit integration. One useful outer distribution for constructing such multivariate distributions is the Pareto distribution. Certain special models based on it have previou sly been used in event history analysis, but those considered here have muc h wider application.