A model for markers and latent health status

We extend the bivariate Wiener process considered by Whitmore and co-worker s and model the joint process of a marker and health status. The health sta tus process is assumed to be latent or unobservable. The time to reach the primary end point or failure (death, onset of disease, etc.) is the time wh en the latent health status process first crosses a failure threshold level . Inferences for the model are based on two kinds of data: censored surviva l data and marker measurements. Covariates, such as treatment variables, ri sk factors and base-line conditions, are related to the model parameters th rough generalized linear regression functions. The model offers a much rich er potential for the study of treatment efficacy than do conventional model s. Treatment effects can be assessed in terms of their influence on both th e failure threshold and the health status process parameters. We derive an explicit formula for the prediction of residual failure times given the cur rent marker level. Also we discuss model validation. This model does not re quire the proportional hazards assumption and hence can be widely used. To demonstrate the usefulness of the model, we apply the methods in analysing data from protocol 116a of the AIDS Clinical Trials Group.