Prediction using partly conditional time-varying coefficients regression models

Data collected longitudinally in time provide the opportunity to develop predictive models of future observations given current data for an individual. Such models may be of particular value in defining individuals at high risk and thereby in suggesting subgroups for targeting of prevention intervention research efforts. In this paper, we propose a method for estimating predictive functions. The method uses an extension of the marginal regression analysis methods of Liang and Zeger (1986, Biometrika 73, 13-22) and is implemented using simple estimating equations. A key feature of the models is that regression coefficients are modelled as smooth functions of the times both at and for prediction. Data from a study of obesity in childhood and early adulthood is used to demonstrate the methodology. Criteria for defining individuals to be at high risk can be defined on the basis of estimated predictive functions. We suggest methods for evaluating the diagnostic accuracy (sensitivity and specificity) of such rules using cross-validation. The method holds promise as a robust and technically easy way of evaluating information about future prognosis that may be gleaned from a patient's current and past clinical status.