EFFECTS OF UNOBSERVED AND PARTIALLY OBSERVED COVARIATE PROCESSES ON SYSTEM FAILURE - A REVIEW OF MODELS AND ESTIMATION STRATEGIES

Stochastically changing covariates may influence survival. They may be observed, unobserved or partly observed. We review the properties of hazard models explicitly representing the effects of unobserved, and p artially observed, stochastic covariates. Such models will increase in importance as new longitudinal population studies, and longitudinal s urveys of high dimensional failure processes in humans, become availab le-many are now in progress. It is shown that marginal survival distri butions and likelihoods generated in analytically closed form make suc h parametrically detailed models computationally tractable. Several wa ys of defining the marginal distribution of the data for constructing a likelihood function are considered. The most complete models can han dle both continuously and discretely evolving covariates. Parameters c an be estimated from multiple data sets to retrospectively and prospec tively evaluate covariate trajectories. Such methods will both extract more information from a longitudinal study and use it in a parametric structure that is logically consistent with the behavior of the under lying processes of substantive interest.