USE OF REPEATED MEASUREMENTS IN REGRESSION-ANALYSIS WITH DICHOTOMOUS RESPONSES

Although many medical follow up studies provide for repeated measurements of patient characteristics at regular intervals, usual methods of analyzing these data typically make use of only one measurement of each characteristic in any single model. For example, regression models for predicting death or other morbid events often use either the first or the most recent measurement of each characteristic. This results from the requirement in standard regression models that the number of independent variables must be constant over the set of individuals and period of observation. In this paper, however, a method is proposed for including these accumulating measurements in the regression analysis as they become available. The method is used to relate the occurrence of Cardiovascular Disease (CVD) to the levels of repeated measurements of serum cholesterol (SC) for participants in the Framingham Heart Study (Kannel 1976). Hierarchical models are described in which an analysis using only the most recent SC can be tested against an analysis using only the first measurement or using all available measurements. For the Framingham data, models available in the more general setting give significantly better fit than the usual models. Further, in contrast with usual practice, the first (baseline) measurement of SC is found to be more predictive than the most recent measurement. Although the regression methodology described is directly applicable to other problems with regularly repeated measurements and dichotomous response, the set of hierarchical models considered will be specific to the problem under study.