Prediction using partly conditional time-varying coefficients regression models

Data collected longitudinally in time provide the opportunity to develop pr edictive models of future observations given current data for an individual . Such models may be of particular value in defining individuals at high ri sk and thereby in suggesting subgroups for targeting of prevention interven tion research efforts. In this paper, we propose a method for estimating pr edictive functions. The method uses an extension of the marginal regression analysis methods of Liang and Zeger (1986, Biometrika 73, 13-22) and is im plemented using simple estimating equations. A keg. feature of the models i s that regression coefficients are modelled as smooth functions of the time s both at and for prediction. Data from a study of obesity in childhood and early adulthood is used to demonstrate the methodology. Criteria for defin ing individuals to be at high risk can be defined on the basis of estimated predictive functions. We suggest methods for evaluating the diagnostic acc uracy (sensitivity and specificity) of such rules using cross-validation. T he method holds promise as a robust and technically easy way of evaluating information about future prognosis that may be gleaned from a patient's cur rent and past clinical status.