A FRAMEWORK FOR CONSISTENT PREDICTION RULES BASED ON MARKERS

Recently interest has developed regarding the statistical properties a nd uses of marker processes in the context of the analysis of failure time data or survival analysis. A marker process is a stochastic proce ss that acts as a time dependent covariate that is internal to the uni t under study in the language of Kalbfleisch & Prentice (1980). As suc h the sample path of the process up to a certain point in time may car ry information about the subsequent hazard for failure. Uses of marker processes in the analysis of survival data are manifold. Here we cons ider the specific area of prediction of future failure times at a poin t in time based on various forms of information about the history of t he marker process. We provide a stochastic framework for the considera tion of prediction functions, demonstrate a simple consistency conditi on that such functions should satisfy, and discuss construction of pre diction functions in a general sense. Several examples are used to ill ustrate the ideas and we show that certain recently suggested imputati on schemes fail to meet the consistency condition. The consistency con dition also elucidates the model assumed by Cox (1983) in his work on surrogate responses. We also briefly consider a closely related backwa rd prediction problem.